Initial commit

bw6_761/Cargo.toml

@@ -0,0 +1,29 @@
+[package]
+name = "ark-bw6-761"
+version = "0.1.0"
+authors = [ "arkworks contributors" ]
+description = "The BW6-761 pairing-friendly elliptic curve"
+homepage = "https://arworks.rs"
+repository = "https://github.com/arkworks/algebra"
+documentation = "https://docs.rs/ark-bw6-761/"
+keywords = ["cryptography", "finite fields", "elliptic curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
+license = "MIT/Apache-2.0"
+edition = "2018"
+
+[dependencies]
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-bls12-377 = { path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+
+[dev-dependencies]
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-curve-tests = { path = "../curve-tests", default-features = false }
+rand = { version = "0.7", default-features = false }
+rand_xorshift = "0.2"
+
+[features]
+default = []
+std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bls12-377/std" ]

bw6_761/src/curves/g1.rs

@@ -0,0 +1,113 @@
+use crate::{Fq, Fr};
+use ark_ec::{
+    models::{ModelParameters, SWModelParameters},
+    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+};
+use ark_ff::{
+    biginteger::{BigInteger384, BigInteger768},
+    field_new,
+};
+
+pub type G1Affine = GroupAffine<Parameters>;
+pub type G1Projective = GroupProjective<Parameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl ModelParameters for Parameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+}
+
+impl SWModelParameters for Parameters {
+    /// COEFF_A = 0
+    #[rustfmt::skip]
+
+    const COEFF_A: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
+
+    /// COEFF_B = -1
+    #[rustfmt::skip]
+    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
+        0xf29a000000007ab6,
+        0x8c391832e000739b,
+        0x77738a6b6870f959,
+        0xbe36179047832b03,
+        0x84f3089e56574722,
+        0xc5a3614ac0b1d984,
+        0x5c81153f4906e9fe,
+        0x4d28be3a9f55c815,
+        0xd72c1d6f77d5f5c5,
+        0x73a18e069ac04458,
+        0xf9dfaa846595555f,
+        0xd0f0a60a5be58c,
+    ]));
+
+    /// COFACTOR =
+    /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194876
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        0x3de580000000007c,
+        0x832ba4061000003b,
+        0xc61c554757551c0c,
+        0xc856a0853c9db94c,
+        0x2c77d5ac34cb12ef,
+        0xad1972339049ce76,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
+        489703175600125849,
+        3883341943836920852,
+        1678256062427438196,
+        5848789333018172718,
+        7127967896440782320,
+        71512347676739162,
+    ]));
+
+    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
+        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    #[inline(always)]
+    fn mul_by_a(_elem: &Self::BaseField) -> Self::BaseField {
+        use ark_ff::Zero;
+        Self::BaseField::zero()
+    }
+}
+
+/// G1_GENERATOR_X =
+/// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237
+#[rustfmt::skip]
+pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
+    0xd6e42d7614c2d770,
+    0x4bb886eddbc3fc21,
+    0x64648b044098b4d2,
+    0x1a585c895a422985,
+    0xf1a9ac17cf8685c9,
+    0x352785830727aea5,
+    0xddf8cb12306266fe,
+    0x6913b4bfbc9e949a,
+    0x3a4b78d67ba5f6ab,
+    0x0f481c06a8d02a04,
+    0x91d4e7365c43edac,
+    0xf4d17cd48beca5,
+]));
+
+/// G1_GENERATOR_Y =
+/// 2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099
+#[rustfmt::skip]
+pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
+    0x97e805c4bd16411f,
+    0x870d844e1ee6dd08,
+    0x1eba7a37cb9eab4d,
+    0xd544c4df10b9889a,
+    0x8fe37f21a33897be,
+    0xe9bf99a43a0885d2,
+    0xd7ee0c9e273de139,
+    0xaa6a9ec7a38dd791,
+    0x8f95d3fcf765da8e,
+    0x42326e7db7357c99,
+    0xe217e407e218695f,
+    0x9d1eb23b7cf684,
+]));

