Update BN254

2026-01-09 23:41:30 +01:00 · 2020-11-29 14:01:25 -08:00
parent b0565ad0c5
commit 31664a0e2e
7 changed files with 108 additions and 413 deletions
--- a/bn254/src/curves/g1.rs
+++ b/bn254/src/curves/g1.rs
@@ -1,5 +1,5 @@
 use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{biginteger::BigInteger256, field_new, Zero};
+use ark_ff::{field_new, Zero};

 use crate::{Fq, Fr};

@@ -13,28 +13,16 @@ impl ModelParameters for Parameters {

 impl SWModelParameters for Parameters {
    /// 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
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, BigInteger256([
-        0x7a17caa950ad28d7,
-        0x1f6ac17ae15521b9,
-        0x334bea4e696bd284,
-        0x2a1f6744ce179d8e,
-    ]));
+    const COEFF_B: Fq = field_new!(Fq, "3");

    /// COFACTOR = 1
    const COFACTOR: &'static [u64] = &[0x1];

    /// 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)
    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");
--- a/bn254/src/curves/g2.rs
+++ b/bn254/src/curves/g2.rs
@@ -1,7 +1,7 @@
 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)]
 pub struct Parameters;
@@ -14,27 +14,14 @@ impl ModelParameters for Parameters {
 impl SWModelParameters for Parameters {
    /// COEFF_A = [0, 0]
    #[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)
    ///         = (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
    #[rustfmt::skip]
    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
@@ -49,12 +36,7 @@ impl SWModelParameters for Parameters {

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    #[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)
    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 =
 /// 10857046999023057135944570762232829481370756359578518086990519993285655852781
 #[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 =
 /// 11559732032986387107991004021392285783925812861821192530917403151452391805634
 #[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 =
 /// 8495653923123431417604973247489272438418190587263600148770280649306958101930
 #[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 =
 /// 4082367875863433681332203403145435568316851327593401208105741076214120093531
 #[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");
--- a/bn254/src/curves/mod.rs
+++ b/bn254/src/curves/mod.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    bn,
    bn::{Bn, BnParameters, TwistType},
 };
-use ark_ff::{biginteger::BigInteger256, field_new};
+use ark_ff::field_new;
 pub mod g1;
 pub mod g2;

@@ -23,47 +23,16 @@ impl BnParameters for Parameters {
    ];
    /// `ate_loop_count` is positive.
    const ATE_LOOP_COUNT_IS_NEGATIVE: bool = false;
+
    const TWIST_MUL_BY_Q_X: Fq2 = field_new!(
        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!(
        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;
    type Fp = Fq;
--- a/bn254/src/fields/fq.rs
+++ b/bn254/src/fields/fq.rs
@@ -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");
--- a/bn254/src/fields/fq12.rs
+++ b/bn254/src/fields/fq12.rs
@@ -1,5 +1,5 @@
 use super::*;
-use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
+use ark_ff::{field_new, fields::*};

 pub type Fq12 = Fp12<Fq12Parameters>;

@@ -14,146 +14,64 @@ impl Fp12Parameters for Fq12Parameters {
    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
        // 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)
-        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)
-        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)
-        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)
-        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)
-        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)
-        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)
-        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)
-        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)
-        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)
-        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)
-        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"),
        ),
    ];
 }
--- a/bn254/src/fields/fq2.rs
+++ b/bn254/src/fields/fq2.rs
@@ -1,5 +1,5 @@
 use super::*;
-use ark_ff::{biginteger::BigInteger256 as BigInteger, field_new, fields::*};
+use ark_ff::{field_new, fields::*};

 pub type Fq2 = Fp2<Fq2Parameters>;

@@ -10,47 +10,22 @@ impl Fp2Parameters for Fq2Parameters {

    /// NONRESIDUE = -1
    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
-        0x68c3488912edefaa,
-        0x8d087f6872aabf4f,
-        0x51e1a24709081231,
-        0x2259d6b14729c0fa,
-    ]));
+    const NONRESIDUE: Fq = field_new!(Fq, "-1");

    /// QUADRATIC_NONRESIDUE = U+2
    #[rustfmt::skip]
    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.
    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
        // NONRESIDUE**(((q^0) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0xd35d438dc58f0d9d,
-            0x0a78eb28f5c70b3d,
-            0x666ea36f7879462c,
-            0xe0a77c19a07df2f,
-        ])),
+        field_new!(Fq, "1"),
        // NONRESIDUE**(((q^1) - 1) / 2)
-        field_new!(Fq, BigInteger([
-            0x68c3488912edefaa,
-            0x8d087f6872aabf4f,
-            0x51e1a24709081231,
-            0x2259d6b14729c0fa,
-        ])),
+        field_new!(Fq, "-1"),
    ];

    #[inline(always)]
--- a/bn254/src/fields/fq6.rs
+++ b/bn254/src/fields/fq6.rs
@@ -1,5 +1,5 @@
 use super::*;
-use ark_ff::{biginteger::BigInteger256, field_new, fields::*};
+use ark_ff::{field_new, fields::*};

 pub type Fq6 = Fp6<Fq6Parameters>;

@@ -11,175 +11,72 @@ impl Fp6Parameters for Fq6Parameters {

    /// NONRESIDUE = U+9
    #[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]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
        // 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)
-        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)
-        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)
-        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)
-        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)
-        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]
    const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
        // 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)
-        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)
-        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)
-        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)
-        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)
-        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"),
        ),
    ];