Add Pallas curve basic functionality (#698)

* added pallas field

* cargo fmt

* starting with pallas

* curve created

* cargo fmt

* adding tests

* adding unit tests

* added unit tests

* one test is failing

* pallas curve basic functionality

math/src/elliptic_curve/short_weierstrass/curves/mod.rs

@@ -1,5 +1,6 @@
 pub mod bls12_377;
 pub mod bls12_381;
+pub mod pallas;
 pub mod stark_curve;
 pub mod test_curve_1;
 pub mod test_curve_2;

math/src/elliptic_curve/short_weierstrass/curves/pallas/curve.rs

@@ -0,0 +1,136 @@
+use crate::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint;
+use crate::elliptic_curve::traits::IsEllipticCurve;
+use crate::field::fields::pallas_field::Pallas255PrimeField;
+use crate::{
+    elliptic_curve::short_weierstrass::traits::IsShortWeierstrass, field::element::FieldElement,
+};
+
+#[derive(Clone, Debug)]
+pub struct PallasCurve;
+
+impl IsEllipticCurve for PallasCurve {
+    type BaseField = Pallas255PrimeField;
+    type PointRepresentation = ShortWeierstrassProjectivePoint<Self>;
+
+    fn generator() -> Self::PointRepresentation {
+        Self::PointRepresentation::new([
+            -FieldElement::<Self::BaseField>::one(),
+            FieldElement::<Self::BaseField>::from(2),
+            FieldElement::one(),
+        ])
+    }
+}
+
+impl IsShortWeierstrass for PallasCurve {
+    fn a() -> FieldElement<Self::BaseField> {
+        FieldElement::from(0)
+    }
+
+    fn b() -> FieldElement<Self::BaseField> {
+        FieldElement::from(5)
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::{
+        cyclic_group::IsGroup, elliptic_curve::traits::EllipticCurveError,
+        field::element::FieldElement,
+    };
+
+    use super::PallasCurve;
+
+    #[allow(clippy::upper_case_acronyms)]
+    type FE = FieldElement<Pallas255PrimeField>;
+
+    fn point_1() -> ShortWeierstrassProjectivePoint<PallasCurve> {
+        let x = FE::from_hex_unchecked(
+            "bd1e740e6b1615ae4c508148ca0c53dbd43f7b2e206195ab638d7f45d51d6b5",
+        );
+        let y = FE::from_hex_unchecked(
+            "13aacd107ca10b7f8aab570da1183b91d7d86dd723eaa2306b0ef9c5355b91d8",
+        );
+        PallasCurve::create_point_from_affine(x, y).unwrap()
+    }
+
+    fn point_1_times_5() -> ShortWeierstrassProjectivePoint<PallasCurve> {
+        let x = FE::from_hex_unchecked(
+            "17a21304fffd6749d6173d4e0acd9724d98a97453b3491c0e5a53b06cf039b13",
+        );
+        let y = FE::from_hex_unchecked(
+            "2f9bde429091a1089e52a6cc5dc789e1a58eeded0cf72dccc33b7af685a982d",
+        );
+        PallasCurve::create_point_from_affine(x, y).unwrap()
+    }
+
+    #[test]
+    fn adding_five_times_point_1_works() {
+        let point_1 = point_1();
+        let point_1_times_5 = point_1_times_5();
+        assert_eq!(point_1.operate_with_self(5_u16), point_1_times_5);
+    }
+
+    #[test]
+    fn create_valid_point_works() {
+        let p = point_1();
+        assert_eq!(
+            *p.x(),
+            FE::from_hex_unchecked(
+                "bd1e740e6b1615ae4c508148ca0c53dbd43f7b2e206195ab638d7f45d51d6b5"
+            )
+        );
+        assert_eq!(
+            *p.y(),
+            FE::from_hex_unchecked(
+                "13aacd107ca10b7f8aab570da1183b91d7d86dd723eaa2306b0ef9c5355b91d8"
+            )
+        );
+        assert_eq!(*p.z(), FE::from_hex_unchecked("1"));
+    }
+
+    #[test]
+    fn create_invalid_points_returns_an_error() {
+        assert_eq!(
+            PallasCurve::create_point_from_affine(FE::from(0), FE::from(1)),
+            Err(EllipticCurveError::InvalidPoint)
+        );
+    }
+
+    #[test]
+    fn equality_works() {
+        let g = PallasCurve::generator();
+        let g2 = g.operate_with_self(2_u16);
+        let g2_other = g.operate_with(&g);
+        assert_ne!(&g2, &g);
+        assert_eq!(&g, &g);
+        assert_eq!(&g2, &g2_other);
+    }
+
+    #[test]
+    fn g_operated_with_g_satifies_ec_equation() {
+        let g = PallasCurve::generator();
+        let g2 = g.operate_with_self(2_u16);
+
+        // get x and y from affine coordinates
+        let g2_affine = g2.to_affine();
+        let x = g2_affine.x();
+        let y = g2_affine.y();
+
+        // calculate both sides of Pallas curve equation
+        let five = PallasCurve::b();
+        let y_sq_0 = x.pow(3_u16) + five;
+        let y_sq_1 = y.pow(2_u16);
+
+        assert_eq!(y_sq_0, y_sq_1);
+    }
+
+    #[test]
+    fn operate_with_self_works_1() {
+        let g = PallasCurve::generator();
+        assert_eq!(
+            g.operate_with(&g).operate_with(&g),
+            g.operate_with_self(3_u16)
+        );
+    }
+}

math/src/elliptic_curve/short_weierstrass/curves/pallas/mod.rs

@@ -0,0 +1 @@
+pub mod curve;