bw6_761/src/curves/g2.rs

@@ -0,0 +1,113 @@
+use crate::{Fq, Fr};
+use ark_ec::{
+    models::{ModelParameters, SWModelParameters},
+    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+};
+use ark_ff::{
+    biginteger::{BigInteger384, BigInteger768},
+    field_new,
+};
+
+pub type G2Affine = GroupAffine<Parameters>;
+pub type G2Projective = GroupProjective<Parameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl ModelParameters for Parameters {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+}
+
+impl SWModelParameters for Parameters {
+    /// COEFF_A = 0
+    #[rustfmt::skip]
+
+    const COEFF_A: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
+
+    /// COEFF_B = 4
+    #[rustfmt::skip]
+    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
+        0x136efffffffe16c9,
+        0x82cf5a6dcffe3319,
+        0x6458c05f1f0e0741,
+        0xd10ae605e52a4eda,
+        0x41ca591c0266e100,
+        0x7d0fd59c3626929f,
+        0x9967dc004d00c112,
+        0x1ccff9c033379af5,
+        0x9ad6ec10a23f63af,
+        0x5cec11251a72c235,
+        0x8d18b1ae789ba83e,
+        10403402007434220,
+    ]));
+
+    /// COFACTOR =
+    /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194869
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        0x3de5800000000075,
+        0x832ba4061000003b,
+        0xc61c554757551c0c,
+        0xc856a0853c9db94c,
+        0x2c77d5ac34cb12ef,
+        0xad1972339049ce76,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
+        14378295991815829998,
+        14586153992421458638,
+        9788477762582722914,
+        12654821707953664524,
+        15185631607604703397,
+        26723985783783076,
+    ]));
+
+    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
+        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    #[inline(always)]
+    fn mul_by_a(_elem: &Self::BaseField) -> Self::BaseField {
+        use ark_ff::Zero;
+        Self::BaseField::zero()
+    }
+}
+
+/// G2_GENERATOR_X =
+///  6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428
+#[rustfmt::skip]
+pub const G2_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
+    0x3d902a84cd9f4f78,
+    0x864e451b8a9c05dd,
+    0xc2b3c0d6646c5673,
+    0x17a7682def1ecb9d,
+    0xbe31a1e0fb768fe3,
+    0x4df125e09b92d1a6,
+    0x0943fce635b02ee9,
+    0xffc8e7ad0605e780,
+    0x8165c00a39341e95,
+    0x8ccc2ae90a0f094f,
+    0x73a8b8cc0ad09e0c,
+    0x11027e203edd9f4,
+]));
+
+/// G2_GENERATOR_Y =
+/// 562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
+    0x9a159be4e773f67c,
+    0x6b957244aa8f4e6b,
+    0xa27b70c9c945a38c,
+    0xacb6a09fda11d0ab,
+    0x3abbdaa9bb6b1291,
+    0xdbdf642af5694c36,
+    0xb6360bb9560b369f,
+    0xac0bd1e822b8d6da,
+    0xfa355d17afe6945f,
+    0x8d6a0fc1fbcad35e,
+    0x72a63c7874409840,
+    0x114976e5b0db280,
+]));

bw6_761/src/curves/mod.rs

@@ -0,0 +1,61 @@
+use crate::*;
+use ark_ec::{
+    bw6,
+    bw6::{BW6Parameters, TwistType, BW6},
+};
+use ark_ff::biginteger::BigInteger768 as BigInteger;
+
+pub mod g1;
+pub mod g2;
+
+#[cfg(test)]
+mod tests;
+
+#[derive(PartialEq, Eq)]
+pub struct Parameters;
+
+impl BW6Parameters for Parameters {
+    const X: BigInteger = BigInteger([
+        0x8508c00000000001,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+        0x0,
+    ]);
+    /// `x` is positive.
+    const X_IS_NEGATIVE: bool = false;
+    // X+1
+    const ATE_LOOP_COUNT_1: &'static [u64] = &[0x8508c00000000002];
+    const ATE_LOOP_COUNT_1_IS_NEGATIVE: bool = false;
+    // X^3-X^2-X
+    const ATE_LOOP_COUNT_2: &'static [i8] = &[
+        -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
+        0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0,
+        1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 1,
+        0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1,
+    ];
+    const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
+    const TWIST_TYPE: TwistType = TwistType::M;
+    type Fp = Fq;
+    type Fp3Params = Fq3Parameters;
+    type Fp6Params = Fq6Parameters;
+    type G1Parameters = g1::Parameters;
+    type G2Parameters = g2::Parameters;
+}
+
+pub type BW6_761 = BW6<Parameters>;
+
+pub type G1Affine = bw6::G1Affine<Parameters>;
+pub type G1Projective = bw6::G1Projective<Parameters>;
+pub type G2Affine = bw6::G2Affine<Parameters>;
+pub type G2Projective = bw6::G2Projective<Parameters>;

