Add the ed25519 curve (#121)

* add ed25519 curve

* changelog

* curve info

* fix

* cleanup the script

* Update ed25519/src/curves/mod.rs

* Update ed25519/src/curves/mod.rs

Co-authored-by: onewayfunc <onewayfunc@gmail.com>

ed25519/src/curves/mod.rs

@@ -0,0 +1,72 @@
+use crate::{Fq, Fr};
+use ark_ec::{
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
+};
+use ark_ff::MontFp;
+
+#[cfg(test)]
+mod tests;
+
+pub type EdwardsAffine = Affine<EdwardsParameters>;
+pub type EdwardsProjective = Projective<EdwardsParameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct EdwardsParameters;
+
+impl CurveConfig for EdwardsParameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 8
+    const COFACTOR: &'static [u64] = &[8];
+
+    /// COFACTOR_INV (mod r) =
+    /// 2713877091499598330239944961141122840321418634767465352250731601857045344121
+    const COFACTOR_INV: Fr =
+        MontFp!("2713877091499598330239944961141122840321418634767465352250731601857045344121");
+}
+
+impl TECurveConfig for EdwardsParameters {
+    /// COEFF_A = -1
+    const COEFF_A: Fq = MontFp!("-1");
+
+    /// COEFF_D = -121665 / 121666
+    const COEFF_D: Fq =
+        MontFp!("37095705934669439343138083508754565189542113879843219016388785533085940283555");
+
+    /// Standard generators from <https://neuromancer.sk/std/other/Ed25519>.
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
+
+    type MontCurveConfig = EdwardsParameters;
+
+    /// Multiplication by `a` is just negation.
+    #[inline(always)]
+    fn mul_by_a(elem: Self::BaseField) -> Self::BaseField {
+        -elem
+    }
+}
+
+// We want to emphasize that this Montgomery curve is not Curve25519.
+impl MontCurveConfig for EdwardsParameters {
+    /// COEFF_A = 486662
+    const COEFF_A: Fq = MontFp!("486662");
+
+    /// COEFF_B = 57896044618658097711785492504343953926634992332820282019728792003956564333285
+    /// This is not one, because ed25519 != curve25519
+    const COEFF_B: Fq =
+        MontFp!("57896044618658097711785492504343953926634992332820282019728792003956564333285");
+
+    type TECurveConfig = EdwardsParameters;
+}
+
+/// GENERATOR_X =
+/// 15112221349535400772501151409588531511454012693041857206046113283949847762202
+const GENERATOR_X: Fq =
+    MontFp!("15112221349535400772501151409588531511454012693041857206046113283949847762202");
+
+/// GENERATOR_Y =
+/// (4/5)
+/// 46316835694926478169428394003475163141307993866256225615783033603165251855960
+const GENERATOR_Y: Fq =
+    MontFp!("46316835694926478169428394003475163141307993866256225615783033603165251855960");