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Update BLS12-381

fq2_neg_nonresidue
Pratyush Mishra 3 years ago
parent
0445d45c07
commit
b0565ad0c5
6 changed files with 98 additions and 416 deletions
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  1. +6
    -35
      bls12_381/src/curves/g1.rs
  2. +6
    -42
      bls12_381/src/curves/g2.rs
  3. +2
    -2
      bls12_381/src/fields/fq.rs
  4. +39
    -156
      bls12_381/src/fields/fq12.rs
  5. +5
    -43
      bls12_381/src/fields/fq2.rs
  6. +40
    -138
      bls12_381/src/fields/fq6.rs

+ 6
- 35
bls12_381/src/curves/g1.rs
View File

@ -3,10 +3,7 @@ use ark_ec::{
bls12,
models::{ModelParameters, SWModelParameters},
};
use ark_ff::{
biginteger::{BigInteger256, BigInteger384},
field_new, Zero,
};
use ark_ff::{field_new, Zero};
pub type G1Affine = bls12::G1Affine<crate::Parameters>;
pub type G1Projective = bls12::G1Projective<crate::Parameters>;
@ -21,18 +18,11 @@ impl ModelParameters for Parameters {
impl SWModelParameters for Parameters {
/// COEFF_A = 0
const COEFF_A: Fq = field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0]));
const COEFF_A: Fq = field_new!(Fq, "0");
/// COEFF_B = 4
#[rustfmt::skip]
const COEFF_B: Fq = field_new!(Fq, BigInteger384([
0xaa270000000cfff3,
0x53cc0032fc34000a,
0x478fe97a6b0a807f,
0xb1d37ebee6ba24d7,
0x8ec9733bbf78ab2f,
0x9d645513d83de7e,
]));
const COEFF_B: Fq = field_new!(Fq, "4");
/// COFACTOR = (x - 1)^2 / 3 = 76329603384216526031706109802092473003
const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];
@ -40,12 +30,7 @@ impl SWModelParameters for Parameters {
/// COFACTOR_INV = COFACTOR^{-1} mod r
/// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
#[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
288839107172787499,
1152722415086798946,
2612889808468387987,
5124657601728438008,
]));
const COFACTOR_INV: Fr = field_new!(Fr, "52435875175126190458656871551744051925719901746859129887267498875565241663483");
/// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -60,23 +45,9 @@ impl SWModelParameters for Parameters {
/// G1_GENERATOR_X =
/// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
#[rustfmt::skip]
pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger384([
0x5cb38790fd530c16,
0x7817fc679976fff5,
0x154f95c7143ba1c1,
0xf0ae6acdf3d0e747,
0xedce6ecc21dbf440,
0x120177419e0bfb75,
]));
pub const G1_GENERATOR_X: Fq = field_new!(Fq, "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
/// G1_GENERATOR_Y =
/// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
#[rustfmt::skip]
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger384([
0xbaac93d50ce72271,
0x8c22631a7918fd8e,
0xdd595f13570725ce,
0x51ac582950405194,
0xe1c8c3fad0059c0,
0xbbc3efc5008a26a,
]));
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");

+ 6
- 42
bls12_381/src/curves/g2.rs
View File

@ -3,10 +3,7 @@ use ark_ec::{
bls12,
models::{ModelParameters, SWModelParameters},
};
use ark_ff::{
biginteger::{BigInteger256, BigInteger384},
field_new, Zero,
};
use ark_ff::{field_new, Zero};
pub type G2Affine = bls12::G2Affine<crate::Parameters>;
pub type G2Projective = bls12::G2Projective<crate::Parameters>;
@ -44,12 +41,7 @@ impl SWModelParameters for Parameters {
/// COFACTOR_INV = COFACTOR^{-1} mod r
/// 26652489039290660355457965112010883481355318854675681319708643586776743290055
#[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
6746407649509787816,
1304054119431494378,
2461312685643913071,
5956596749362435284,
]));
const COFACTOR_INV: Fr = field_new!(Fr, "26652489039290660355457965112010883481355318854675681319708643586776743290055");
/// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -67,47 +59,19 @@ pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_
/// G2_GENERATOR_X_C0 =
/// 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
#[rustfmt::skip]
pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger384([
0xf5f28fa202940a10,
0xb3f5fb2687b4961a,
0xa1a893b53e2ae580,
0x9894999d1a3caee9,
0x6f67b7631863366b,
0x58191924350bcd7,
]));
pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160");
/// G2_GENERATOR_X_C1 =
/// 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758
#[rustfmt::skip]
pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger384([
0xa5a9c0759e23f606,
0xaaa0c59dbccd60c3,
0x3bb17e18e2867806,
0x1b1ab6cc8541b367,
0xc2b6ed0ef2158547,
0x11922a097360edf3,
]));
pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758");
/// G2_GENERATOR_Y_C0 =
/// 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905
#[rustfmt::skip]
pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger384([
0x4c730af860494c4a,
0x597cfa1f5e369c5a,
0xe7e6856caa0a635a,
0xbbefb5e96e0d495f,
0x7d3a975f0ef25a2,
0x83fd8e7e80dae5,
]));
pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905");
/// G2_GENERATOR_Y_C1 =
/// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582
#[rustfmt::skip]
pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger384([
0xadc0fc92df64b05d,
0x18aa270a2b1461dc,
0x86adac6a3be4eba0,
0x79495c4ec93da33a,
0xe7175850a43ccaed,
0xb2bc2a163de1bf2,
]));
pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");

