Initial commit

2026-01-09 23:41:30 +01:00 · 2020-10-11 19:50:41 -07:00
commit 43ca2132fd
209 changed files with 18825 additions and 0 deletions
--- a/mnt4_753/src/curves/g1.rs
+++ b/mnt4_753/src/curves/g1.rs
@@ -0,0 +1,104 @@
+use ark_ec::{
+    mnt4,
+    models::{ModelParameters, SWModelParameters},
+};
+use ark_ff::{biginteger::BigInteger768, field_new};
+
+use crate::{Fq, Fr, FR_ONE};
+
+pub type G1Affine = mnt4::G1Affine<crate::Parameters>;
+pub type G1Projective = mnt4::G1Projective<crate::Parameters>;
+pub type G1Prepared = mnt4::G1Prepared<crate::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 = 2
+    #[rustfmt::skip]
+    const COEFF_A: Fq = field_new!(Fq, BigInteger768([
+            3553860551672651396,
+            2565472393707818253,
+            3424927325234966109,
+            17487811826058095619,
+            15730291918544907998,
+            4332070408724822737,
+            7212646118208244402,
+            12904649141092619460,
+            9289117987390442562,
+            2254330573517213976,
+            3065472942259520298,
+            271095073719429,
+    ]));
+
+    /// COEFF_B = 0x01373684A8C9DCAE7A016AC5D7748D3313CD8E39051C596560835DF0C9E50A5B59B882A92C78DC537E51A16703EC9855C77FC3D8BB21C8D68BB8CFB9DB4B8C8FBA773111C36C8B1B4E8F1ECE940EF9EAAD265458E06372009C9A0491678EF4
+    #[rustfmt::skip]
+    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
+            2672638521926201442,
+            17587766986973859626,
+            1309143029066506763,
+            1756412671449422902,
+            5395165286423163724,
+            589638022240022974,
+            7360845090332416697,
+            9829497896347590557,
+            9341553552113883496,
+            5888515763059971584,
+            10173739464651404689,
+            456607542322059,
+    ]));
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[1];
+
+    /// COFACTOR^(-1) mod r =
+    /// 1
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = FR_ONE;
+
+    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
+        (G1_GENERATOR_X, G1_GENERATOR_Y);
+}
+
+// Generator of G1
+// X = 7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569,
+// Y = 6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648,
+/// G1_GENERATOR_X =
+#[rustfmt::skip]
+pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
+    9433494781491502420,
+    373642694095780604,
+    7974079134466535382,
+    15325904219470166885,
+    16825705122208020751,
+    898733863352481713,
+    3802318585082797759,
+    14417069684372068941,
+    4332882897981414838,
+    15138727514183191816,
+    16850594895992448907,
+    30598511593902
+]));
+
+/// G1_GENERATOR_Y =
+#[rustfmt::skip]
+pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
+    15710199097794077134,
+    3645667958306606136,
+    8298269426007169475,
+    5277073422205725562,
+    10451808582969862130,
+    14392820246664025579,
+    4365987620174557815,
+    14007263953321073101,
+    1355600847400958219,
+    3872959105252355444,
+    18016882244107198324,
+    424779036457857
+]));
--- a/mnt4_753/src/curves/g2.rs
+++ b/mnt4_753/src/curves/g2.rs
@@ -0,0 +1,177 @@
+use ark_ec::{
+    mnt4,
+    mnt4::MNT4Parameters,
+    models::{ModelParameters, SWModelParameters},
+};
+use ark_ff::{biginteger::BigInteger768, field_new};
+
+use crate::{Fq, Fq2, Fr, FQ_ZERO, G1_COEFF_A_NON_RESIDUE};
+
+pub type G2Affine = mnt4::G2Affine<crate::Parameters>;
+pub type G2Projective = mnt4::G2Projective<crate::Parameters>;
+pub type G2Prepared = mnt4::G2Prepared<crate::Parameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl ModelParameters for Parameters {
+    type BaseField = Fq2;
+    type ScalarField = Fr;
+}
+
+/// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
+#[rustfmt::skip]
+pub const MUL_BY_A_C0: Fq = G1_COEFF_A_NON_RESIDUE;
+
+/// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
+#[rustfmt::skip]
+pub const MUL_BY_A_C1: Fq = G1_COEFF_A_NON_RESIDUE;
+
+impl SWModelParameters for Parameters {
+    const COEFF_A: Fq2 = crate::Parameters::TWIST_COEFF_A;
