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Update BN254

fq2_neg_nonresidue
Pratyush Mishra 3 years ago
parent
b0565ad0c5
commit
31664a0e2e
7 changed files with 108 additions and 413 deletions
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  1. +8
    -34
      bn254/src/curves/g1.rs
  2. +10
    -48
      bn254/src/curves/g2.rs
  3. +6
    -37
      bn254/src/curves/mod.rs
  4. +2
    -2
      bn254/src/fields/fq.rs
  5. +38
    -120
      bn254/src/fields/fq12.rs
  6. +6
    -31
      bn254/src/fields/fq2.rs
  7. +38
    -141
      bn254/src/fields/fq6.rs

+ 8
- 34
bn254/src/curves/g1.rs
View File

@ -1,5 +1,5 @@
use ark_ec::models::{ModelParameters, SWModelParameters}; use ark_ec::models::{ModelParameters, SWModelParameters};
use ark_ff::{biginteger::BigInteger256, field_new, Zero};
use ark_ff::{field_new, Zero};
use crate::{Fq, Fr}; use crate::{Fq, Fr};
@ -13,28 +13,16 @@ impl ModelParameters for Parameters {
impl SWModelParameters for Parameters { impl SWModelParameters for Parameters {
/// COEFF_A = 0 /// COEFF_A = 0
const COEFF_A: Fq = field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0]));
const COEFF_A: Fq = field_new!(Fq, "0");
/// COEFF_B = 3 /// COEFF_B = 3
#[rustfmt::skip]
const COEFF_B: Fq = field_new!(Fq, BigInteger256([
0x7a17caa950ad28d7,
0x1f6ac17ae15521b9,
0x334bea4e696bd284,
0x2a1f6744ce179d8e,
]));
const COEFF_B: Fq = field_new!(Fq, "3");
/// COFACTOR = 1 /// COFACTOR = 1
const COFACTOR: &'static [u64] = &[0x1]; const COFACTOR: &'static [u64] = &[0x1];
/// COFACTOR_INV = COFACTOR^{-1} mod r = 1 /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
#[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
0xac96341c4ffffffb,
0x36fc76959f60cd29,
0x666ea36f7879462e,
0xe0a77c19a07df2f,
]));
const COFACTOR_INV: Fr = field_new!(Fr, "1");
/// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y) /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -46,22 +34,8 @@ impl SWModelParameters for Parameters {
} }
} }
/// G1_GENERATOR_X =
/// 1
#[rustfmt::skip]
pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger256([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0x0e0a77c19a07df2f,
]));
/// G1_GENERATOR_X = 1
pub const G1_GENERATOR_X: Fq = field_new!(Fq, "1");
/// G1_GENERATOR_Y =
/// 2
#[rustfmt::skip]
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger256([
0xa6ba871b8b1e1b3a,
0x14f1d651eb8e167b,
0xccdd46def0f28c58,
0x1c14ef83340fbe5e,
]));
/// G1_GENERATOR_Y = 2
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "2");

