lambdaworks-math 0.13.0

Modular math library for cryptography
Documentation 
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use crate::cyclic_group::IsGroup;
use crate::elliptic_curve::traits::IsEllipticCurve;
use crate::field::element::FieldElement;
use core::fmt::Debug;

/// Trait to add elliptic curves behaviour to a struct.
/// We use the short Weierstrass form equation: `y^2 = x^3 + a * x  + b`.
pub trait IsShortWeierstrass: IsEllipticCurve + Clone + Debug {
    /// `a` coefficient for the equation `y^2 = x^3 + a * x  + b`.
    fn a() -> FieldElement<Self::BaseField>;

    /// `b` coefficient for the equation  `y^2 = x^3 + a * x  + b`.
    fn b() -> FieldElement<Self::BaseField>;

    /// Evaluates the residual of the Short Weierstrass equation
    /// R = y^2 - x^3 - ax - b
    /// If R == 0, then the point is in the curve
    /// Use in affine coordinates
    fn defining_equation(
        x: &FieldElement<Self::BaseField>,
        y: &FieldElement<Self::BaseField>,
    ) -> FieldElement<Self::BaseField> {
        y.square() - ((x.square() + Self::a()) * x + Self::b())
    }

    // Evaluates the projective equation:
    // y^2 * z = x^3 + a * x * z^2 + b * z^3
    fn defining_equation_projective(
        x: &FieldElement<Self::BaseField>,
        y: &FieldElement<Self::BaseField>,
        z: &FieldElement<Self::BaseField>,
    ) -> FieldElement<Self::BaseField> {
        y.square() * z - ((x.square() + Self::a() * z.square()) * x + Self::b() * z.square() * z)
    }

    // Evaluates the jacobian equation:
    // y^2  = x^3 + a * x * z^4 + b * z^6
    fn defining_equation_jacobian(
        x: &FieldElement<Self::BaseField>,
        y: &FieldElement<Self::BaseField>,
        z: &FieldElement<Self::BaseField>,
    ) -> FieldElement<Self::BaseField> {
        y.square()
            - ((x.square() + Self::a() * z.square().square()) * x
                + Self::b() * z.square().square() * z.square())
    }
}

pub trait Compress {
    type G1Point: IsGroup;
    type G2Point: IsGroup;
    type G1Compressed;
    type G2Compressed;
    type Error;

    /// Gives a compressed representation of a G1 point in the elliptic curve
    /// Providing the x coordinate and an additional bit provides a way of retrieving the
    /// y coordinate by sending less information
    #[cfg(feature = "alloc")]
    fn compress_g1_point(point: &Self::G1Point) -> Self::G1Compressed;

    /// Gives a compressed representation of a G2 point in the elliptic curve
    /// Providing the x coordinate and an additional bit provides a way of retrieving the
    /// y coordinate by sending less information
    #[cfg(feature = "alloc")]
    fn compress_g2_point(point: &Self::G2Point) -> Self::G2Compressed;

    /// Given a slice of bytes, representing the x coordinate plus additional bits, recovers
    /// the elliptic curve point in G1
    fn decompress_g1_point(input_bytes: &mut [u8]) -> Result<Self::G1Point, Self::Error>;

    /// Given a slice of bytes, representing the x coordinate plus additional bits, recovers
    /// the elliptic curve point in G2
    fn decompress_g2_point(input_bytes: &mut [u8]) -> Result<Self::G2Point, Self::Error>;
}