ark-curves-cherry-picked/bls12_381/src/curves/g1.rs

use ark_ec::{
    bls12,
    bls12::Bls12Parameters,
    models::CurveConfig,
    short_weierstrass::{Affine, SWCurveConfig},
    AffineCurve, ProjectiveCurve,
};
use ark_ff::{Field, MontFp, Zero};
use ark_std::ops::Neg;

use crate::*;

pub type G1Affine = bls12::G1Affine<crate::Parameters>;
pub type G1Projective = bls12::G1Projective<crate::Parameters>;

#[derive(Clone, Default, PartialEq, Eq)]
pub struct Parameters;

impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;

    /// COFACTOR = (x - 1)^2 / 3  = 76329603384216526031706109802092473003
    const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
    const COFACTOR_INV: Fr =
        MontFp!("52435875175126190458656871551744051925719901746859129887267498875565241663483");
}

impl SWCurveConfig for Parameters {
    /// COEFF_A = 0
    const COEFF_A: Fq = Fq::ZERO;

    /// COEFF_B = 4
    const COEFF_B: Fq = MontFp!("4");

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);

    #[inline(always)]
    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }

    #[inline]
    fn is_in_correct_subgroup_assuming_on_curve(p: &G1Affine) -> bool {
        // Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
        //
        // Check that endomorphism_p(P) == -[X^2]P

        // An early-out optimization described in Section 6.
        // If uP == P but P != point of infinity, then the point is not in the right
        // subgroup.
        let x_times_p = p.mul_bigint(crate::Parameters::X);
        if x_times_p.eq(p) && !p.infinity {
            return false;
        }

        let minus_x_squared_times_p = x_times_p.mul_bigint(crate::Parameters::X).neg();
        let endomorphism_p = endomorphism(p);
        minus_x_squared_times_p.eq(&endomorphism_p)
    }
}

/// G1_GENERATOR_X =
/// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
pub const G1_GENERATOR_X: Fq = MontFp!("3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");

/// G1_GENERATOR_Y =
/// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
pub const G1_GENERATOR_Y: Fq = MontFp!("1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");

/// BETA is a non-trivial cubic root of unity in Fq.
pub const BETA: Fq = MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");

pub fn endomorphism(p: &Affine<Parameters>) -> Affine<Parameters> {
    // Endomorphism of the points on the curve.
    // endomorphism_p(x,y) = (BETA * x, y)
    // where BETA is a non-trivial cubic root of unity in Fq.
    let mut res = (*p).clone();
    res.x *= BETA;
    res
}