Add Pallas and Vesta curves (#21)

Co-authored-by: Ying Tong Lai <yingtong@electriccoin.co>
Co-authored-by: Daira Hopwood <daira@jacaranda.org>
Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>
Co-authored-by: therealyingtong <yingtong@z.cash>

pallas/src/curves/mod.rs

@@ -0,0 +1,49 @@
+use crate::{fq::Fq, fr::Fr};
+use ark_ec::{
+    models::{ModelParameters, SWModelParameters},
+    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+};
+use ark_ff::{field_new, Zero};
+
+#[cfg(test)]
+mod tests;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct PallasParameters;
+
+impl ModelParameters for PallasParameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+}
+
+pub type Affine = GroupAffine<PallasParameters>;
+pub type Projective = GroupProjective<PallasParameters>;
+
+impl SWModelParameters for PallasParameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = field_new!(Fq, "0");
+
+    /// COEFF_B = 5
+    const COEFF_B: Fq = field_new!(Fq, "5");
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[0x1];
+
+    /// COFACTOR_INV = 1
+    const COFACTOR_INV: Fr = field_new!(Fr, "1");
+
+    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
+        (G_GENERATOR_X, G_GENERATOR_Y);
+
+    #[inline(always)]
+    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+        Self::BaseField::zero()
+    }
+}
+
+/// G_GENERATOR_X = -1
+pub const G_GENERATOR_X: Fq = field_new!(Fq, "-1");
+
+/// G_GENERATOR_Y = 2
+pub const G_GENERATOR_Y: Fq = field_new!(Fq, "2");

pallas/src/curves/tests.rs

@@ -0,0 +1,39 @@
+#![allow(unused_imports)]
+use ark_ff::{
+    fields::{Field, FpParameters, PrimeField, SquareRootField},
+    One, Zero,
+};
+use ark_serialize::CanonicalSerialize;
+use ark_std::test_rng;
+
+use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
+use core::ops::{AddAssign, MulAssign};
+use rand::Rng;
+
+use crate::{Affine, PallasParameters, Projective};
+
+use ark_curve_tests::{
+    curves::{curve_tests, sw_tests},
+    groups::group_test,
+};
+
+#[test]
+fn test_projective_curve() {
+    curve_tests::<Projective>();
+    sw_tests::<PallasParameters>();
+}
+
+#[test]
+fn test_projective_group() {
+    let mut rng = test_rng();
+    let a: Projective = rng.gen();
+    let b: Projective = rng.gen();
+    group_test(a, b);
+}
+
+#[test]
+fn test_generator() {
+    let generator = Affine::prime_subgroup_generator();
+    assert!(generator.is_on_curve());
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}