+ 2
- 2
bls12_381/src/fields/fq.rs
View File

@ -111,5 +111,5 @@ impl FpParameters for FqParameters {
]);
}
pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0]));
pub const FQ_ONE: Fq = field_new!(Fq, "1");
pub const FQ_ZERO: Fq = field_new!(Fq, "0");

+ 39
- 156
bls12_381/src/fields/fq12.rs
View File

@ -1,5 +1,5 @@
use crate::*;
use ark_ff::{biginteger::BigInteger384, field_new, fields::*};
use ark_ff::{field_new, fields::*};
pub type Fq12 = Fp12<Fq12Parameters>;
@ -11,183 +11,66 @@ impl Fp12Parameters for Fq12Parameters {
const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
#[rustfmt::skip]
const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
// Fq2(u + 1)**(((q^0) - 1) / 6)
FQ2_ONE,
// Fq2(u + 1)**(((q^1) - 1) / 6)
// Fp2::NONRESIDUE^(((q^0) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x7089552b319d465,
0xc6695f92b50a8313,
0x97e83cccd117228f,
0xa35baecab2dc29ee,
0x1ce393ea5daace4d,
0x8f2220fb0fb66eb,
])),
field_new!(Fq, BigInteger384([
0xb2f66aad4ce5d646,
0x5842a06bfc497cec,
0xcf4895d42599d394,
0xc11b9cba40a8e8d0,
0x2e3813cbe5a0de89,
0x110eefda88847faf,
])),
field_new!(Fq, "1"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^2) - 1) / 6)
// Fp2::NONRESIDUE^(((q^1) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0xecfb361b798dba3a,
0xc100ddb891865a2c,
0xec08ff1232bda8e,
0xd5c13cc6f1ca4721,
0x47222a47bf7b5c04,
0x110f184e51c5f59,
])),
FQ_ZERO,
field_new!(Fq, "3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
field_new!(Fq, "151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
),
// Fq2(u + 1)**(((q^3) - 1) / 6)
// Fp2::NONRESIDUE^(((q^2) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x3e2f585da55c9ad1,
0x4294213d86c18183,
0x382844c88b623732,
0x92ad2afd19103e18,
0x1d794e4fac7cf0b9,
0xbd592fc7d825ec8,
])),
field_new!(Fq, BigInteger384([
0x7bcfa7a25aa30fda,
0xdc17dec12a927e7c,
0x2f088dd86b4ebef1,
0xd1ca2087da74d4a7,
0x2da2596696cebc1d,
0xe2b7eedbbfd87d2,
])),
field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^4) - 1) / 6)
// Fp2::NONRESIDUE^(((q^3) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x30f1361b798a64e8,
0xf3b8ddab7ece5a2a,
0x16a8ca3ac61577f7,
0xc26a2ff874fd029b,
0x3636b76660701c6e,
0x51ba4ab241b6160,
])),
FQ_ZERO,
field_new!(Fq, "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
field_new!(Fq, "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
),
// Fq2(u + 1)**(((q^5) - 1) / 6)
// Fp2::NONRESIDUE^(((q^4) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x3726c30af242c66c,
0x7c2ac1aad1b6fe70,
0xa04007fbba4b14a2,
0xef517c3266341429,
0x95ba654ed2226b,
0x2e370eccc86f7dd,
])),
field_new!(Fq, BigInteger384([
0x82d83cf50dbce43f,
0xa2813e53df9d018f,
0xc6f0caa53c65e181,
0x7525cf528d50fe95,
0x4a85ed50f4798a6b,
0x171da0fd6cf8eebd,
])),
field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^6) - 1) / 6)
// Fp2::NONRESIDUE^(((q^5) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x43f5fffffffcaaae,
0x32b7fff2ed47fffd,
0x7e83a49a2e99d69,
0xeca8f3318332bb7a,
0xef148d1ea0f4c069,
0x40ab3263eff0206,
])),
FQ_ZERO,
field_new!(Fq, "3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
field_new!(Fq, "877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
),
// Fq2(u + 1)**(((q^7) - 1) / 6)
// Fp2::NONRESIDUE^(((q^6) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0xb2f66aad4ce5d646,
0x5842a06bfc497cec,
0xcf4895d42599d394,
0xc11b9cba40a8e8d0,
0x2e3813cbe5a0de89,
0x110eefda88847faf,
])),
field_new!(Fq, BigInteger384([