+ 10
- 48
bn254/src/curves/g2.rs
View File

@ -1,7 +1,7 @@
use ark_ec::models::{ModelParameters, SWModelParameters}; use ark_ec::models::{ModelParameters, SWModelParameters};
use ark_ff::{biginteger::BigInteger256, field_new, Zero};
use ark_ff::{field_new, Zero};
use crate::{g1, Fq, Fq2, Fr};
use crate::{Fq, Fq2, Fr};
#[derive(Clone, Default, PartialEq, Eq)] #[derive(Clone, Default, PartialEq, Eq)]
pub struct Parameters; pub struct Parameters;
@ -14,27 +14,14 @@ impl ModelParameters for Parameters {
impl SWModelParameters for Parameters { impl SWModelParameters for Parameters {
/// COEFF_A = [0, 0] /// COEFF_A = [0, 0]
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_A: Fq2 = field_new!(Fq2,
g1::Parameters::COEFF_A,
g1::Parameters::COEFF_A,
);
const COEFF_A: Fq2 = field_new!(Fq2, field_new!(Fq, "0"), field_new!(Fq, "0"));
/// COEFF_B = 3/(u+9) /// COEFF_B = 3/(u+9)
/// = (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690) /// = (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_B: Fq2 = field_new!(Fq2, const COEFF_B: Fq2 = field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x3bf938e377b802a8,
0x020b1b273633535d,
0x26b7edf049755260,
0x2514c6324384a86d,
])),
field_new!(Fq, BigInteger256([
0x38e7ecccd1dcff67,
0x65f0b37d93ce0d3e,
0xd749d0dd22ac00aa,
0x0141b9ce4a688d4d,
])),
field_new!(Fq, "19485874751759354771024239261021720505790618469301721065564631296452457478373"),
field_new!(Fq, "266929791119991161246907387137283842545076965332900288569378510910307636690"),
); );
/// COFACTOR = (36 * X^4) + (36 * X^3) + (30 * X^2) + 6*X + 1 /// COFACTOR = (36 * X^4) + (36 * X^3) + (30 * X^2) + 6*X + 1
@ -49,12 +36,7 @@ impl SWModelParameters for Parameters {
/// COFACTOR_INV = COFACTOR^{-1} mod r /// COFACTOR_INV = COFACTOR^{-1} mod r
#[rustfmt::skip] #[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger256([
0x7fff17d53ff2895e,
0xd0617390cf7919e5,
0xb9af426b22d0eb61,
0x270485e31bd72a4d,
]));
const COFACTOR_INV: Fr = field_new!(Fr, "10944121435919637613327163357776759465618812564592884533313067514031822496649");
/// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y) /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -74,39 +56,19 @@ pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_
/// G2_GENERATOR_X_C0 = /// G2_GENERATOR_X_C0 =
/// 10857046999023057135944570762232829481370756359578518086990519993285655852781 /// 10857046999023057135944570762232829481370756359578518086990519993285655852781
#[rustfmt::skip] #[rustfmt::skip]
pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger256([
0x8e83b5d102bc2026,
0xdceb1935497b0172,
0xfbb8264797811adf,
0x19573841af96503b,
]));
pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "10857046999023057135944570762232829481370756359578518086990519993285655852781");
/// G2_GENERATOR_X_C1 = /// G2_GENERATOR_X_C1 =
/// 11559732032986387107991004021392285783925812861821192530917403151452391805634 /// 11559732032986387107991004021392285783925812861821192530917403151452391805634
#[rustfmt::skip] #[rustfmt::skip]
pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger256([
0xafb4737da84c6140,
0x6043dd5a5802d8c4,
0x09e950fc52a02f86,
0x14fef0833aea7b6b,
]));
pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "11559732032986387107991004021392285783925812861821192530917403151452391805634");
/// G2_GENERATOR_Y_C0 = /// G2_GENERATOR_Y_C0 =
/// 8495653923123431417604973247489272438418190587263600148770280649306958101930 /// 8495653923123431417604973247489272438418190587263600148770280649306958101930
#[rustfmt::skip] #[rustfmt::skip]
pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger256([
0x619dfa9d886be9f6,
0xfe7fd297f59e9b78,
0xff9e1a62231b7dfe,
0x28fd7eebae9e4206,
]));
pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "8495653923123431417604973247489272438418190587263600148770280649306958101930");
/// G2_GENERATOR_Y_C1 = /// G2_GENERATOR_Y_C1 =
/// 4082367875863433681332203403145435568316851327593401208105741076214120093531 /// 4082367875863433681332203403145435568316851327593401208105741076214120093531
#[rustfmt::skip] #[rustfmt::skip]
pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger256([
0x64095b56c71856ee,
0xdc57f922327d3cbb,
0x55f935be33351076,
0x0da4a0e693fd6482,
]));
pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "4082367875863433681332203403145435568316851327593401208105741076214120093531");