bw6_761/src/curves/tests.rs

@@ -0,0 +1,77 @@
+use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
+use ark_ff::{test_rng, Field, One, PrimeField};
+use rand::Rng;
+
+use crate::*;
+
+use ark_curve_tests::{curves::*, groups::*};
+
+#[test]
+fn test_g1_projective_curve() {
+    curve_tests::<G1Projective>();
+
+    sw_tests::<g1::Parameters>();
+}
+
+#[test]
+fn test_g1_projective_group() {
+    let mut rng = test_rng();
+    let a: G1Projective = rng.gen();
+    let b: G1Projective = rng.gen();
+    group_test(a, b);
+}
+
+#[test]
+fn test_g1_generator() {
+    let generator = G1Affine::prime_subgroup_generator();
+    assert!(generator.is_on_curve());
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_g2_projective_curve() {
+    curve_tests::<G2Projective>();
+
+    sw_tests::<g2::Parameters>();
+}
+
+#[test]
+fn test_g2_projective_group() {
+    let mut rng = test_rng();
+    let a: G2Projective = rng.gen();
+    let b: G2Projective = rng.gen();
+    group_test(a, b);
+}
+
+#[test]
+fn test_g2_generator() {
+    let generator = G2Affine::prime_subgroup_generator();
+    assert!(generator.is_on_curve());
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_bilinearity() {
+    let mut rng = test_rng();
+    let a: G1Projective = rng.gen();
+    let b: G2Projective = rng.gen();
+    let s: Fr = rng.gen();
+
+    let sa = a.mul(s);
+    let sb = b.mul(s);
+
+    let ans1 = BW6_761::pairing(sa, b);
+    let ans2 = BW6_761::pairing(a, sb);
+    let ans3 = BW6_761::pairing(a, b).pow(s.into_repr());
+
+    assert_eq!(ans1, ans2);
+    assert_eq!(ans2, ans3);
+
+    assert_ne!(ans1, Fq6::one());
+    assert_ne!(ans2, Fq6::one());
+    assert_ne!(ans3, Fq6::one());
+
+    assert_eq!(ans1.pow(Fr::characteristic()), Fq6::one());
+    assert_eq!(ans2.pow(Fr::characteristic()), Fq6::one());
+    assert_eq!(ans3.pow(Fr::characteristic()), Fq6::one());
+}

