Update BLS12-381

2026-01-09 15:31:34 +01:00 · 2020-11-28 14:58:25 -08:00
parent 0445d45c07
commit b0565ad0c5
6 changed files with 98 additions and 416 deletions
--- a/bls12_381/src/curves/g1.rs
+++ b/bls12_381/src/curves/g1.rs
@@ -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");
--- a/bls12_381/src/curves/g2.rs
+++ b/bls12_381/src/curves/g2.rs
@@ -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");
--- a/bls12_381/src/fields/fq.rs
+++ b/bls12_381/src/fields/fq.rs
@@ -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");
--- a/bls12_381/src/fields/fq12.rs
+++ b/bls12_381/src/fields/fq12.rs
@@ -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"),
        ),
    ];
 }
--- a/bls12_381/src/fields/fq2.rs
+++ b/bls12_381/src/fields/fq2.rs
@@ -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)]
--- a/bls12_381/src/fields/fq6.rs
+++ b/bls12_381/src/fields/fq6.rs
@@ -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>;

@@ -12,97 +12,41 @@ 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)
+        // Fp2::NONRESIDUE^(((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])),
+            field_new!(Fq, "1"),
+            field_new!(Fq, "0"),
        ),
-        // Fq2(u + 1)**(((q^1) - 1) / 3)
+        // Fp2::NONRESIDUE^(((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,
-            ])),
+            field_new!(Fq, "0"),
+            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
        ),
-        // Fq2(u + 1)**(((q^2) - 1) / 3)
+        // Fp2::NONRESIDUE^(((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])),
+            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            field_new!(Fq, "0"),
        ),
-        // Fq2(u + 1)**(((q^3) - 1) / 3)
+        // Fp2::NONRESIDUE^(((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,
-            ])),
+            field_new!(Fq, "0"),
+            field_new!(Fq, "1"),
        ),
-        // Fq2(u + 1)**(((q^4) - 1) / 3)
+        // Fp2::NONRESIDUE^(((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])),
+            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            field_new!(Fq, "0"),
        ),
-        // Fq2(u + 1)**(((q^5) - 1) / 3)
+        // Fp2::NONRESIDUE^(((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,
-            ])),
+            field_new!(Fq, "0"),
+            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
        ),
 ];

@@ -110,75 +54,33 @@ impl Fp6Parameters for Fq6Parameters {
    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"),
        ),
    ];