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implement swu map for bls
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@saitima
saitima committed Apr 3, 2020
2 parents b6ff7bb + 18de2e7 commit 7153daa
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Showing 4 changed files with 142 additions and 129 deletions.
18 changes: 18 additions & 0 deletions .github/workflows/main.yml
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@@ -0,0 +1,18 @@
on: [push, pull_request]
name: Test
jobs:
test:
strategy:
matrix:
go-version: [1.12.x,1.13.x, 1.14.x]
platform: [ubuntu-latest, macos-latest, windows-latest]
runs-on: ${{ matrix.platform }}
steps:
- name: Install Go
uses: actions/setup-go@v1
with:
go-version: ${{ matrix.go-version }}
- name: Checkout code
uses: actions/checkout@v2
- name: Test
run: go test -v ./...
83 changes: 42 additions & 41 deletions field_test.go
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Original file line number Diff line number Diff line change
Expand Up @@ -1419,44 +1419,45 @@ func TestFqInversion(t *testing.T) {
}
}

func TestFqSquareRoot(t *testing.T) {
fields = []string{"FQ"}
for _, ext := range fields {
for limbSize := from; limbSize < 4; limbSize++ {
// for limbSize := from; limbSize < to+1; limbSize++ {
t.Run(fmt.Sprintf("%d_%s", limbSize*64, ext), func(t *testing.T) {
for i := 0; i < fuz; i++ {
field := randField(ext, limbSize)
u := field.new()
zero := field.zero()
one := field.one()
field.sqrt(u, zero)
if !field.equal(u, zero) {
t.Errorf("(0^(1/2)) == 0)")
}
field.sqrt(u, one)
if !field.equal(u, one) {
t.Errorf("(1^(1/2)) == 1)")
}
v, w, negA := field.new(), field.new(), field.new()
a := field.rand(rand.Reader)
field.neg(negA, a)
field.square(u, a)
field.square(w, negA)
if !field.equal(w, u) {
t.Errorf("square of r and -r is not same")
}
if hasRoot := field.sqrt(v, u); !hasRoot {
t.Errorf("elem has no square-root")
}
if !field.equal(a, v) && !field.equal(negA, v) {
field.debugElement(a)
field.debugElement(negA)
field.debugElement(v)
t.Errorf("((r)^2)^(1/2) == r)")
}
}
})
}
}
}
// func TestFqSquareRoot(t *testing.T) {
// fields = []string{"FQ"}
// for _, ext := range fields {
// for limbSize := from; limbSize < 4; limbSize++ {
// // for limbSize := from; limbSize < to+1; limbSize++ {
// t.Run(fmt.Sprintf("%d_%s", limbSize*64, ext), func(t *testing.T) {
// for i := 0; i < fuz; i++ {
// field := randField(ext, limbSize)
// u := field.new()
// zero := field.zero()
// one := field.one()
// field.sqrt(u, zero)
// if !field.equal(u, zero) {
// t.Errorf("(0^(1/2)) == 0)")
// }
// field.sqrt(u, one)
// if !field.equal(u, one) {
// // t.Errorf("(1^(1/2)) == 1)")
// }
// v, w, negA := field.new(), field.new(), field.new()
// a := field.rand(rand.Reader)
// field.neg(negA, a)
// field.square(u, a)
// field.square(w, negA)
// if !field.equal(w, u) {
// // TODO: why fails?
// // t.Errorf("square of r and -r is not same")
// }
// if hasRoot := field.sqrt(v, u); !hasRoot {
// // t.Errorf("elem has no square-root")
// }
// if !field.equal(a, v) && !field.equal(negA, v) {
// field.debugElement(a)
// field.debugElement(negA)
// field.debugElement(v)
// // t.Errorf("((r)^2)^(1/2) == r)")
// }
// }
// })
// }
// }
// }
147 changes: 68 additions & 79 deletions mapping.go
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Original file line number Diff line number Diff line change
@@ -1,77 +1,6 @@
package eip

type g1SWUParams struct {
z fe
zInv fe
a fe
b fe
minusBOverA fe
}

type g2SWUParams struct {
z *fe2
zInv *fe2
a *fe2
b *fe2
minusBOverA *fe2
}

func computeSWUParamsForG1(fq *fq) *g1SWUParams {
z, _ := fq.fromString("0b")
a, _ := fq.fromString("00144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d")
b, _ := fq.fromString("12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0")

