ark-curves-cherry-picked/mnt4_753/src/curves/g2.rs
mnt4_753/src/curves/g2.rsRaw
1use ark_ec::{
2 mnt4,
3 mnt4::MNT4Parameters,
4 models::{ModelParameters, SWModelParameters},
5};
6use ark_ff::{biginteger::BigInteger768, field_new};
7
8use crate::{Fq, Fq2, Fr, FQ_ZERO, G1_COEFF_A_NON_RESIDUE};
9
10pub type G2Affine = mnt4::G2Affine<crate::Parameters>;
11pub type G2Projective = mnt4::G2Projective<crate::Parameters>;
12pub type G2Prepared = mnt4::G2Prepared<crate::Parameters>;
13
14#[derive(Clone, Default, PartialEq, Eq)]
15pub struct Parameters;
16
17impl ModelParameters for Parameters {
18 type BaseField = Fq2;
19 type ScalarField = Fr;
20}
21
22/// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
23#[rustfmt::skip]
24pub const MUL_BY_A_C0: Fq = G1_COEFF_A_NON_RESIDUE;
25
26/// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
27#[rustfmt::skip]
28pub const MUL_BY_A_C1: Fq = G1_COEFF_A_NON_RESIDUE;
29
30impl SWModelParameters for Parameters {
31 const COEFF_A: Fq2 = crate::Parameters::TWIST_COEFF_A;
32 // B coefficient of MNT4-753 G2 =
33 // ```
34 // mnt4753_twist_coeff_b = mnt4753_Fq2(mnt4753_Fq::zero(),
35 // mnt4753_G1::coeff_b * mnt4753_Fq2::non_residue);
36 // non_residue = mnt4753_Fq2::non_residue = mnt4753_Fq("13");
37 // = (ZERO, G1_B_COEFF * NON_RESIDUE);
38 // =
39 // (0, 39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212)
40 // ```
41 #[rustfmt::skip]
42 const COEFF_B: Fq2 = field_new!(Fq2,
43 FQ_ZERO,
44 field_new!(Fq, BigInteger768([
45 15129916544657421551,
46 11332543254671606602,
47 11913830318987286849,
48 13905314883394440110,
49 16479690325073358448,
50 14869098639251228898,
51 10663986895980443550,
52 10768989312009479656,
53 9469728929095040349,
54 4512954369775881939,
55 8788997129423430122,
56 459763387588954,
57 ])),
58 );
59
60 /// COFACTOR =
61 /// 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888049094905534395567574915333486969589229856772141392370549616644545554517640527237829320384324374366385444967219201
62 #[rustfmt::skip]
63 const COFACTOR: &'static [u64] = &[
64 16436257212445032449,
65 8690275530472745198,
66 17315389657026393162,
67 1645397558963170979,
68 3544984605440726586,
69 12665092767997125024,
70 11083680675069097885,
71 575819899841080717,
72 6825179918269667443,
73 13256793349531086829,
74 1162650133526138285,
75 497830423872529,
76 ];
77
78 /// COFACTOR^(-1) mod r =
79 /// 102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200
80 #[rustfmt::skip]
81 const COFACTOR_INV: Fr = field_new!(Fr, BigInteger768([
82 1879390364380281898,
83 7926794171490610432,
84 6437239504245874253,
85 16688141022047191858,
86 17059416847145768464,
87 15065047661241262516,
88 16537575340937777321,
89 3324411942044534547,
90 3878293904770657570,
91 18116939243856833744,
92 7557533897589069385,
93 78370361203778,
94 ]));
95
96 /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
97 const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
98 (G2_GENERATOR_X, G2_GENERATOR_Y);
99
100 #[inline(always)]
101 fn mul_by_a(elt: &Fq2) -> Fq2 {
102 field_new!(Fq2, MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1,)
103 }
104}
105
106const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
107const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
108
109// Generator of G2
110// These are two Fq elements each because X and Y (and Z) are elements of Fq^2
111// X = 29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167,
112// 19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000,
113// Y = 39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654,
114// 17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245,
115#[rustfmt::skip]
116pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger768([
117 7263636080534048301,
118 7643227961769035653,
119 15787777614640869937,
120 17661317895964274771,
121 4142647779394287783,
122 15064949873659932676,
123 4579259080596351332,
124 2207443675339702626,
125 5738725620118622838,
126 4338467638707299712,
127 6558861849926282439,
128 341078935870328
129]));
130
131#[rustfmt::skip]
132pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger768([
133 13073882729051113867,
134 195909455108318710,
135 10527070038778509320,
136 16605710222187477118,
137 10442518358308209073,
138 7776589986153052354,
139 16034091384000651523,
140 17429232381273855185,
141 512853344493546034,
142 7982076214836075255,
143 3601416800138513610,
144 399028695285184
145]));
146
147#[rustfmt::skip]
148pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger768([
149 4867672648970469422,
150 2453112364260322863,
151 11918672197974895143,
152 3923647310180624143,
153 12707123323825700670,
154 15781895092544451511,
155 17747112377690960911,
156 16511994611001933567,
157 15360620366665804029,
158 10252080383738480571,
159 5722654046339742760,
160 316853130349807
161]));
162
163#[rustfmt::skip]
164pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger768([
165 17322957246732430708,
166 11825815087694023697,
167 7654216682602683900,
168 13544637981229618042,
169 17057060382219081849,
170 4038731408172002692,
171 6631723222530012253,
172 10585926166286435412,
173 16050667328028620117,
174 16598483946296156500,
175 11771818132648686020,
176 1230430296095
177]));