0x7089552b319d465,
0xc6695f92b50a8313,
0x97e83cccd117228f,
0xa35baecab2dc29ee,
0x1ce393ea5daace4d,
0x8f2220fb0fb66eb,
])),
field_new!(Fq, "-1"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^8) - 1) / 6)
// Fp2::NONRESIDUE^(((q^7) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0xcd03c9e48671f071,
0x5dab22461fcda5d2,
0x587042afd3851b95,
0x8eb60ebe01bacb9e,
0x3f97d6e83d050d2,
0x18f0206554638741,
])),
FQ_ZERO,
field_new!(Fq, "151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
field_new!(Fq, "3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
),
// Fq2(u + 1)**(((q^9) - 1) / 6)
// Fp2::NONRESIDUE^(((q^8) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x7bcfa7a25aa30fda,
0xdc17dec12a927e7c,
0x2f088dd86b4ebef1,
0xd1ca2087da74d4a7,
0x2da2596696cebc1d,
0xe2b7eedbbfd87d2,
])),
field_new!(Fq, BigInteger384([
0x3e2f585da55c9ad1,
0x4294213d86c18183,
0x382844c88b623732,
0x92ad2afd19103e18,
0x1d794e4fac7cf0b9,
0xbd592fc7d825ec8,
])),
field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^10) - 1) / 6)
// Fp2::NONRESIDUE^(((q^9) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x890dc9e4867545c3,
0x2af322533285a5d5,
0x50880866309b7e2c,
0xa20d1b8c7e881024,
0x14e4f04fe2db9068,
0x14e56d3f1564853a,
])),
FQ_ZERO,
field_new!(Fq, "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
field_new!(Fq, "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
),
// Fq2(u + 1)**(((q^11) - 1) / 6)
// Fp2::NONRESIDUE^(((q^10) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x82d83cf50dbce43f,
0xa2813e53df9d018f,
0xc6f0caa53c65e181,
0x7525cf528d50fe95,
0x4a85ed50f4798a6b,
0x171da0fd6cf8eebd,
])),
field_new!(Fq, BigInteger384([
0x3726c30af242c66c,
0x7c2ac1aad1b6fe70,
0xa04007fbba4b14a2,
0xef517c3266341429,
0x95ba654ed2226b,
0x2e370eccc86f7dd,
])),
field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
field_new!(Fq, "0"),
),
// Fp2::NONRESIDUE^(((q^11) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, "877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
field_new!(Fq, "3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
),
];
}

+ 5
- 43
bls12_381/src/fields/fq2.rs
View File

@ -1,5 +1,5 @@
use crate::*;
use ark_ff::{biginteger::BigInteger384 as BigInteger, field_new, fields::*};
use ark_ff::{field_new, fields::*};
pub type Fq2 = Fp2<Fq2Parameters>;
@ -10,57 +10,19 @@ impl Fp2Parameters for Fq2Parameters {
/// NONRESIDUE = -1
#[rustfmt::skip]
const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
0x43f5fffffffcaaae,
0x32b7fff2ed47fffd,
0x7e83a49a2e99d69,
0xeca8f3318332bb7a,
0xef148d1ea0f4c069,
0x40ab3263eff0206,
]));
const NONRESIDUE: Fq = field_new!(Fq, "-1");
/// QUADRATIC_NONRESIDUE = (U + 1)
#[rustfmt::skip]
const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
field_new!(Fq, BigInteger([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
field_new!(Fq, BigInteger([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
);
const QUADRATIC_NONRESIDUE: (Fq, Fq) = (FQ_ONE, FQ_ONE);
/// Coefficients for the Frobenius automorphism.
#[rustfmt::skip]
const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
// Fq(-1)**(((q^0) - 1) / 2)
field_new!(Fq, BigInteger([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
field_new!(Fq, "1"),
// Fq(-1)**(((q^1) - 1) / 2)
field_new!(Fq, BigInteger([
0x43f5fffffffcaaae,
0x32b7fff2ed47fffd,
0x7e83a49a2e99d69,
0xeca8f3318332bb7a,
0xef148d1ea0f4c069,
0x40ab3263eff0206,
])),
field_new!(Fq, "-1"),
];
#[inline(always)]

