elliptic-curve: LinearCombinationExt => LinearCombination (#1501)

Replaces the old, significantly less flexible `LinearCombination` trait
with the newer `LinearCombinationExt` trait, removing the old trait
completely and renaming the new one.

The bounds for `CurveArithmetic::ProjectivePoint` have also been updated
accordingly.

elliptic-curve/src/arithmetic.rs

@@ -44,7 +44,8 @@ pub trait CurveArithmetic: Curve {
         + DefaultIsZeroes
         + From<Self::AffinePoint>
         + Into<Self::AffinePoint>
-        + LinearCombination
+        + LinearCombination<[(Self::ProjectivePoint, Self::Scalar)]>
+        + LinearCombination<[(Self::ProjectivePoint, Self::Scalar); 2]>
         + MulByGenerator
         + group::Curve<AffineRepr = Self::AffinePoint>
         + group::Group<Scalar = Self::Scalar>;

elliptic-curve/src/dev.rs

@@ -661,7 +661,8 @@ impl group::Curve for ProjectivePoint {
     }
 }
 
-impl LinearCombination for ProjectivePoint {}
+impl LinearCombination<[(ProjectivePoint, Scalar)]> for ProjectivePoint {}
+impl<const N: usize> LinearCombination<[(ProjectivePoint, Scalar); N]> for ProjectivePoint {}
 
 impl Add<ProjectivePoint> for ProjectivePoint {
     type Output = ProjectivePoint;

elliptic-curve/src/ops.rs

@@ -149,28 +149,16 @@ fn invert_batch_internal<
 
 /// Linear combination.
 ///
-/// This trait enables crates to provide an optimized implementation of
-/// linear combinations (e.g. Shamir's Trick), or otherwise provides a default
-/// non-optimized implementation.
-// TODO(tarcieri): replace this with a trait from the `group` crate? (see zkcrypto/group#25)
-pub trait LinearCombination: Group {
-    /// Calculates `x * k + y * l`.
-    fn lincomb(x: &Self, k: &Self::Scalar, y: &Self, l: &Self::Scalar) -> Self {
-        (*x * k) + (*y * l)
-    }
-}
-
-/// Linear combination (extended version).
+/// This trait enables optimized implementations of linear combinations (e.g. Shamir's Trick).
 ///
-/// This trait enables providing an optimized implementation of
-/// linear combinations (e.g. Shamir's Trick).
-// TODO(tarcieri): replace the current `LinearCombination` with this in the next release
-pub trait LinearCombinationExt<PointsAndScalars>: group::Curve
+/// It's generic around `PointsAndScalars` to allow overlapping impls. For example, const generic
+/// impls can use the input size to determine the size needed to store temporary variables.
+pub trait LinearCombination<PointsAndScalars>: group::Curve
 where
     PointsAndScalars: AsRef<[(Self, Self::Scalar)]> + ?Sized,
 {
     /// Calculates `x1 * k1 + ... + xn * kn`.
-    fn lincomb_ext(points_and_scalars: &PointsAndScalars) -> Self {
+    fn lincomb(points_and_scalars: &PointsAndScalars) -> Self {
         points_and_scalars
             .as_ref()
             .iter()
@@ -180,14 +168,6 @@ where
     }
 }
 
-/// Blanket impl of the legacy [`LinearCombination`] trait for types which impl the new
-/// [`LinearCombinationExt`] trait for 2-element arrays.
-impl<P: LinearCombinationExt<[(P, Self::Scalar); 2]>> LinearCombination for P {
-    fn lincomb(x: &Self, k: &Self::Scalar, y: &Self, l: &Self::Scalar) -> Self {
-        Self::lincomb_ext(&[(*x, *k), (*y, *l)])
-    }
-}
-
 /// Multiplication by the generator.
 ///
 /// May use optimizations (e.g. precomputed tables) when available.