+    // B coefficient of MNT4-753 G2 =
+    // ```
+    // mnt4753_twist_coeff_b = mnt4753_Fq2(mnt4753_Fq::zero(),
+    //                                  mnt4753_G1::coeff_b * mnt4753_Fq2::non_residue);
+    // non_residue = mnt4753_Fq2::non_residue = mnt4753_Fq("13");
+    //  = (ZERO, G1_B_COEFF * NON_RESIDUE);
+    //  =
+    //  (0, 39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212)
+    // ```
+    #[rustfmt::skip]
+    const COEFF_B: Fq2 = field_new!(Fq2,
+        FQ_ZERO,
+        field_new!(Fq, BigInteger768([
+            15129916544657421551,
+            11332543254671606602,
+            11913830318987286849,
+            13905314883394440110,
+            16479690325073358448,
+            14869098639251228898,
+            10663986895980443550,
+            10768989312009479656,
+            9469728929095040349,
+            4512954369775881939,
+            8788997129423430122,
+            459763387588954,
+        ])),
+    );
+
+    /// COFACTOR =
+    /// 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888049094905534395567574915333486969589229856772141392370549616644545554517640527237829320384324374366385444967219201
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        16436257212445032449,
+        8690275530472745198,
+        17315389657026393162,
+        1645397558963170979,
+        3544984605440726586,
+        12665092767997125024,
+        11083680675069097885,
+        575819899841080717,
+        6825179918269667443,
+        13256793349531086829,
+        1162650133526138285,
+        497830423872529,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger768([
+        1879390364380281898,
+        7926794171490610432,
+        6437239504245874253,
+        16688141022047191858,
+        17059416847145768464,
+        15065047661241262516,
+        16537575340937777321,
+        3324411942044534547,
+        3878293904770657570,
+        18116939243856833744,
+        7557533897589069385,
+        78370361203778,
+    ]));
+
+    /// 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(elt: &Fq2) -> Fq2 {
+        field_new!(Fq2, MUL_BY_A_C0 * &elt.c0, MUL_BY_A_C1 * &elt.c1,)
+    }
+}
+
+const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
+const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+
+// Generator of G2
+// These are two Fq elements each because X and Y (and Z) are elements of Fq^2
+// X = 29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167,
+// 19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000,
+// Y = 39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654,
+// 17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245,
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger768([
+    7263636080534048301,
+    7643227961769035653,
+    15787777614640869937,
+    17661317895964274771,
+    4142647779394287783,
+    15064949873659932676,
+    4579259080596351332,
+    2207443675339702626,
+    5738725620118622838,
+    4338467638707299712,
+    6558861849926282439,
+    341078935870328
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger768([
+    13073882729051113867,
+    195909455108318710,
+    10527070038778509320,
+    16605710222187477118,
+    10442518358308209073,
+    7776589986153052354,
+    16034091384000651523,
+    17429232381273855185,
+    512853344493546034,
+    7982076214836075255,
+    3601416800138513610,
+    399028695285184
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger768([
+    4867672648970469422,
+    2453112364260322863,
+    11918672197974895143,
+    3923647310180624143,
+    12707123323825700670,
+    15781895092544451511,
+    17747112377690960911,
+    16511994611001933567,
+    15360620366665804029,
+    10252080383738480571,
+    5722654046339742760,
+    316853130349807
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger768([
+    17322957246732430708,
+    11825815087694023697,
+    7654216682602683900,
+    13544637981229618042,
+    17057060382219081849,
+    4038731408172002692,
+    6631723222530012253,
+    10585926166286435412,
+    16050667328028620117,
