elliptic-curve: add LinearCombination trait (#832)

Adds a trait for computing `x * k + y * l`.

This allows curve implementations to provide optimized arithmetic when
available (e.g. Shamir's Trick)

elliptic-curve/src/ops.rs

@@ -5,6 +5,9 @@ pub use core::ops::{Add, AddAssign, Mul, Neg, Sub, SubAssign};
 use crypto_bigint::{ArrayEncoding, ByteArray, Integer};
 use subtle::CtOption;
 
+#[cfg(feature = "arithmetic")]
+use crate::ProjectiveArithmetic;
+
 /// Perform an inversion on a field element (i.e. base field element or scalar)
 pub trait Invert {
     /// Field element type
@@ -23,6 +26,26 @@ impl<F: ff::Field> Invert for F {
     }
 }
 
+/// 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)
+#[cfg(feature = "arithmetic")]
+#[cfg_attr(docsrs, doc(cfg(feature = "arithmetic")))]
+pub trait LinearCombination: ProjectiveArithmetic {
+    /// Calculates `x * k + y * l`.
+    fn lincomb(
+        x: &Self::ProjectivePoint,
+        k: &Self::Scalar,
+        y: &Self::ProjectivePoint,
+        l: &Self::Scalar,
+    ) -> Self::ProjectivePoint {
+        (*x * k) + (*y * l)
+    }
+}
+
 /// Modular reduction.
 pub trait Reduce<UInt: Integer + ArrayEncoding>: Sized {
     /// Perform a modular reduction, returning a field element.