+ 6
- 37
bn254/src/curves/mod.rs
View File

@ -3,7 +3,7 @@ use ark_ec::{
bn, bn,
bn::{Bn, BnParameters, TwistType}, bn::{Bn, BnParameters, TwistType},
}; };
use ark_ff::{biginteger::BigInteger256, field_new};
use ark_ff::field_new;
pub mod g1; pub mod g1;
pub mod g2; pub mod g2;
@ -23,47 +23,16 @@ impl BnParameters for Parameters {
]; ];
/// `ate_loop_count` is positive. /// `ate_loop_count` is positive.
const ATE_LOOP_COUNT_IS_NEGATIVE: bool = false; const ATE_LOOP_COUNT_IS_NEGATIVE: bool = false;
const TWIST_MUL_BY_Q_X: Fq2 = field_new!( const TWIST_MUL_BY_Q_X: Fq2 = field_new!(
Fq2, Fq2,
field_new!(
Fq,
BigInteger256([
0xb5773b104563ab30,
0x347f91c8a9aa6454,
0x7a007127242e0991,
0x1956bcd8118214ec,
])
),
field_new!(
Fq,
BigInteger256([
0x6e849f1ea0aa4757,
0xaa1c7b6d89f89141,
0xb6e713cdfae0ca3a,
0x26694fbb4e82ebc3,
])
),
field_new!(Fq, "21575463638280843010398324269430826099269044274347216827212613867836435027261"),
field_new!(Fq, "10307601595873709700152284273816112264069230130616436755625194854815875713954"),
); );
const TWIST_MUL_BY_Q_Y: Fq2 = field_new!( const TWIST_MUL_BY_Q_Y: Fq2 = field_new!(
Fq2, Fq2,
field_new!(
Fq,
BigInteger256([
0xe4bbdd0c2936b629,
0xbb30f162e133bacb,
0x31a9d1b6f9645366,
0x253570bea500f8dd,
])
),
field_new!(
Fq,
BigInteger256([
0xa1d77ce45ffe77c7,
0x07affd117826d1db,
0x6d16bd27bb7edc6b,
0x2c87200285defecc,
])
),
field_new!(Fq, "2821565182194536844548159561693502659359617185244120367078079554186484126554"),
field_new!(Fq, "3505843767911556378687030309984248845540243509899259641013678093033130930403"),
); );
const TWIST_TYPE: TwistType = TwistType::D; const TWIST_TYPE: TwistType = TwistType::D;
type Fp = Fq; type Fp = Fq;

+ 2
- 2
bn254/src/fields/fq.rs
View File

@ -92,5 +92,5 @@ 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]));
pub const FQ_ONE: Fq = field_new!(Fq, "1");
pub const FQ_ZERO: Fq = field_new!(Fq, "0");