+ 40
- 138
bls12_381/src/fields/fq6.rs
View File

@ -1,5 +1,5 @@
use crate::*;
use ark_ff::{biginteger::BigInteger384, field_new, fields::*};
use ark_ff::{field_new, fields::*};
pub type Fq6 = Fp6<Fq6Parameters>;
@ -12,173 +12,75 @@ impl Fp6Parameters for Fq6Parameters {
/// NONRESIDUE = (U + 1)
#[rustfmt::skip]
const NONRESIDUE: Fq2 = field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
field_new!(Fq, BigInteger384([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
field_new!(Fq, "1"),
field_new!(Fq, "1"),
);
#[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
// Fq2(u + 1)**(((q^0) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
// Fp2::NONRESIDUE^(((q^0) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, "1"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^1) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, BigInteger384([
0xcd03c9e48671f071,
0x5dab22461fcda5d2,
0x587042afd3851b95,
0x8eb60ebe01bacb9e,
0x3f97d6e83d050d2,
0x18f0206554638741,
])),
// Fp2::NONRESIDUE^(((q^1) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, "0"),
field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
),
// Fq2(u + 1)**(((q^2) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x30f1361b798a64e8,
0xf3b8ddab7ece5a2a,
0x16a8ca3ac61577f7,
0xc26a2ff874fd029b,
0x3636b76660701c6e,
0x51ba4ab241b6160,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
// Fp2::NONRESIDUE^(((q^2) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^3) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, BigInteger384([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
// Fp2::NONRESIDUE^(((q^3) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, "0"),
field_new!(Fq, "1"),
),
// Fq2(u + 1)**(((q^4) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0xcd03c9e48671f071,
0x5dab22461fcda5d2,
0x587042afd3851b95,
0x8eb60ebe01bacb9e,
0x3f97d6e83d050d2,
0x18f0206554638741,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
// Fp2::NONRESIDUE^(((q^4) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((q^5) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, BigInteger384([
0x30f1361b798a64e8,
0xf3b8ddab7ece5a2a,
0x16a8ca3ac61577f7,
0xc26a2ff874fd029b,
0x3636b76660701c6e,
0x51ba4ab241b6160,
])),
// Fp2::NONRESIDUE^(((q^5) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, "0"),
field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
),
];
];
#[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
// Fq2(u + 1)**(((2q^0) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x760900000002fffd,
0xebf4000bc40c0002,
0x5f48985753c758ba,
0x77ce585370525745,
0x5c071a97a256ec6d,
0x15f65ec3fa80e493,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, "1"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((2q^1) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x890dc9e4867545c3,
0x2af322533285a5d5,
0x50880866309b7e2c,
0xa20d1b8c7e881024,
0x14e4f04fe2db9068,
0x14e56d3f1564853a,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((2q^2) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0xcd03c9e48671f071,
0x5dab22461fcda5d2,
0x587042afd3851b95,
0x8eb60ebe01bacb9e,
0x3f97d6e83d050d2,
0x18f0206554638741,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((2q^3) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x43f5fffffffcaaae,
0x32b7fff2ed47fffd,
0x7e83a49a2e99d69,
0xeca8f3318332bb7a,
0xef148d1ea0f4c069,
0x40ab3263eff0206,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, "-1"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((2q^4) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0x30f1361b798a64e8,
0xf3b8ddab7ece5a2a,
0x16a8ca3ac61577f7,
0xc26a2ff874fd029b,
0x3636b76660701c6e,
0x51ba4ab241b6160,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
field_new!(Fq, "0"),
),
// Fq2(u + 1)**(((2q^5) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger384([
0xecfb361b798dba3a,
0xc100ddb891865a2c,
0xec08ff1232bda8e,
0xd5c13cc6f1ca4721,
0x47222a47bf7b5c04,
0x110f184e51c5f59,
])),
field_new!(Fq, BigInteger384([0x0, 0x0, 0x0, 0x0, 0x0, 0x0])),
field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
field_new!(Fq, "0"),
),
];

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