bw6_761/src/fields/fq.rs

@@ -0,0 +1,175 @@
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
+};
+
+pub type Fq = Fp768<FqParameters>;
+
+pub struct 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, 0, 0, 0, 0, 0, 0]));
+
+impl Fp768Parameters for FqParameters {}
+impl FftParameters for FqParameters {
+    type BigInt = BigInteger;
+
+    // The internal representation of this type is six 64-bit unsigned
+    // integers in little-endian order. Values are always in
+    // Montgomery form; i.e., Scalar(a) = aR mod p, with R=2^768.
+
+    // (MODULUS - 1) % 2^TWO_ADICITY == 0
+    const TWO_ADICITY: u32 = 1;
+
+    // least_quadratic_nonresidue(MODULUS) in Sage.
+    #[rustfmt::skip]
+    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
+        17481284903592032950u64,
+        10104133845767975835u64,
+        8607375506753517913u64,
+        13706168424391191299u64,
+        9580010308493592354u64,
+        14241333420363995524u64,
+        6665632285037357566u64,
+        5559902898979457045u64,
+        15504799981718861253u64,
+        8332096944629367896u64,
+        18005297320867222879u64,
+        58811391084848524u64,
+    ]);
+}
+impl FpParameters for FqParameters {
+    /// MODULUS = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
+    #[rustfmt::skip]
+    const MODULUS: BigInteger = BigInteger([
+       0xf49d00000000008b,
+       0xe6913e6870000082,
+       0x160cf8aeeaf0a437,
+       0x98a116c25667a8f8,
+       0x71dcd3dc73ebff2e,
+       0x8689c8ed12f9fd90,
+       0x03cebaff25b42304,
+       0x707ba638e584e919,
+       0x528275ef8087be41,
+       0xb926186a81d14688,
+       0xd187c94004faff3e,
+       0x122e824fb83ce0a
+    ]);
+
+    const MODULUS_BITS: u32 = 761;
+
+    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
+
+    // gap to 64-bit machine word
+    const REPR_SHAVE_BITS: u32 = 7;
+
+    // 2^768 % MODULUS
+    #[rustfmt::skip]
+    const R: BigInteger = BigInteger([
+        144959613005956565u64,
+        6509995272855063783u64,
+        11428286765660613342u64,
+        15738672438262922740u64,
+        17071399330169272331u64,
+        13899911246788437003u64,
+        12055474021000362245u64,
+        2545351818702954755u64,
+        8887388221587179644u64,
+        5009280847225881135u64,
+        15539704305423854047u64,
+        23071597697427581u64,
+    ]);
+
+    // R^2
+    #[rustfmt::skip]
+    const R2: BigInteger = BigInteger([
+        14305184132582319705u64,
+        8868935336694416555u64,
+        9196887162930508889u64,
+        15486798265448570248u64,
+        5402985275949444416u64,
+        10893197322525159598u64,
+        3204916688966998390u64,
+        12417238192559061753u64,
+        12426306557607898622u64,
+        1305582522441154384u64,
+        10311846026977660324u64,
+        48736111365249031u64,
+    ]);
+
+    // (-1/MODULUS) % 2^64
+    const INV: u64 = 744663313386281181u64;
+
+    /// GENERATOR = 2
+    // primitive_root(MODULUS)
+    #[rustfmt::skip]
+    const GENERATOR: BigInteger = BigInteger([
+        289919226011913130u64,
+        13019990545710127566u64,
+        4409829457611675068u64,
+        13030600802816293865u64,
+        15696054586628993047u64,
+        9353078419867322391u64,
+        5664203968291172875u64,
+        5090703637405909511u64,
+        17774776443174359288u64,
+        10018561694451762270u64,
+        12632664537138156478u64,
+        46143195394855163u64,
+    ]);
+
+    // (MODULUS - 1) / 2
+    #[rustfmt::skip]
+    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0x7a4e800000000045,
+        0xf3489f3438000041,
+        0x0b067c577578521b,
+        0x4c508b612b33d47c,
+        0x38ee69ee39f5ff97,
+        0x4344e476897cfec8,
+        0x81e75d7f92da1182,
+        0xb83dd31c72c2748c,
+        0x29413af7c043df20,
+        0x5c930c3540e8a344,
+        0x68c3e4a0027d7f9f,
+        0x9174127dc1e705,
+    ]);
+
+    // T =
+    // 3445725192157866269698394841137828771239834456268075054756895080104811711121745868043841591644705843820432283876893306725580879560277123879674755849562650799475802549689254425186271815711798397975949850214984556421382456559534149
+    // (MODULUS - 1) / 2 ^ TWO_ADICITY
+    #[rustfmt::skip]
+    const T: BigInteger = BigInteger([
+        0x7a4e800000000045,
+        0xf3489f3438000041,
+        0x0b067c577578521b,
+        0x4c508b612b33d47c,
+        0x38ee69ee39f5ff97,
+        0x4344e476897cfec8,
+        0x81e75d7f92da1182,
+        0xb83dd31c72c2748c,
+        0x29413af7c043df20,
+        0x5c930c3540e8a344,
+        0x68c3e4a0027d7f9f,
+        0x9174127dc1e705,
+    ]);
+
+    // (T - 1)/2 =
+    // 1722862596078933134849197420568914385619917228134037527378447540052405855560872934021920795822352921910216141938446653362790439780138561939837377924781325399737901274844627212593135907855899198987974925107492278210691228279767074
+    #[rustfmt::skip]
+    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0xbd27400000000022,
+        0xf9a44f9a1c000020,
+        0x05833e2bbabc290d,
+        0xa62845b09599ea3e,
+        0x1c7734f71cfaffcb,
+        0x21a2723b44be7f64,
+        0x40f3aebfc96d08c1,
+        0x5c1ee98e39613a46,
+        0x14a09d7be021ef90,
+        0xae49861aa07451a2,
+        0xb461f250013ebfcf,
+        0x48ba093ee0f382,
+    ]);
+}