+ 38
- 120
bn254/src/fields/fq12.rs
View File

@ -1,5 +1,5 @@
use super::*; use super::*;
use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
use ark_ff::{field_new, fields::*};
pub type Fq12 = Fp12<Fq12Parameters>; pub type Fq12 = Fp12<Fq12Parameters>;
@ -14,146 +14,64 @@ impl Fp12Parameters for Fq12Parameters {
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[ const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
// Fp2::NONRESIDUE^(((q^0) - 1) / 6) // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
FQ2_ONE,
field_new!(Fq2,
field_new!(Fq, "1"),
field_new!(Fq, "0"),
),
// Fp2::NONRESIDUE^(((q^1) - 1) / 6) // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xaf9ba69633144907,
0xca6b1d7387afb78a,
0x11bded5ef08a2087,
0x02f34d751a1f3a7c,
])),
field_new!(Fq, BigInteger256([
0xa222ae234c492d72,
0xd00f02a4565de15b,
0xdc2ff3a253dfc926,
0x10a75716b3899551,
])),
field_new!(Fq2,
field_new!(Fq, "8376118865763821496583973867626364092589906065868298776909617916018768340080"),
field_new!(Fq, "16469823323077808223889137241176536799009286646108169935659301613961712198316"),
), ),
// Fp2::NONRESIDUE^(((q^2) - 1) / 6) // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xca8d800500fa1bf2,
0xf0c5d61468b39769,
0x0e201271ad0d4418,
0x04290f65bad856e6,
])),
FQ_ZERO,
field_new!(Fq2,
field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556617"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^3) - 1) / 6) // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x365316184e46d97d,
0x0af7129ed4c96d9f,
0x659da72fca1009b5,
0x08116d8983a20d23,
])),
field_new!(Fq, BigInteger256([
0xb1df4af7c39c1939,
0x3d9f02878a73bf7f,
0x9b2220928caf0ae0,
0x26684515eff054a6,
])),
field_new!(Fq2,
field_new!(Fq, "11697423496358154304825782922584725312912383441159505038794027105778954184319"),
field_new!(Fq, "303847389135065887422783454877609941456349188919719272345083954437860409601"),
), ),
// Fp2::NONRESIDUE^(((q^4) - 1) / 6) // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
FQ_ZERO,
field_new!(Fq2,
field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^5) - 1) / 6) // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x86b76f821b329076,
0x408bf52b4d19b614,
0x53dfb9d0d985e92d,
0x051e20146982d2a7,
])),
field_new!(Fq, BigInteger256([
0x0fbc9cd47752ebc7,
0x6d8fffe33415de24,
0xbef22cf038cf41b9,
0x15c0edff3c66bf54,
])),
field_new!(Fq2,
field_new!(Fq, "3321304630594332808241809054958361220322477375291206261884409189760185844239"),
field_new!(Fq, "5722266937896532885780051958958348231143373700109372999374820235121374419868"),
), ),
// Fp2::NONRESIDUE^(((q^6) - 1) / 6) // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x68c3488912edefaa,
0x8d087f6872aabf4f,
0x51e1a24709081231,
0x2259d6b14729c0fa,
])),
FQ_ZERO,
field_new!(Fq2,
field_new!(Fq, "-1"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^7) - 1) / 6) // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x8c84e580a568b440,
0xcd164d1de0c21302,
0xa692585790f737d5,
0x2d7100fdc71265ad,
])),
field_new!(Fq, BigInteger256([
0x99fdddf38c33cfd5,
0xc77267ed1213e931,
0xdc2052142da18f36,
0x1fbcf75c2da80ad7,
])),
field_new!(Fq2,
field_new!(Fq, "13512124006075453725662431877630910996106405091429524885779419978626457868503"),
field_new!(Fq, "5418419548761466998357268504080738289687024511189653727029736280683514010267"),
), ),
// Fp2::NONRESIDUE^(((q^8) - 1) / 6) // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
FQ_ZERO,
field_new!(Fq2,
field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^9) - 1) / 6) // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x05cd75fe8a3623ca,
0x8c8a57f293a85cee,
0x52b29e86b7714ea8,
0x2852e0e95d8f9306,
])),
field_new!(Fq, BigInteger256([
0x8a41411f14e0e40e,
0x59e26809ddfe0b0d,
0x1d2e2523f4d24d7d,
0x09fc095cf1414b83,
])),
field_new!(Fq2,
field_new!(Fq, "10190819375481120917420622822672549775783927716138318623895010788866272024264"),
field_new!(Fq, "21584395482704209334823622290379665147239961968378104390343953940207365798982"),
), ),
// Fp2::NONRESIDUE^(((q^10) - 1) / 6) // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x08cfc388c494f1ab,
0x19b315148d1373d4,
0x584e90fdcb6c0213,
0x09e1685bdf2f8849,
])),
FQ_ZERO,
field_new!(Fq2,
field_new!(Fq, "2203960485148121921418603742825762020974279258880205651967"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^11) - 1) / 6) // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xb5691c94bd4a6cd1,
0x56f575661b581478,
0x64708be5a7fb6f30,
0x2b462e5e77aecd82,
])),
field_new!(Fq, BigInteger256([
0x2c63ef42612a1180,
0x29f16aae345bec69,
0xf95e18c648b216a4,
0x1aa36073a4cae0d4,
])),
field_new!(Fq2,
field_new!(Fq, "18566938241244942414004596690298913868373833782006617400804628704885040364344"),
field_new!(Fq, "16165975933942742336466353786298926857552937457188450663314217659523851788715"),
), ),
]; ];
} }

