Add the curve25519 curve (#124)

* add ed25519 curve

* changelog

* curve info

* fix

* edit

* update

* add more explanation

* Update curve25519/src/curves/mod.rs

* Update curve25519/src/curves/mod.rs

* fixed the comment

* Update curve25519/src/curves/mod.rs

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

curve25519/src/curves/mod.rs

@@ -0,0 +1,71 @@
+use crate::{Fq, Fr};
+use ark_ec::{
+    models::CurveConfig,
+    twisted_edwards::{Affine, MontCurveConfig, MontgomeryAffine, Projective, TECurveConfig},
+};
+use ark_ff::MontFp;
+
+#[cfg(test)]
+mod tests;
+
+pub type EdwardsAffine = Affine<Curve25519Config>;
+pub type EdwardsProjective = Projective<Curve25519Config>;
+pub type NonZeroMontgomeryAffine = MontgomeryAffine<Curve25519Config>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Curve25519Config;
+
+impl CurveConfig for Curve25519Config {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 8
+    const COFACTOR: &'static [u64] = &[8];
+
+    /// COFACTOR_INV (mod r) =
+    /// 2713877091499598330239944961141122840321418634767465352250731601857045344121
+    const COFACTOR_INV: Fr =
+        MontFp!("2713877091499598330239944961141122840321418634767465352250731601857045344121");
+}
+
+// We want to emphasize that this twisted Edwards curve is not ed25519.
+// Ed25519 has COEFF_A = -1 and COEFF_D = -121665 / 121666.
+impl TECurveConfig for Curve25519Config {
+    /// COEFF_A = 486664
+    const COEFF_A: Fq = MontFp!("486664");
+
+    /// COEFF_D = 486660
+    const COEFF_D: Fq = MontFp!("486660");
+
+    /// Standard generators from <https://neuromancer.sk/std/other/Curve25519>.
+    /// The Montgomery form is
+    ///     x = 0x09,
+    ///     y = 0x20ae19a1b8a086b4e01edd2c7748d14c923d4d7e6d7c61b229e9c5a27eced3d9
+    /// The twisted Edwards form is
+    ///     x = 0x547c4350219f5e19dd26a3d6668b74346a8eb726eb2396e1228cfa397ffe6bd4
+    ///     y = 0x6666666666666666666666666666666666666666666666666666666666666658
+    const GENERATOR: EdwardsAffine = EdwardsAffine::new_unchecked(GENERATOR_X, GENERATOR_Y);
+
+    type MontCurveConfig = Curve25519Config;
+}
+
+impl MontCurveConfig for Curve25519Config {
+    /// COEFF_A = 486662
+    const COEFF_A: Fq = MontFp!("486662");
+
+    /// COEFF_B = 1
+    const COEFF_B: Fq = MontFp!("1");
+
+    type TECurveConfig = Curve25519Config;
+}
+
+/// GENERATOR_X =
+/// 38213832894368730265794714087330135568483813637251082400757400312561599933396
+const GENERATOR_X: Fq =
+    MontFp!("38213832894368730265794714087330135568483813637251082400757400312561599933396");
+
+/// GENERATOR_Y =
+/// (4/5)
+/// 46316835694926478169428394003475163141307993866256225615783033603165251855960
+const GENERATOR_Y: Fq =
+    MontFp!("46316835694926478169428394003475163141307993866256225615783033603165251855960");