1use ark_ec::{
 2    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
 3    twisted_edwards_extended::{GroupAffine, GroupProjective},
 4};
 5use ark_ff::MontFp;
 6
 7use crate::{Fq, Fr};
 8
 9#[cfg(test)]
10mod tests;
11
12pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
13pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
14
15/// `Baby-JubJub` is a twisted Edwards curve. These curves have equations of the
16/// form: ax² + y² = 1 + dx²y².
17/// over some base finite field Fq.
18///
19/// Baby-JubJub's curve equation: x² + y² = 1 + (168696/168700)x²y²
20///
21/// q = 21888242871839275222246405745257275088548364400416034343698204186575808495617
22#[derive(Clone, Default, PartialEq, Eq)]
23pub struct EdwardsParameters;
24
25impl ModelParameters for EdwardsParameters {
26    type BaseField = Fq;
27    type ScalarField = Fr;
28
29    /// COFACTOR = 8
30    const COFACTOR: &'static [u64] = &[8];
31
32    /// COFACTOR^(-1) mod r =
33    /// 2394026564107420727433200628387514462817212225638746351800188703329891451411
34    const COFACTOR_INV: Fr = MontFp!(
35        Fr,
36        "2394026564107420727433200628387514462817212225638746351800188703329891451411"
37    );
38}
39
40impl TEModelParameters for EdwardsParameters {
41    /// COEFF_A = 1
42    const COEFF_A: Fq = MontFp!(Fq, "1");
43
44    #[inline(always)]
45    fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
46        *elem
47    }
48
49    /// COEFF_D = 168696/168700 mod q
50    ///         = 9706598848417545097372247223557719406784115219466060233080913168975159366771
51    const COEFF_D: Fq = MontFp!(
52        Fq,
53        "9706598848417545097372247223557719406784115219466060233080913168975159366771"
54    );
55
56    /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
57    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
58
59    type MontgomeryModelParameters = EdwardsParameters;
60}
61
62impl MontgomeryModelParameters for EdwardsParameters {
63    /// COEFF_A = 168698
64    const COEFF_A: Fq = MontFp!(Fq, "168698");
65    /// COEFF_B = 168700
66    const COEFF_B: Fq = MontFp!(Fq, "168700");
67
68    type TEModelParameters = EdwardsParameters;
69}
70
71const GENERATOR_X: Fq = MontFp!(
72    Fq,
73    "19698561148652590122159747500897617769866003486955115824547446575314762165298"
74);
75
76const GENERATOR_Y: Fq = MontFp!(
77    Fq,
78    "19298250018296453272277890825869354524455968081175474282777126169995084727839"
79);