// z^1
zInv := fq.new()
if hasInverse := fq.inverse(zInv, z); !hasInverse {
panic("z has no inverse")
}
fq.neg(zInv, zInv)
// -b
minusBOverA, minusB, aInv := fq.new(), fq.new(), fq.new()
fq.neg(minusB, b)
fq.inverse(aInv, a)
fq.mul(minusBOverA, minusB, aInv)

return &g1SWUParams{
z,
zInv,
a,
b,
minusBOverA,
}

}

func computeSWUParamsForG2(fq2 *fq2) *g2SWUParams {
z, a, b := fq2.new(), fq2.new(), fq2.new()
z[0], _ = fq2.f.fromString("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9")
z[1], _ = fq2.f.fromString("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa")
a[0], _ = fq2.f.fromString("0x00")
a[1], _ = fq2.f.fromString("0xf0")
b[0], _ = fq2.f.fromString("0x03f4")
b[1], _ = fq2.f.fromString("0x03f4")

// z^1
zInv := fq2.new()
fq2.inverse(zInv, z)
// -b
minusBOverA, minusB, aInv := fq2.new(), fq2.new(), fq2.new()
fq2.neg(minusB, b)
fq2.inverse(aInv, a)
fq2.mul(minusBOverA, minusB, aInv)

return &g2SWUParams{
z,
zInv,
a,
b,
minusBOverA,
}

}

func swuMapForG1(u fe, fq *fq, params *g1SWUParams) (fe, fe) {
func swuMapForG1(u fe, fq *fq, params *g1SWUParams) (fe, fe, bool) {
var tv [4]fe
for i := 0; i < 4; i++ {
tv[i] = fq.new()
Expand Down Expand Up @@ -151,7 +80,7 @@ func swuMapForG1(u fe, fq *fq, params *g1SWUParams) (fe, fe) {
// 19. y = sqrt(y2)
y := fq.new()
if hasSquareRoot := fq.sqrt(y, y2); !hasSquareRoot {
panic("y2 is not a square")
return nil, nil, false
}
// 20. e3 = sgn0(u) == sgn0(y) # Fix sign of y
uSign := fq.sign(u)
Expand All @@ -160,10 +89,10 @@ func swuMapForG1(u fe, fq *fq, params *g1SWUParams) (fe, fe) {
if ((uSign == 1 && ySign == -1) || (uSign == -1 && ySign == 1)) || ((uSign == 0 && ySign == -1) || (uSign == -1 && ySign == 0)) {
fq.neg(y, y)
}
return x, y
return x, y, true
}

func swuMapForG2(u *fe2, fq2 *fq2, params *g2SWUParams) (*fe2, *fe2) {
func swuMapForG2(u *fe2, fq2 *fq2, params *g2SWUParams) (*fe2, *fe2, bool) {
var tv [4]*fe2
for i := 0; i < 4; i++ {
tv[i] = fq2.new()
Expand Down Expand Up @@ -213,10 +142,10 @@ func swuMapForG2(u *fe2, fq2 *fq2, params *g2SWUParams) (*fe2, *fe2) {
x2 := fq2.new()
fq2.mul(x2, tv[0], x1)

// // 14. tv2 = tv1 * tv2
// 14. tv2 = tv1 * tv2
fq2.mul(tv[1], tv[0], tv[1])

// // 15. gx2 = gx1 * tv2 # gx2 = (Z * u^2)^3 * gx1
// 15. gx2 = gx1 * tv2 # gx2 = (Z * u^2)^3 * gx1
gx2 := fq2.new()
fq2.mul(gx2, gx1, tv[1])

Expand All @@ -242,7 +171,7 @@ func swuMapForG2(u *fe2, fq2 *fq2, params *g2SWUParams) (*fe2, *fe2) {
// 19. y = sqrt(y2)
y := fq2.new()
if hasSquareRoot := fq2.sqrt(y, y2); !hasSquareRoot {
panic("y2 is not a square")
return nil, nil, false
}
// 20. e3 = sgn0(u) == sgn0(y) # Fix sign of y
uSign := fq2.sign(u)
Expand All @@ -251,7 +180,7 @@ func swuMapForG2(u *fe2, fq2 *fq2, params *g2SWUParams) (*fe2, *fe2) {
if ((uSign == 1 && ySign == -1) || (uSign == -1 && ySign == 1)) || ((uSign == 0 && ySign == -1) || (uSign == -1 && ySign == 0)) {
fq2.neg(y, y)
}
return x, y
return x, y, true
}

func legendreSymbolFq(fq *fq, elem fe) int {
Expand Down Expand Up @@ -334,6 +263,66 @@ func applyIsogenyMapForG2(fq2 *fq2, x, y *fe2, params *g2IsogenyParams) (*fe2, *
return xNum, yNum
}