+    16598483946296156500,
+    11771818132648686020,
+    1230430296095
+]));
--- a/mnt4_753/src/curves/mod.rs
+++ b/mnt4_753/src/curves/mod.rs
@@ -0,0 +1,90 @@
+use ark_ec::models::mnt4::{MNT4Parameters, MNT4};
+use ark_ff::{biginteger::BigInteger768, field_new, fields::FpParameters, Fp2};
+
+use crate::{Fq, Fq2, Fq2Parameters, Fq4Parameters, FqParameters, Fr, FrParameters};
+
+pub mod g1;
+pub mod g2;
+
+#[cfg(test)]
+mod tests;
+
+pub use self::{
+    g1::{G1Affine, G1Prepared, G1Projective},
+    g2::{G2Affine, G2Prepared, G2Projective},
+};
+
+pub type MNT4_753 = MNT4<Parameters>;
+
+pub struct Parameters;
+
+impl MNT4Parameters for Parameters {
+    const TWIST: Fp2<Self::Fp2Params> = field_new!(Fq2, FQ_ZERO, FQ_ONE);
+    // A coefficient of MNT4-753 G2 =
+    // ```
+    // mnt4753_twist_coeff_a = mnt4753_Fq2(mnt4753_G1::coeff_a * non_residue, mnt6753_Fq::zero());
+    //  = (A_COEFF * NONRESIDUE, ZERO)
+    //  = (26, ZERO)
+    // ```
+    #[rustfmt::skip]
+    const TWIST_COEFF_A: Fp2<Self::Fp2Params> = field_new!(Fq2,
+        G1_COEFF_A_NON_RESIDUE,
+        FQ_ZERO,
+    );
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt4753.ml
+    const ATE_LOOP_COUNT: &'static [u64] = &[
+        8824542903220142080,
+        7711082599397206192,
+        8303354903384568230,
+        5874150271971943936,
+        9717849827920685054,
+        95829799234282493,
+    ];
+    const ATE_IS_LOOP_COUNT_NEG: bool = true;
+    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger768 =
+        BigInteger768([0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0]);
+    const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = true;
+    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger768 = BigInteger768([
+        8824542903220142079,
+        7711082599397206192,
+        8303354903384568230,
+        5874150271971943936,
+        9717849827920685054,
+        95829799234282493,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+    ]);
+    type Fp = Fq;
+    type Fr = Fr;
+    type Fp2Params = Fq2Parameters;
+    type Fp4Params = Fq4Parameters;
+    type G1Parameters = self::g1::Parameters;
+    type G2Parameters = self::g2::Parameters;
+}
+
+// 26
+pub const G1_COEFF_A_NON_RESIDUE: Fq = field_new!(
+    Fq,
+    BigInteger768([
+        16948538951764659373,
+        10775354577659735631,
+        12766795894854242596,
+        8684022258823474090,
+        973489465296612807,
+        3883945490221946200,
+        16178634811223492029,
+        16155746945640075033,
+        17642042187059426365,
+        10295720303844380352,
+        13265853240981244259,
+        39422991244875,
+    ])
+);
+pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
+pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
+pub const FR_ZERO: Fr = field_new!(Fr, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
+pub const FR_ONE: Fr = field_new!(Fr, FrParameters::R);
--- a/mnt4_753/src/curves/tests.rs
+++ b/mnt4_753/src/curves/tests.rs
@@ -0,0 +1,90 @@
+use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
+use ark_ff::{test_rng, Field, One, PrimeField, UniformRand};
+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 = MNT4_753::pairing(sa, b);
+    let ans2 = MNT4_753::pairing(a, sb);
+    let ans3 = MNT4_753::pairing(a, b).pow(s.into_repr());
+
+    assert_eq!(ans1, ans2);
+    assert_eq!(ans2, ans3);
+
+    assert_ne!(ans1, Fq4::one());
+    assert_ne!(ans2, Fq4::one());
+    assert_ne!(ans3, Fq4::one());
+
+    assert_eq!(ans1.pow(Fr::characteristic()), Fq4::one());
+    assert_eq!(ans2.pow(Fr::characteristic()), Fq4::one());
+    assert_eq!(ans3.pow(Fr::characteristic()), Fq4::one());
+}
+
+#[test]
+fn test_product_of_pairings() {
+    let rng = &mut test_rng();
+
+    let a = G1Projective::rand(rng).into_affine();
+    let b = G2Projective::rand(rng).into_affine();
+    let c = G1Projective::rand(rng).into_affine();
+    let d = G2Projective::rand(rng).into_affine();
+    let ans1 = MNT4_753::pairing(a, b) * &MNT4_753::pairing(c, d);
+    let ans2 = MNT4_753::product_of_pairings(&[(a.into(), b.into()), (c.into(), d.into())]);