bw6_761/src/fields/fq3.rs

@@ -0,0 +1,200 @@
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::fp3::{Fp3, Fp3Parameters},
+};
+
+use crate::Fq;
+
+pub type Fq3 = Fp3<Fq3Parameters>;
+
+pub struct Fq3Parameters;
+
+impl Fp3Parameters for Fq3Parameters {
+    type Fp = Fq;
+
+    /// NONRESIDUE = -4
+    // Fq3 = Fq[u]/u^3+4
+    #[rustfmt::skip]
+    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
+        0xe12e00000001e9c2,
+        0x63c1e3faa001cd69,
+        0xb1b4384fcbe29cf6,
+        0xc79630bc713d5a1d,
+        0x30127ac071851e2d,
+        0x0979f350dcd36af1,
+        0x6a66defed8b361f2,
+        0x53abac78b24d4e23,
+        0xb7ab89dede485a92,
+        0x5c3a0745675e8452,
+        0x446f17918c5f5700,
+        0xfdf24e3267fa1e,
+    ]));
+
+    // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
+    const TWO_ADICITY: u32 = 1;
+
+    // (T-1)/2 with T = (MODULUS^3-1) / 2^TWO_ADICITY
+    #[rustfmt::skip]
+    const T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+        0xb5e7c000000a3eac,
+        0xf79b99dbf41cf4ab,
+        0xe9372b1919e55ee5,
+        0xbb7bbc4936c1980b,
+        0x7c0cb9d4399b36e1,
+        0x73304a5507bb1ae0,
+        0x92f639be8963936f,
+        0x4f574ac2439ba816,
+        0x670d9bd389dd29ef,
+        0x606ddf900d2124f1,
+        0x928fb14985ec3270,
+        0x6b2f2428c5f420f3,
+        0xac9ade29d5ab5fbe,
+        0xec0d0434c4005822,
+        0x973f10d7f3c5c108,
+        0x6d5e83fc81095979,
+        0xdac3e6e4e1647752,
+        0x227febf93994603e,
+        0x4ab8755d894167d1,
+        0x4fd2d3f67d8b537a,
+        0x33e196a4d5f4030a,
+        0x88b51fb72092df1a,
+        0xa67e5b1e8fc48316,
+        0xb0855eb2a00d7dab,
+        0xe875dd2da6751442,
+        0x777594a243e25676,
+        0x294e0f70376a85a8,
+        0x83f431c7988e4f18,
+        0x8e8fb6af3ca2f5f1,
+        0x7297896b4b9e90f1,
+        0xff38f54664d66123,
+        0xb5ecf80bfff41e13,
+        0x1662a3666bb8392a,
+        0x07a0968e8742d3e1,
+        0xf12927e564bcdfdc,
+        0x5de9825a0e,
+    ];
+
+    // NONRESIDUE^T % q
+    #[rustfmt::skip]
+    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
+        field_new!(Fq, BigInteger([
+            0xf29a000000007ab6,
+            0x8c391832e000739b,
+            0x77738a6b6870f959,
+            0xbe36179047832b03,
+            0x84f3089e56574722,
+            0xc5a3614ac0b1d984,
+            0x5c81153f4906e9fe,
+            0x4d28be3a9f55c815,
+            0xd72c1d6f77d5f5c5,
+            0x73a18e069ac04458,
+            0xf9dfaa846595555f,
+            0xd0f0a60a5be58c,
+        ])),
+        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
+        field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0])),
+    );
+
+    // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
+        field_new!(Fq, BigInteger([
+            0x0202ffffffff85d5,
+            0x5a5826358fff8ce7,
+            0x9e996e43827faade,
+            0xda6aff320ee47df4,
+            0xece9cb3e1d94b80b,
+            0xc0e667a25248240b,
+            0xa74da5bfdcad3905,
+            0x2352e7fe462f2103,
+            0x7b56588008b1c87c,
+            0x45848a63e711022f,
+            0xd7a81ebb9f65a9df,
+            0x51f77ef127e87d,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x7f96b51bd840c549,
+            0xd59782096496171f,
+            0x49b046fd9ce14bbc,
+            0x4b6163bba7527a56,
+            0xef6c92fb771d59f1,
+            0x0425bedbac1dfdc7,
+            0xd3ac39de759c0ffd,
+            0x9f43ed0e063a81d0,
+            0x5bd7d20b4f9a3ce2,
+            0x0411f03c36cf5c3c,
+            0x2d658fd49661c472,
+            0x1100249ae760b93,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x67a04ae427bfb5f8,
+            0x9d32d491eb6a5cff,
+            0x43d03c1cb68051d4,
+            0x0b75ca96f69859a5,
+            0x0763497f5325ec60,
+            0x48076b5c278dd94d,
+            0x8ca3965ff91efd06,
+            0x1e6077657ea02f5d,
+            0xcdd6c153a8c37724,
+            0x28b5b634e5c22ea4,
+            0x9e01e3efd42e902c,
+            0xe3d6815769a804,
+
+        ])),
+    ];
+
+    // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
+        field_new!(Fq, BigInteger([
+            0x0202ffffffff85d5,
+            0x5a5826358fff8ce7,
+            0x9e996e43827faade,
+            0xda6aff320ee47df4,
+            0xece9cb3e1d94b80b,
+            0xc0e667a25248240b,
+            0xa74da5bfdcad3905,
+            0x2352e7fe462f2103,
+            0x7b56588008b1c87c,
+            0x45848a63e711022f,
+            0xd7a81ebb9f65a9df,
+            0x51f77ef127e87d,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x67a04ae427bfb5f8,
+            0x9d32d491eb6a5cff,
+            0x43d03c1cb68051d4,
+            0x0b75ca96f69859a5,
+            0x0763497f5325ec60,
+            0x48076b5c278dd94d,
+            0x8ca3965ff91efd06,
+            0x1e6077657ea02f5d,
+            0xcdd6c153a8c37724,
+            0x28b5b634e5c22ea4,
+            0x9e01e3efd42e902c,
+            0xe3d6815769a804,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x7f96b51bd840c549,
+            0xd59782096496171f,
+            0x49b046fd9ce14bbc,
+            0x4b6163bba7527a56,
+            0xef6c92fb771d59f1,
+            0x0425bedbac1dfdc7,
+            0xd3ac39de759c0ffd,
+            0x9f43ed0e063a81d0,
+            0x5bd7d20b4f9a3ce2,
+            0x0411f03c36cf5c3c,
+            0x2d658fd49661c472,
+            0x1100249ae760b93,
+        ])),
+    ];
+
+    #[inline(always)]
+    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
+        let original = -(*fe);
+        let double = original + &original;
+        double + &double
+    }
+}

