1use ark_ec::{
  2    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
  3    twisted_edwards_extended::{GroupAffine, GroupProjective},
  4};
  5use ark_ff::{biginteger::BigInteger320, field_new};
  6
  7use crate::{fq::Fq, fr::Fr};
  8
  9#[cfg(test)]
 10mod tests;
 11
 12pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
 13pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
 14
 15#[derive(Clone, Default, PartialEq, Eq)]
 16pub struct EdwardsParameters;
 17
 18impl ModelParameters for EdwardsParameters {
 19    type BaseField = Fq;
 20    type ScalarField = Fr;
 21}
 22
 23// Many parameters need to be written down in the Montgomery residue form,
 24// discussed below. Some useful numbers:
 25// R for Fq: 223364648326281414938801705359223029554923725549792420683051274872200260503540791531766876
 26// R for Fr: 104384076783966083500464392945960916666734135485183910065100558776489954102951241798239545
 27
 28impl TEModelParameters for EdwardsParameters {
 29    /// COEFF_A = -1
 30    /// Needs to be in the Montgomery residue form in Fq
 31    /// I.e., -1 * R for Fq
 32    ///     = 252557637842979910814547544293825421990201153003031094870216460866964386803867699028196261
 33    #[rustfmt::skip]
 34    const COEFF_A: Fq = field_new!(Fq, BigInteger320([
 35        17882590928154426277u64,
 36        6901912683734848330u64,
 37        364575608937879866u64,
 38        8740893163049517815u64,
 39        2181130330288u64,
 40    ]));
 41
 42    /// COEFF_D = 4212
 43    /// Needs to be in the Montgomery residue form in Fq
 44    /// I.e., 4212 * R for Fq
 45    ///     = 389461279836940033614665658623660232171971995346409183754923941118154161474636585314923000
 46    #[rustfmt::skip]
 47    const COEFF_D: Fq = field_new!(Fq, BigInteger320([
 48        8040159930071495160u64,
 49        16503302848883893212u64,
 50        4541498709509651666u64,
 51        11429056610118256373u64,
 52        3363453258354u64,
 53    ]));
 54
 55    /// COFACTOR = 4
 56    const COFACTOR: &'static [u64] = &[4];
 57
 58    /// COFACTOR_INV (mod r) =
 59    /// 29745142885578832859584328103315528221570304936126890280067991221921526670592508030983158
 60    /// Needs to be in the Montgomery residue form in Fr
 61    /// I.e., 29745142885578832859584328103315528221570304936126890280067991221921526670592508030983158 * R for Fr
 62    ///     = 55841162081570353734700426339805757388253838807422867796343130916044015196330318480543044
 63    #[rustfmt::skip]
 64    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger320([
 65        6539529304383425860u64,
 66        7567022062893857598u64,
 67        17399624368177871129u64,
 68        14575354999847441509u64,
 69        482253688048u64,
 70    ]));
 71
 72    /// Generated randomly
 73    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
 74
 75    type MontgomeryModelParameters = EdwardsParameters;
 76
 77    /// Multiplication by `a` is just negation.
 78    #[inline(always)]
 79    fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
 80        -*elem
 81    }
 82}
 83
 84impl MontgomeryModelParameters for EdwardsParameters {
 85    /// COEFF_A = 203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204
 86    /// Needs to be in the Montgomery residue form in Fq
 87    /// I.e., 203563247015667910991582090642011229452721346107806307863040223071914240315202967004285204 * R for Fq
 88    ///     = 184958108588233737086787169006685138672129232027042887479256778022373554352621152610883766
 89    #[rustfmt::skip]
 90    const COEFF_A: Fq = field_new!(Fq, BigInteger320([
 91        13866101745789245622u64,
 92        14126297534943667090u64,
 93        11307578615387704385u64,
 94        8263080598809044705u64,
 95        1597329401399u64,
 96    ]));
 97    /// COEFF_B = 272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931
 98    /// Needs to be in the Montgomery residue form in Fq
 99    //  I.e., 272359039153593414761767159011037222092403532445017207690227512667250406992205523555677931 * R for Fq
100    //      = 320157167097726084542307919580965705308273073979019302261176143711555219255114245445508756
101    #[rustfmt::skip]
102    const COEFF_B: Fq = field_new!(Fq, BigInteger320([
103        3452336036810055316u64,
104        18124271906235581187u64,
105        7868316676197606962u64,
106        9218705727289990924u64,
107        2764931259177u64,
108    ]));
109
110    type TEModelParameters = EdwardsParameters;
111}
112
113/// GENERATOR_X =
114/// 282406820114868156776872298252698015906762052916420164316497572033519876761239463633892227
115/// Needs to be in the Montgomery residue form in Fq
116/// I.e., 282406820114868156776872298252698015906762052916420164316497572033519876761239463633892227 * R for Fq
117///     = 6917556742108450905978293995070573074174231920036503115659104908111915200040057661385715
118#[rustfmt::skip]
119const GENERATOR_X: Fq = field_new!(Fq, BigInteger320([
120    797921980254612467u64,
121    14323677897559322103u64,
122    16879595040064082265u64,
123    5138786402348661261u64,
124    59741186014u64,
125]));
126
127/// GENERATOR_Y =
128/// 452667754940241021433619311795265643711152068500301853535337412655162600774122192283142703
129/// Needs to be in the Montgomery residue form in Fq
130/// I.e., 452667754940241021433619311795265643711152068500301853535337412655162600774122192283142703 * R for Fq
131///     = 411219337323952690830344109182130393590959634960952808951091963301565250764467583592890490
132#[rustfmt::skip]
133const GENERATOR_Y: Fq = field_new!(Fq, BigInteger320([
134    16522567711648317562u64,
135    4273808507945498262u64,
136    17459848913470201097u64,
137    16519670308098023011u64,
138    3551359510243u64,
139]));