+    assert_eq!(ans1, ans2);
+}
--- a/mnt4_753/src/fields/fq.rs
+++ b/mnt4_753/src/fields/fq.rs
@@ -0,0 +1,170 @@
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
+};
+
+pub type Fq = Fp768<FqParameters>;
+
+pub struct FqParameters;
+
+impl Fp768Parameters for FqParameters {}
+impl FftParameters for FqParameters {
+    type BigInt = BigInteger;
+
+    const TWO_ADICITY: u32 = 15;
+
+    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
+        0x3b079c7556ac378,
+        0x2c8c74d04a3f00d4,
+        0xd3b001061b90d4cf,
+        0x946e77514891b0e6,
+        0x79caec8ad6dc9ea1,
+        0xbefd780edc81435d,
+        0xe093d4dca630b154,
+        0x43a0f673199f1c12,
+        0x92276c78436253ff,
+        0xe249d1cf014fcd24,
+        0x96f36471fb7c3ec5,
+        0x1080b8906b7c4,
+    ]);
+
+    const SMALL_SUBGROUP_BASE: Option<u32> = Some(5);
+    const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = Some(2);
+    /// LARGE_SUBGROUP_ROOT_OF_UNITY =
+    /// 12249458902762217747626832919710926618510011455364963726393752854649914979954138109976331601455448780251166045203053508523342111624583986869301658366625356826888785691823710598470775453742133593634524619429629803955083254436531
+    const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<BigInteger> = Some(BigInteger([
+        8926681816978929800,
+        10873079436792120119,
+        6519893728366769435,
+        7899277225737766970,
+        8416573500933450083,
+        12951641800297678468,
+        7093775028595490583,
+        14327009285082556021,
+        18228411097456927576,
+        2823658094446565457,
+        1708328092507553067,
+        109589007594791,
+    ]));
+}
+impl FpParameters for FqParameters {
+    /// MODULUS = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689601
+    const MODULUS: BigInteger = BigInteger([
+        0x5e9063de245e8001,
+        0xe39d54522cdd119f,
+        0x638810719ac425f0,
+        0x685acce9767254a4,
+        0xb80f0da5cb537e38,
+        0xb117e776f218059d,
+        0x99d124d9a15af79d,
+        0x7fdb925e8a0ed8d,
+        0x5eb7e8f96c97d873,
+        0xb7f997505b8fafed,
+        0x10229022eee2cdad,
+        0x1c4c62d92c411,
+    ]);
+
+    const MODULUS_BITS: u32 = 753;
+
+    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
+
+    const REPR_SHAVE_BITS: u32 = 15;
+
+    const R: BigInteger = BigInteger([
+        0x98a8ecabd9dc6f42,
+        0x91cd31c65a034686,
+        0x97c3e4a0cd14572e,
+        0x79589819c788b601,
+        0xed269c942108976f,
+        0x1e0f4d8acf031d68,
+        0x320c3bb713338559,
+        0x598b4302d2f00a62,
+        0x4074c9cbfd8ca621,
+        0xfa47edb3865e88c,
+        0x95455fb31ff9a195,
+        0x7b479ec8e242,
+    ]);
+
+    const R2: BigInteger = BigInteger([
+        0x84717088cfd190c8,
+        0xc7d9ff8e7df03c0a,
+        0xa24bea56242b3507,
+        0xa896a656a0714c7d,
+        0x80a46659ff6f3ddf,
+        0x2f47839ef88d7ce8,
+        0xa8c86d4604a3b597,
+        0xe03c79cac4f7ef07,
+        0x2505daf1f4a81245,
+        0x8e4605754c381723,
+        0xb081f15bcbfdacaf,
+        0x2a33e89cb485,
+    ]);
+
+    const INV: u64 = 0xf2044cfbe45e7fff;
+
+    const GENERATOR: BigInteger = BigInteger([
+        0xa8f627f0e629635e,
+        0x202afce346c36872,
+        0x85e1ece733493254,
+        0x6d76e610664ac389,
+        0xdf542f3f04441585,
+        0x3aa4885bf6d4dd80,
+        0xeb8b63c1c0fffc74,
+        0xd2488e985f6cfa4e,
+        0xcce1c2a623f7a66a,
+        0x2a060f4d5085b19a,
+        0xa9111a596408842f,
+        0x11ca8d50bf627,
+    ]);
+
+    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0xaf4831ef122f4000,
+        0x71ceaa29166e88cf,
+        0x31c40838cd6212f8,
+        0x342d6674bb392a52,
+        0xdc0786d2e5a9bf1c,
+        0xd88bf3bb790c02ce,
+        0xcce8926cd0ad7bce,
+        0x83fedc92f45076c6,
+        0xaf5bf47cb64bec39,
+        0xdbfccba82dc7d7f6,
+        0x88114811777166d6,
+        0xe26316c96208,
+    ]);
+
+    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
+
+    /// T = (MODULUS - 1) / 2^S =