+ 6
- 31
bn254/src/fields/fq2.rs
View File

@ -1,5 +1,5 @@
use super::*; use super::*;
use ark_ff::{biginteger::BigInteger256 as BigInteger, field_new, fields::*};
use ark_ff::{field_new, fields::*};
pub type Fq2 = Fp2<Fq2Parameters>; pub type Fq2 = Fp2<Fq2Parameters>;
@ -10,47 +10,22 @@ impl Fp2Parameters for Fq2Parameters {
/// NONRESIDUE = -1 /// NONRESIDUE = -1
#[rustfmt::skip] #[rustfmt::skip]
const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
0x68c3488912edefaa,
0x8d087f6872aabf4f,
0x51e1a24709081231,
0x2259d6b14729c0fa,
]));
const NONRESIDUE: Fq = field_new!(Fq, "-1");
/// QUADRATIC_NONRESIDUE = U+2 /// QUADRATIC_NONRESIDUE = U+2
#[rustfmt::skip] #[rustfmt::skip]
const QUADRATIC_NONRESIDUE: (Fq, Fq) = ( const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
field_new!(Fq, BigInteger([
12014063508332092218u64,
1509222997478479483u64,
14762033076929465432u64,
2023505479389396574u64,
])),
field_new!(Fq, BigInteger([
202099033278250856u64,
8885205928937022213u64,
5545221690922665192u64,
39800542322357402u64,
])),
field_new!(Fq, "2"),
field_new!(Fq, "1"),
); );
/// Coefficients for the Frobenius automorphism. /// Coefficients for the Frobenius automorphism.
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[ const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
// NONRESIDUE**(((q^0) - 1) / 2) // NONRESIDUE**(((q^0) - 1) / 2)
field_new!(Fq, BigInteger([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0xe0a77c19a07df2f,
])),
field_new!(Fq, "1"),
// NONRESIDUE**(((q^1) - 1) / 2) // NONRESIDUE**(((q^1) - 1) / 2)
field_new!(Fq, BigInteger([
0x68c3488912edefaa,
0x8d087f6872aabf4f,
0x51e1a24709081231,
0x2259d6b14729c0fa,
])),
field_new!(Fq, "-1"),
]; ];
#[inline(always)] #[inline(always)]

