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* add field * add curve * update readme * fix readme
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169 changes: 169 additions & 0 deletions
169
math/src/elliptic_curve/short_weierstrass/curves/secp256r1/curve.rs
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,169 @@ | ||
| use crate::elliptic_curve::short_weierstrass::point::ShortWeierstrassProjectivePoint; | ||
| use crate::elliptic_curve::traits::IsEllipticCurve; | ||
| use crate::field::fields::secp256r1_field::Secp256r1PrimeField; | ||
| use crate::{ | ||
| elliptic_curve::short_weierstrass::traits::IsShortWeierstrass, field::element::FieldElement, | ||
| }; | ||
|
|
||
| /// This implementation is not constant time and cannot be used to sign messages. You can use it to check signatures | ||
| #[derive(Clone, Debug)] | ||
| pub struct Secp256r1Curve; | ||
|
|
||
| impl IsEllipticCurve for Secp256r1Curve { | ||
| type BaseField = Secp256r1PrimeField; | ||
| type PointRepresentation = ShortWeierstrassProjectivePoint<Self>; | ||
|
|
||
| fn generator() -> Self::PointRepresentation { | ||
| Self::PointRepresentation::new([ | ||
| FieldElement::<Self::BaseField>::from_hex_unchecked( | ||
| "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", | ||
| ), | ||
| FieldElement::<Self::BaseField>::from_hex_unchecked( | ||
| "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", | ||
| ), | ||
| FieldElement::one(), | ||
| ]) | ||
| } | ||
| } | ||
|
|
||
| impl IsShortWeierstrass for Secp256r1Curve { | ||
| fn a() -> FieldElement<Self::BaseField> { | ||
| FieldElement::<Self::BaseField>::from_hex_unchecked( | ||
| "ffffffff00000001000000000000000000000000fffffffffffffffffffffffc", | ||
| ) | ||
| } | ||
| fn b() -> FieldElement<Self::BaseField> { | ||
| FieldElement::<Self::BaseField>::from_hex_unchecked( | ||
| "5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", | ||
| ) | ||
| } | ||
| } | ||
|
|
||
| #[cfg(test)] | ||
| mod tests { | ||
| use super::*; | ||
| use crate::{ | ||
| cyclic_group::IsGroup, elliptic_curve::traits::EllipticCurveError, | ||
| field::element::FieldElement, unsigned_integer::element::U256, | ||
| }; | ||
|
|
||
| use super::Secp256r1Curve; | ||
|
|
||
| #[allow(clippy::upper_case_acronyms)] | ||
| type FE = FieldElement<Secp256r1PrimeField>; | ||
|
|
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| fn point_1() -> ShortWeierstrassProjectivePoint<Secp256r1Curve> { | ||
| let x = FE::from_hex_unchecked( | ||
| "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", | ||
| ); | ||
| let y = FE::from_hex_unchecked( | ||
| "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", | ||
| ); | ||
| Secp256r1Curve::create_point_from_affine(x, y).unwrap() | ||
| } | ||
|
|
||
| fn point_1_times_5() -> ShortWeierstrassProjectivePoint<Secp256r1Curve> { | ||
| let x = FE::from_hex_unchecked( | ||
| "51590B7A515140D2D784C85608668FDFEF8C82FD1F5BE52421554A0DC3D033ED", | ||
| ); | ||
| let y = FE::from_hex_unchecked( | ||
| "E0C17DA8904A727D8AE1BF36BF8A79260D012F00D4D80888D1D0BB44FDA16DA4", | ||
| ); | ||
| Secp256r1Curve::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( | ||
| "6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296" | ||
| ) | ||
| ); | ||
| assert_eq!( | ||
| *p.y(), | ||
| FE::from_hex_unchecked( | ||
| "4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5" | ||
| ) | ||
| ); | ||
| assert_eq!(*p.z(), FE::from_hex_unchecked("1")); | ||
| } | ||
|
|
||
| #[test] | ||
| fn create_invalid_points_returns_an_error() { | ||
| assert_eq!( | ||
| Secp256r1Curve::create_point_from_affine(FE::from(0), FE::from(1)), | ||
| Err(EllipticCurveError::InvalidPoint) | ||
| ); | ||
| } | ||
|
|
||
| #[test] | ||
| fn equality_works() { | ||
| let g = Secp256r1Curve::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 = Secp256r1Curve::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 Secp256r1 curve equation | ||
| let a = Secp256r1Curve::a(); | ||
| let b = Secp256r1Curve::b(); | ||
| let y_sq_0 = x.pow(3_u16) + (a * x) + b; | ||
| 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 = Secp256r1Curve::generator(); | ||
| assert_eq!( | ||
| g.operate_with(&g).operate_with(&g), | ||
| g.operate_with_self(3_u16) | ||
| ); | ||
| } | ||
|
|
||
| #[test] | ||
| fn generator_has_right_order() { | ||
| let g = Secp256r1Curve::generator(); | ||
| assert_eq!( | ||
| g.operate_with_self(U256::from_hex_unchecked( | ||
| "0xffffffff00000000ffffffffffffffffbce6faada7179e84f3b9cac2fc632551" | ||
| )) | ||
| .to_affine(), | ||
| ShortWeierstrassProjectivePoint::neutral_element() | ||
| ); | ||
| } | ||
|
|
||
| #[test] | ||
| fn inverse_works() { | ||
| let g = Secp256r1Curve::generator(); | ||
| assert_eq!( | ||
| g.operate_with_self(U256::from_hex_unchecked( | ||
| "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC63254C" | ||
| )) | ||
| .to_affine(), | ||
| g.operate_with_self(5u64).neg().to_affine() | ||
| ); | ||
| } | ||
| } |
1 change: 1 addition & 0 deletions
1
math/src/elliptic_curve/short_weierstrass/curves/secp256r1/mod.rs
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1 @@ | ||
| pub mod curve; |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,17 @@ | ||
| use crate::{ | ||
| field::fields::montgomery_backed_prime_fields::{IsModulus, MontgomeryBackendPrimeField}, | ||
| unsigned_integer::element::U256, | ||
| }; | ||
|
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| type Secp256r1MontgomeryBackendPrimeField<T> = MontgomeryBackendPrimeField<T, 4>; | ||
|
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| #[derive(Debug, Clone, PartialEq, Eq)] | ||
| pub struct MontgomeryConfigSecp256r1PrimeField; | ||
| impl IsModulus<U256> for MontgomeryConfigSecp256r1PrimeField { | ||
| const MODULUS: U256 = U256::from_hex_unchecked( | ||
| "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff", | ||
| ); | ||
| } | ||
|
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||
| pub type Secp256r1PrimeField = | ||
| Secp256r1MontgomeryBackendPrimeField<MontgomeryConfigSecp256r1PrimeField>; |