1use crate::*;
 2use ark_ec::{
 3    bls12,
 4    bls12::Bls12Parameters,
 5    models::{ModelParameters, SWModelParameters},
 6    short_weierstrass_jacobian::GroupAffine,
 7    AffineCurve, ProjectiveCurve,
 8};
 9use ark_ff::{biginteger::BigInteger256, field_new, Zero};
10use ark_std::ops::Neg;
11
12pub type G1Affine = bls12::G1Affine<crate::Parameters>;
13pub type G1Projective = bls12::G1Projective<crate::Parameters>;
14
15#[derive(Clone, Default, PartialEq, Eq)]
16pub struct Parameters;
17
18impl ModelParameters for Parameters {
19    type BaseField = Fq;
20    type ScalarField = Fr;
21}
22
23impl SWModelParameters for Parameters {
24    /// COEFF_A = 0
25    const COEFF_A: Fq = field_new!(Fq, "0");
26
27    /// COEFF_B = 4
28    #[rustfmt::skip]
29    const COEFF_B: Fq = field_new!(Fq, "4");
30
31    /// COFACTOR = (x - 1)^2 / 3  = 76329603384216526031706109802092473003
32    const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];
33
34    /// COFACTOR_INV = COFACTOR^{-1} mod r
35    /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
36    #[rustfmt::skip]
37    const COFACTOR_INV: Fr = field_new!(Fr, "52435875175126190458656871551744051925719901746859129887267498875565241663483");
38
39    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
40    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
41        (G1_GENERATOR_X, G1_GENERATOR_Y);
42
43    #[inline(always)]
44    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
45        Self::BaseField::zero()
46    }
47
48    fn is_in_correct_subgroup_assuming_on_curve(p: &GroupAffine<Parameters>) -> bool {
49        // Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
50        //
51        // Check that endomorphism_p(P) == -[X^2]P
52
53        let x = BigInteger256::new([crate::Parameters::X[0], 0, 0, 0]);
54
55        // An early-out optimization described in Section 6.
56        // If uP == P but P != point of infinity, then the point is not in the right subgroup.
57        let x_times_p = p.mul(x);
58        if x_times_p.eq(p) && !p.infinity {
59            return false;
60        }
61
62        let minus_x_squared_times_p = x_times_p.mul(x).neg();
63        let endomorphism_p = endomorphism(p);
64        minus_x_squared_times_p.eq(&endomorphism_p)
65    }
66}
67
68/// G1_GENERATOR_X =
69/// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
70#[rustfmt::skip]
71pub const G1_GENERATOR_X: Fq = field_new!(Fq, "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
72
73/// G1_GENERATOR_Y =
74/// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
75#[rustfmt::skip]
76pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");
77
78/// BETA is a non-trivial cubic root of unity in Fq.
79pub const BETA: Fq = field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");
80
81pub fn endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
82    // Endomorphism of the points on the curve.
83    // endomorphism_p(x,y) = (BETA * x, y) where BETA is a non-trivial cubic root of unity in Fq.
84    let mut res = (*p).clone();
85    res.x *= BETA;
86    res
87}