+ 38
- 141
bn254/src/fields/fq6.rs
View File

@ -1,5 +1,5 @@
use super::*; use super::*;
use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
use ark_ff::{field_new, fields::*};
pub type Fq6 = Fp6<Fq6Parameters>; pub type Fq6 = Fp6<Fq6Parameters>;
@ -11,175 +11,72 @@ impl Fp6Parameters for Fq6Parameters {
/// NONRESIDUE = U+9 /// NONRESIDUE = U+9
#[rustfmt::skip] #[rustfmt::skip]
const NONRESIDUE: Fq2 = field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xf60647ce410d7ff7,
0x2f3d6f4dd31bd011,
0x2943337e3940c6d1,
0x1d9598e8a7e39857,
])),
field_new!(Fq, BigInteger256([
202099033278250856u64,
8885205928937022213u64,
5545221690922665192u64,
39800542322357402u64,
])),
);
const NONRESIDUE: Fq2 = field_new!(Fq2, field_new!(Fq, "9"), field_new!(Fq, "1"));
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[ const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
// Fp2::NONRESIDUE^(((q^0) - 1) / 3) // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0xe0a77c19a07df2f,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
field_new!(Fq2,
field_new!(Fq, "1"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^1) - 1) / 3) // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xb5773b104563ab30,
0x347f91c8a9aa6454,
0x7a007127242e0991,
0x1956bcd8118214ec,
])),
field_new!(Fq, BigInteger256([
0x6e849f1ea0aa4757,
0xaa1c7b6d89f89141,
0xb6e713cdfae0ca3a,
0x26694fbb4e82ebc3,
])),
field_new!(Fq2,
field_new!(Fq, "21575463638280843010398324269430826099269044274347216827212613867836435027261"),
field_new!(Fq, "10307601595873709700152284273816112264069230130616436755625194854815875713954"),
), ),
// Fp2::NONRESIDUE^(((q^2) - 1) / 3) // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
field_new!(Fq2,
field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^3) - 1) / 3) // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xc9af22f716ad6bad,
0xb311782a4aa662b2,
0x19eeaf64e248c7f4,
0x20273e77e3439f82,
])),
field_new!(Fq, BigInteger256([
0xacc02860f7ce93ac,
0x3933d5817ba76b4c,
0x69e6188b446c8467,
0xa46036d4417cc55,
])),
field_new!(Fq2,
field_new!(Fq, "3772000881919853776433695186713858239009073593817195771773381919316419345261"),
field_new!(Fq, "2236595495967245188281701248203181795121068902605861227855261137820944008926"),
), ),
// Fp2::NONRESIDUE^(((q^4) - 1) / 3) // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
field_new!(Fq2,
field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^(((q^5) - 1) / 3) // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xf91aba2654e8e3b1,
0x4771cb2fdc92ce12,
0xdcb16ae0fc8bdf35,
0x274aa195cd9d8be4,
])),
field_new!(Fq, BigInteger256([
0x5cfc50ae18811f8b,
0x4bb28433cb43988c,
0x4fd35f13c3b56219,
0x301949bd2fc8883a,
])),
field_new!(Fq2,
field_new!(Fq, "18429021223477853657660792034369865839114504446431234726392080002137598044644"),
field_new!(Fq, "9344045779998320333812420223237981029506012124075525679208581902008406485703"),
), ),
]; ];
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[ const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
// Fp2::NONRESIDUE^((2*(q^0) - 2) / 3) // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0xd35d438dc58f0d9d,
0x0a78eb28f5c70b3d,
0x666ea36f7879462c,
0xe0a77c19a07df2f,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
field_new!(Fq2,
field_new!(Fq, "1"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^((2*(q^1) - 2) / 3) // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x7361d77f843abe92,
0xa5bb2bd3273411fb,
0x9c941f314b3e2399,
0x15df9cddbb9fd3ec,
])),
field_new!(Fq, BigInteger256([
0x5dddfd154bd8c949,
0x62cb29a5a4445b60,
0x37bc870a0c7dd2b9,
0x24830a9d3171f0fd,
])),
field_new!(Fq2,
field_new!(Fq, "2581911344467009335267311115468803099551665605076196740867805258568234346338"),
field_new!(Fq, "19937756971775647987995932169929341994314640652964949448313374472400716661030"),
), ),
// Fp2::NONRESIDUE^((2*(q^2) - 2) / 3) // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x71930c11d782e155,
0xa6bb947cffbe3323,
0xaa303344d4741444,
0x2c3b3f0d26594943,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
field_new!(Fq2,
field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^((2*(q^3) - 2) / 3) // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x448a93a57b6762df,
0xbfd62df528fdeadf,
0xd858f5d00e9bd47a,
0x6b03d4d3476ec58,
])),
field_new!(Fq, BigInteger256([
0x2b19daf4bcc936d1,
0xa1a54e7a56f4299f,
0xb533eee05adeaef1,
0x170c812b84dda0b2,
])),
field_new!(Fq2,
field_new!(Fq, "5324479202449903542726783395506214481928257762400643279780343368557297135718"),
field_new!(Fq, "16208900380737693084919495127334387981393726419856888799917914180988844123039"),
), ),
// Fp2::NONRESIDUE^((2*(q^4) - 2) / 3) // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x3350c88e13e80b9c,
0x7dce557cdb5e56b9,
0x6001b4b8b615564a,
0x2682e617020217e0,
])),
field_new!(Fq, BigInteger256([0x0, 0x0, 0x0, 0x0])),
field_new!(Fq2,
field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
field_new!(Fq, "0"),
), ),
// Fp2::NONRESIDUE^((2*(q^5) - 2) / 3) // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
field_new!(Fq2,
field_new!(Fq, BigInteger256([
0x843420f1d8dadbd6,
0x31f010c9183fcdb2,
0x436330b527a76049,
0x13d47447f11adfe4,
])),
field_new!(Fq, BigInteger256([
0xef494023a857fa74,
0x2a925d02d5ab101a,
0x83b015829ba62f10,
0x2539111d0c13aea3,
])),
field_new!(Fq2,
field_new!(Fq, "13981852324922362344252311234282257507216387789820983642040889267519694726527"),
field_new!(Fq, "7629828391165209371577384193250820201684255241773809077146787135900891633097"),
), ),
]; ];

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