1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146

// Copyright (C) 2019-2021 Aleo Systems Inc.
// This file is part of the snarkVM library.

// The snarkVM library is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.

// The snarkVM library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with the snarkVM library. If not, see <https://www.gnu.org/licenses/>.

use snarkvm_fields::{field, Zero};
use snarkvm_utilities::biginteger::{BigInteger256, BigInteger384};

use crate::{
    bls12_377::{g1::Bls12_377G1Parameters, Fq, Fq2, Fr},
    traits::{ModelParameters, ShortWeierstrassParameters},
};

#[derive(Clone, Default, PartialEq, Eq)]
pub struct Bls12_377G2Parameters;

impl ModelParameters for Bls12_377G2Parameters {
    type BaseField = Fq2;
    type ScalarField = Fr;
}

impl ShortWeierstrassParameters for Bls12_377G2Parameters {
    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (G2_GENERATOR_X, G2_GENERATOR_Y);
    /// COEFF_A = [0, 0]
    const COEFF_A: Fq2 = field!(Fq2, Bls12_377G1Parameters::COEFF_A, Bls12_377G1Parameters::COEFF_A,);
    // As per https://eprint.iacr.org/2012/072.pdf,
    // this curve has b' = b/i, where b is the COEFF_B of G1, and x^6 -i is
    // the irreducible poly used to extend from Fp2 to Fp12.
    // In our case, i = u (App A.3, T_6).
    /// COEFF_B = [0,
    /// 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906]
    const COEFF_B: Fq2 = field!(
        Fq2,
        field!(Fq, BigInteger384([0, 0, 0, 0, 0, 0])),
        field!(
            Fq,
            BigInteger384([
                9255502405446297221,
                10229180150694123945,
                9215585410771530959,
                13357015519562362907,
                5437107869987383107,
                16259554076827459,
            ])
        ),
    );
    /// COFACTOR =
    /// 7923214915284317143930293550643874566881017850177945424769256759165301436616933228209277966774092486467289478618404761412630691835764674559376407658497
    const COFACTOR: &'static [u64] = &[
        0x0000000000000001,
        0x452217cc90000000,
        0xa0f3622fba094800,
        0xd693e8c36676bd09,
        0x8c505634fae2e189,
        0xfbb36b00e1dcc40c,
        0xddd88d99a6f6a829,
        0x26ba558ae9562a,
    ];
    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// = 6764900296503390671038341982857278410319949526107311149686707033187604810669
    const COFACTOR_INV: Fr = field!(
        Fr,
        BigInteger256([
            15499857013495546999,
            4613531467548868169,
            14546778081091178013,
            549402535258503313,
        ])
    );

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

pub const G2_GENERATOR_X: Fq2 = field!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
pub const G2_GENERATOR_Y: Fq2 = field!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);

/// G2_GENERATOR_X_C0 =
/// 233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294
pub const G2_GENERATOR_X_C0: Fq = field!(
    Fq,
    BigInteger384([
        0x68904082f268725b,
        0x668f2ea74f45328b,
        0xebca7a65802be84f,
        0x1e1850f4c1ada3e6,
        0x830dc22d588ef1e9,
        0x1862a81767c0982,
    ])
);

/// G2_GENERATOR_X_C1 =
/// 140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118
pub const G2_GENERATOR_X_C1: Fq = field!(
    Fq,
    BigInteger384([
        0x5f02a915c91c7f39,
        0xf8c553ba388da2a7,
        0xd51a416dbd198850,
        0xe943c6f38ae3073a,
        0xffe24aa8259a4981,
        0x11853391e73dfdd,
    ])
);

/// G2_GENERATOR_Y_C0 =
/// 63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423
pub const G2_GENERATOR_Y_C0: Fq = field!(
    Fq,
    BigInteger384([
        0xd5b19b897881430f,
        0x5be9118a5b371ed,
        0x6063f91f86c131ee,
        0x3244a61be8f4ec19,
        0xa02e425b9f9a3a12,
        0x18af8c04f3360d2,
    ])
);

/// G2_GENERATOR_Y_C1 =
/// 149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491
pub const G2_GENERATOR_Y_C1: Fq = field!(
    Fq,
    BigInteger384([
        0x57601ac71a5b96f5,
        0xe99acc1714f2440e,
        0x2339612f10118ea9,
        0x8321e68a3b1cd722,
        0x2b543b050cc74917,
        0x590182b396c112,
    ])
);