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

// 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::{FftParameters, FieldParameters, Fp256, Fp256Parameters};
use snarkvm_utilities::biginteger::BigInteger256 as BigInteger;

/// BLS12-377 scalar field.
///
/// Roots of unity computed from modulus and R using this sage code:
///
/// ```ignore
/// q = 8444461749428370424248824938781546531375899335154063827935233455917409239041
/// R = 6014086494747379908336260804527802945383293308637734276299549080986809532403 # Montgomery R
/// s = 47
/// o = q - 1
/// F = GF(q)
/// g = F.multiplicative_generator()
/// assert g.multiplicative_order() == o
/// g2 = g ** (o/2**s)
/// assert g2.multiplicative_order() == 2**s
/// def into_chunks(val, width, n):
///     return [int(int(val) // (2 ** (width * i)) % 2 ** width) for i in range(n)]
/// print("Gen: ", g * R % q)
/// print("Gen: ", into_chunks(g * R % q, 64, 4))
/// print("2-adic gen: ", into_chunks(g2 * R % q, 64, 4))
/// ```
pub type Fr = Fp256<FrParameters>;

pub struct FrParameters;

impl Fp256Parameters for FrParameters {}

impl FftParameters for FrParameters {
    type BigInteger = BigInteger;

    #[rustfmt::skip]
    const TWO_ADICITY: u32 = 47;
    /// TODO (howardwu): CRITICAL - Fix this after a migration plan has been determined.
    ///  - 0x3c3d3ca739381fb2,
    ///  - 0x9a14cda3ec99772b,
    ///  - 0xd7aacc7c59724826,
    ///  - 0xd1ba211c5cc349c,
    ///  + 12646347781564978760u64,
    ///  + 6783048705277173164u64,
    ///  + 268534165941069093u64,
    ///  + 1121515446318641358u64,
    #[rustfmt::skip]
    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
        0x3c3d3ca739381fb2,
        0x9a14cda3ec99772b,
        0xd7aacc7c59724826,
        0xd1ba211c5cc349c,
    ]);
}

impl FieldParameters for FrParameters {
    #[rustfmt::skip]
    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
    /// GENERATOR = 22
    /// Encoded in Montgomery form, so the value is
    /// (22 * R) % q = 5642976643016801619665363617888466827793962762719196659561577942948671127251
    #[rustfmt::skip]
    const GENERATOR: BigInteger = BigInteger([
        2984901390528151251u64,
        10561528701063790279u64,
        5476750214495080041u64,
        898978044469942640u64,
    ]);
    #[rustfmt::skip]
    const INV: u64 = 725501752471715839u64;
    /// MODULUS = 8444461749428370424248824938781546531375899335154063827935233455917409239041
    #[rustfmt::skip]
    const MODULUS: BigInteger = BigInteger([
        725501752471715841u64,
        6461107452199829505u64,
        6968279316240510977u64,
        1345280370688173398u64,
    ]);
    #[rustfmt::skip]
    const MODULUS_BITS: u32 = 253;
    /// (r - 1)/2 =
    /// 4222230874714185212124412469390773265687949667577031913967616727958704619520
    #[rustfmt::skip]
    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
        0x8508c00000000000,
        0xacd53b7f68000000,
        0x305a268f2e1bd800,
        0x955b2af4d1652ab,
    ]);
    #[rustfmt::skip]
    const R: BigInteger = BigInteger([
        9015221291577245683u64,
        8239323489949974514u64,
        1646089257421115374u64,
        958099254763297437u64,
    ]);
    #[rustfmt::skip]
    const R2: BigInteger = BigInteger([
        2726216793283724667u64,
        14712177743343147295u64,
        12091039717619697043u64,
        81024008013859129u64,
    ]);
    #[rustfmt::skip]
    const REPR_SHAVE_BITS: u32 = 3;
    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t

    /// t = (r - 1) / 2^s =
    /// 60001509534603559531609739528203892656505753216962260608619555
    #[rustfmt::skip]
    const T: BigInteger = BigInteger([
        0xedfda00000021423,
        0x9a3cb86f6002b354,
        0xcabd34594aacc168,
        0x2556,
    ]);
    /// (t - 1) / 2 =
    /// 30000754767301779765804869764101946328252876608481130304309777
    #[rustfmt::skip]
    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
        0x76fed00000010a11,
        0x4d1e5c37b00159aa,
        0x655e9a2ca55660b4,
        0x12ab,
    ]);
}