bw6_761/src/fields/fq6.rs

@@ -0,0 +1,106 @@
+use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO};
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::fp6_2over3::{Fp6, Fp6Parameters},
+};
+
+pub type Fq6 = Fp6<Fq6Parameters>;
+
+pub struct Fq6Parameters;
+
+impl Fp6Parameters for Fq6Parameters {
+    type Fp3Params = Fq3Parameters;
+
+    /// NONRESIDUE = (0, 1, 0)
+    #[rustfmt::skip]
+    const NONRESIDUE: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
+        field_new!(Fq, BigInteger([
+            0x0202ffffffff85d5,
+            0x5a5826358fff8ce7,
+            0x9e996e43827faade,
+            0xda6aff320ee47df4,
+            0xece9cb3e1d94b80b,
+            0xc0e667a25248240b,
+            0xa74da5bfdcad3905,
+            0x2352e7fe462f2103,
+            0x7b56588008b1c87c,
+            0x45848a63e711022f,
+            0xd7a81ebb9f65a9df,
+            0x51f77ef127e87d,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x8cfcb51bd8404a93,
+            0x495e69d68495a383,
+            0xd23cbc9234705263,
+            0x8d2b4c2b5fcf4f52,
+            0x6a798a5d20c612ce,
+            0x3e825d90eb6c2443,
+            0x772b249f2c9525fe,
+            0x521b2ed366e4b9bb,
+            0x84abb49bd7c4471d,
+            0x907062359c0f17e3,
+            0x3385e55030cc6f12,
+            0x3f11a3a41a2606,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x7f96b51bd840c549,
+            0xd59782096496171f,
+            0x49b046fd9ce14bbc,
+            0x4b6163bba7527a56,
+            0xef6c92fb771d59f1,
+            0x0425bedbac1dfdc7,
+            0xd3ac39de759c0ffd,
+            0x9f43ed0e063a81d0,
+            0x5bd7d20b4f9a3ce2,
+            0x0411f03c36cf5c3c,
+            0x2d658fd49661c472,
+            0x1100249ae760b93,
+        ])),
+        field_new!(Fq, BigInteger([
+            0xf29a000000007ab6,
+            0x8c391832e000739b,
+            0x77738a6b6870f959,
+            0xbe36179047832b03,
+            0x84f3089e56574722,
+            0xc5a3614ac0b1d984,
+            0x5c81153f4906e9fe,
+            0x4d28be3a9f55c815,
+            0xd72c1d6f77d5f5c5,
+            0x73a18e069ac04458,
+            0xf9dfaa846595555f,
+            0xd0f0a60a5be58c,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x67a04ae427bfb5f8,
+            0x9d32d491eb6a5cff,
+            0x43d03c1cb68051d4,
+            0x0b75ca96f69859a5,
+            0x0763497f5325ec60,
+            0x48076b5c278dd94d,
+            0x8ca3965ff91efd06,
+            0x1e6077657ea02f5d,
+            0xcdd6c153a8c37724,
+            0x28b5b634e5c22ea4,
+            0x9e01e3efd42e902c,
+            0xe3d6815769a804,
+        ])),
+        field_new!(Fq, BigInteger([
+            0x75064ae427bf3b42,
+            0x10f9bc5f0b69e963,
+            0xcc5cb1b14e0f587b,
+            0x4d3fb306af152ea1,
+            0x827040e0fccea53d,
+            0x82640a1166dbffc8,
+            0x30228120b0181307,
+            0xd137b92adf4a6748,
+            0xf6aaa3e430ed815e,
+            0xb514282e4b01ea4b,
+            0xa422396b6e993acc,
+            0x12e5db4d0dc277,
+        ])),
+    ];
+}

