Add GLVParameters trait definition

CHANGELOG.md

@@ -2,6 +2,8 @@
 
 ## Pending
 
+- [\#301](https://github.com/arkworks-rs/algebra/pull/201) (ark-ec) Add `GLVParameters` trait definition.
+
 ### Breaking changes
 
 - [\#300](https://github.com/arkworks-rs/algebra/pull/300) (ark-ec) Change the implementation of `Hash` trait of `GroupProjective` to use the affine coordinates.

ec/src/glv.rs

@@ -0,0 +1,35 @@
+use crate::ModelParameters;
+
+/// The GLV parameters that are useful to compute the endomorphism
+/// and scalar decomposition.
+pub trait GLVParameters: Send + Sync + 'static + ModelParameters {
+    type CurveAffine;
+    type CurveProjective;
+
+    // phi(P) = lambda*P for all P
+    // constants that are used to calculate phi(P)
+    const COEFF_A1: Self::BaseField;
+    const COEFF_A2: Self::BaseField;
+    const COEFF_A3: Self::BaseField;
+    const COEFF_B1: Self::BaseField;
+    const COEFF_B2: Self::BaseField;
+    const COEFF_B3: Self::BaseField;
+    const COEFF_C1: Self::BaseField;
+    const COEFF_C2: Self::BaseField;
+
+    // constants that are used to perform scalar decomposition
+    // This is a matrix which is practically the LLL reduced bases
+    const COEFF_N11: Self::ScalarField;
+    const COEFF_N12: Self::ScalarField;
+    const COEFF_N21: Self::ScalarField;
+    const COEFF_N22: Self::ScalarField;
+
+    /// mapping a point G to phi(G):= lambda G where psi is the endomorphism
+    fn endomorphism(base: &Self::CurveAffine) -> Self::CurveAffine;
+
+    /// decompose a scalar s into k1, k2, s.t. s = k1 + lambda k2
+    fn scalar_decomposition(k: &Self::ScalarField) -> (Self::ScalarField, Self::ScalarField);
+
+    /// perform GLV multiplication
+    fn glv_mul(base: &Self::CurveAffine, scalar: &Self::ScalarField) -> Self::CurveProjective;
+}

ec/src/lib.rs

@@ -32,6 +32,8 @@ use zeroize::Zeroize;
 pub mod models;
 pub use self::models::*;
 
+pub mod glv;
+
 pub mod group;
 
 pub mod msm;