elliptic-curve: add MulByGenerator trait

Adds a trait for performing scalar multiplication by the generator
point, which may use optimizations (e.g. precomputed tables) when
available

elliptic-curve/src/arithmetic.rs

@@ -1,7 +1,8 @@
 //! Elliptic curve arithmetic traits.
 
 use crate::{
-    ops::LinearCombination, AffineXCoordinate, Curve, FieldBytes, IsHigh, PrimeCurve, ScalarCore,
+    ops::{LinearCombination, MulByGenerator},
+    AffineXCoordinate, Curve, FieldBytes, IsHigh, PrimeCurve, ScalarCore,
 };
 use core::fmt::Debug;
 use subtle::{ConditionallySelectable, ConstantTimeEq};
@@ -42,6 +43,7 @@ pub trait CurveArithmetic: Curve {
         + From<Self::AffinePoint>
         + Into<Self::AffinePoint>
         + LinearCombination
+        + MulByGenerator
         + group::Curve<AffineRepr = Self::AffinePoint>
         + group::Group<Scalar = Self::Scalar>;
 

elliptic-curve/src/ops.rs

@@ -42,6 +42,18 @@ pub trait LinearCombination: Group {
     }
 }
 
+/// Multiplication by the generator.
+///
+/// May use optimizations (e.g. precomputed tables) when available.
+// TODO(tarcieri): replace this with `Group::mul_by_generator``? (see zkcrypto/group#44)
+pub trait MulByGenerator: Group {
+    /// Multiply by the generator of the prime-order subgroup.
+    #[must_use]
+    fn mul_by_generator(scalar: &Self::Scalar) -> Self {
+        Self::generator() * scalar
+    }
+}
+
 /// Modular reduction.
 pub trait Reduce<Uint: Integer + ArrayEncoding>: Sized {
     /// Perform a modular reduction, returning a field element.