bw6_761/src/fields/fr.rs

@@ -0,0 +1 @@
+pub use ark_bls12_377::{Fq as Fr, FqParameters as FrParameters};

bw6_761/src/fields/mod.rs

@@ -0,0 +1,14 @@
+pub mod fr;
+pub use self::fr::*;
+
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fq3;
+pub use self::fq3::*;
+
+pub mod fq6;
+pub use self::fq6::*;
+
+#[cfg(test)]
+mod tests;

bw6_761/src/fields/tests.rs

@@ -0,0 +1,51 @@
+use ark_ff::{test_rng, Field, PrimeField};
+use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
+use rand::Rng;
+
+use crate::*;
+
+use ark_curve_tests::fields::*;
+
+#[test]
+fn test_fr() {
+    let mut rng = test_rng();
+    let a: Fr = rng.gen();
+    let b: Fr = rng.gen();
+    field_test(a, b);
+    sqrt_field_test(a);
+    primefield_test::<Fr>();
+}
+
+#[test]
+fn test_fq() {
+    let mut rng = test_rng();
+    let a: Fq = rng.gen();
+    let b: Fq = rng.gen();
+    field_test(a, b);
+    primefield_test::<Fq>();
+    sqrt_field_test(a);
+
+    let byte_size = a.serialized_size();
+    let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
+    assert_eq!(byte_size, buffer_size);
+    field_serialization_test::<Fq>(byte_size);
+}
+
+#[test]
+fn test_fq3() {
+    let mut rng = test_rng();
+    let a: Fq3 = rng.gen();
+    let b: Fq3 = rng.gen();
+    field_test(a, b);
+    sqrt_field_test(a);
+    frobenius_test::<Fq3, _>(Fq::characteristic(), 13);
+}
+
+#[test]
+fn test_fq6() {
+    let mut rng = test_rng();
+    let a: Fq6 = rng.gen();
+    let b: Fq6 = rng.gen();
+    field_test(a, b);
+    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
+}

bw6_761/src/lib.rs

@@ -0,0 +1,34 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the BW6_761 curve generated in [[EG20]](https://eprint.iacr.org/2020/351).
+//! The name denotes that it is a curve generated using the Brezing--Weng method, and that
+//! its embedding degree is 6.
+//! The main feature of this curve is that the scalar field equals the base field of the BLS12_377 curve.
+//!
+//! Curve information:
+//! * Base field: q = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
+//! * Scalar field: r = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+//! * valuation(q - 1, 2) = 1
+//! * valuation(r - 1, 2) = 46
+//!
+//! G1 curve equation: y^2 = x^3 + ax + b, where
+//! * a = 0,
+//! * b = -1,
+//!
+//! G2 curve equation: y^2 = x^3 + Ax + B
+//! * A = 0
+//! * B = 4
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;