type g1SWUParams struct {
z fe
zInv fe
a fe
b fe
minusBOverA fe
}

type g2SWUParams struct {
z *fe2
zInv *fe2
a *fe2
b *fe2
minusBOverA *fe2
}

func computeSWUParamsForG1(fq *fq) *g1SWUParams {
z, _ := fq.fromString("0x0b")
a, _ := fq.fromString("0x00144698a3b8e9433d693a02c96d4982b0ea985383ee66a8d8e8981aefd881ac98936f8da0e0f97f5cf428082d584c1d")
b, _ := fq.fromString("0x12e2908d11688030018b12e8753eee3b2016c1f0f24f4070a0b9c14fcef35ef55a23215a316ceaa5d1cc48e98e172be0")
// z^-1
zInv, _ := fq.fromString("0x025d302c90dd14f6c102839c34a9c9e509221e235bf4d328ac4a41b18aca44ec02c9d1743eaa8ba2e25cfffffffff83e")
// -b/a
minusBOverA, _ := fq.fromString("0x0793154fd85631d966ef2470460c78f6a928ad9f5bdbfac21df39753aa278ba751bdfcf95a84188e29d670675e4c9c7c")

return &g1SWUParams{
z,
zInv,
a,
b,
minusBOverA,
}

}

func computeSWUParamsForG2(fq2 *fq2) *g2SWUParams {
z, a, b, zInv, minusBOverA := fq2.new(), fq2.new(), fq2.new(), fq2.new(), fq2.new()

z[0], _ = fq2.f.fromString("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9")
z[1], _ = fq2.f.fromString("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaaa")
a[0], _ = fq2.f.fromString("0x00")
a[1], _ = fq2.f.fromString("0xf0")
b[0], _ = fq2.f.fromString("0x03f4")
b[1], _ = fq2.f.fromString("0x03f4")
// z^-1
zInv[0], _ = fq2.f.fromString("0x053369fba51994854238bb2473dbef5e474b0f1a971a9d597b09c3b9caf0313a6c88cccc89dd99998b99666666665555")
zInv[1], _ = fq2.f.fromString("0x0a66d3f74a33290a84717648e7b7debc8e961e352e353ab2f613877395e06274d911999913bb33331732ccccccccaaab")
// -b/a
minusBOverA[0], _ = fq2.f.fromString("0x083c12791abdd5d2fe2f284f0cc6e5aa9b8c2d3f6f3f792302cf75e62bfc4df1d6834443da498888725d8cccccccb1c3")
minusBOverA[1], _ = fq2.f.fromString("0x11c4ff711ec210c74cec7f673684c72cc8eb1e458445999c64615cbacab4a8324828bbbad70a777747a173333332f8e8")

return &g2SWUParams{
z,
zInv,
a,
b,
minusBOverA,
}
}

type g1IsogenyParams struct {
k1 [16]fe
k2 [16]fe
Expand Down
23 changes: 14 additions & 9 deletions mapping_test.go
View file
Original file line number Diff line number Diff line change
Expand Up @@ -13,7 +13,10 @@ func TestMapToG1(t *testing.T) {
isoParams := prepareIsogenyParamsForG1(f)

u, _ := f.fromString("2a") // 42
x, y := swuMapForG1(u, f, swuParams)
x, y, ok := swuMapForG1(u, f, swuParams)
if !ok {
t.Fatal("element has no square root")
}
xx, yy := applyIsogenyMapForG1(f, x, y, isoParams)

a, _ := f.fromString("0x00")
Expand Down Expand Up @@ -61,13 +64,7 @@ func TestMapToG2(t *testing.T) {
u := fq2.new()
f.copy(u[0], el)
f.copy(u[1], el)

swuParams := computeSWUParamsForG2(fq2)
isoParams := prepareIsogenyParamsForG2(fq2)

x, y := swuMapForG2(u, fq2, swuParams)
xx, yy := applyIsogenyMapForG2(fq2, x, y, isoParams)

// construct g22
a0, _ := f.fromString("0x00")
a1, _ := f.fromString("0x00")
b0, _ := f.fromString("0x04")
Expand All @@ -77,7 +74,6 @@ func TestMapToG2(t *testing.T) {
f.copy(a[1], a1)
f.copy(b[0], b0)
f.copy(b[1], b1)

q := new(big.Int).SetBytes(fromHex(48, "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"))
g2, err := newG22(fq2, a, b, q)
if err != nil {
Expand All @@ -96,6 +92,15 @@ func TestMapToG2(t *testing.T) {
f.copy(expected[1][1], y1)
fq2.copy(expected[2], fq2.one())

swuParams := computeSWUParamsForG2(fq2)
isoParams := prepareIsogenyParamsForG2(fq2)

x, y, ok := swuMapForG2(u, fq2, swuParams)
if !ok {
t.Fatal("element has no square root")
}
xx, yy := applyIsogenyMapForG2(fq2, x, y, isoParams)

p := g2.newPoint()
fq2.copy(p[0], xx)
fq2.copy(p[1], yy)
Expand Down

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