+    /// 1278640471433073529124274133033466709233725278318907137200424283478556909563327233064541435662546964154604216671394463687571830033251476599169665701965732619291119517454523942352538645255842982596454713491581459512424155325
+    const T: BigInteger = BigInteger([
+        0x233ebd20c7bc48bd,
+        0x4be1c73aa8a459ba,
+        0xa948c71020e33588,
+        0xfc70d0b599d2ece4,
+        0xb3b701e1b4b96a6,
+        0xef3b622fceede430,
+        0xdb1b33a249b342b5,
+        0xb0e60ffb724bd141,
+        0x5fdabd6fd1f2d92f,
+        0x9b5b6ff32ea0b71f,
+        0x882220452045ddc5,
+        0x3898c5b25,
+    ]);
+
+    /// (T - 1) / 2 =
+    /// 639320235716536764562137066516733354616862639159453568600212141739278454781663616532270717831273482077302108335697231843785915016625738299584832850982866309645559758727261971176269322627921491298227356745790729756212077662
+    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0x119f5e9063de245e,
+        0x25f0e39d54522cdd,
+        0x54a4638810719ac4,
+        0x7e38685acce97672,
+        0x59db80f0da5cb53,
+        0xf79db117e776f218,
+        0xed8d99d124d9a15a,
+        0xd87307fdb925e8a0,
+        0xafed5eb7e8f96c97,
+        0xcdadb7f997505b8f,
+        0xc41110229022eee2,
+        0x1c4c62d92,
+    ]);
+}
--- a/mnt4_753/src/fields/fq2.rs
+++ b/mnt4_753/src/fields/fq2.rs
@@ -0,0 +1,77 @@
+use crate::{Fq, FQ_ONE};
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::fp2::{Fp2, Fp2Parameters},
+};
+
+pub type Fq2 = Fp2<Fq2Parameters>;
+
+pub struct Fq2Parameters;
+
+impl Fp2Parameters for Fq2Parameters {
+    type Fp = Fq;
+
+    // non_residue = 13
+    #[rustfmt::skip]
+    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
+            11881297496860141143,
+            13588356353764843511,
+            9969398190777826186,
+            17325157081734070311,
+            16341533986183788031,
+            8322434028726676858,
+            13631157743146294957,
+            8365783422740577875,
+            3010239015809771096,
+            11776256826687733591,
+            7214251687253691272,
+            268626707558702
+    ]));
+
+    // qnr = (8, 1)
+    const QUADRATIC_NONRESIDUE: (Self::Fp, Self::Fp) = (
+        field_new!(
+            Fq,
+            BigInteger([
+                587330122779359758,
+                14352661462510473462,
+                17802452401246596498,
+                18018663494943049411,
+                17948754733747257098,
+                10253180574146027531,
+                6683223122694781837,
+                13573468617269213174,
+                5059368039312883748,
+                950479668716233863,
+                9936591501985804621,
+                88719447132658
+            ])
+        ),
+        FQ_ONE,
+    );
+
+    // Coefficients:
+    // [1, 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600]
+    // see https://github.com/o1-labs/snarky/blob/2cf5ef3a14989e57c17518832b3c52590068fc48/src/camlsnark_c/libsnark-caml/depends/libff/libff/algebra/curves/mnt753/mnt4753/mnt4753_init.cpp
+    const FROBENIUS_COEFF_FP2_C1: &'static [Self::Fp] = &[
+        FQ_ONE,
+        field_new!(
+            Fq,
+            BigInteger([
+                14260497802974073023,
+                5895249896161266456,
+                14682908860938702530,
+                17222385991615618722,
+                14621060510943733448,
+                10594887362868996148,
+                7477357615964975684,
+                12570239403004322603,
+                2180620924574446161,
+                12129628062772479841,
+                8853285699251153944,
+                362282887012814
+            ])
+        ),
+    ];
+}
--- a/mnt4_753/src/fields/fq4.rs
+++ b/mnt4_753/src/fields/fq4.rs
@@ -0,0 +1,68 @@
+use crate::{Fq, Fq2, Fq2Parameters, FQ_ONE, FQ_ZERO};
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::fp4::{Fp4, Fp4Parameters},
+};
+
+pub type Fq4 = Fp4<Fq4Parameters>;
+
+pub struct Fq4Parameters;
+
+impl Fp4Parameters for Fq4Parameters {
+    type Fp2Params = Fq2Parameters;
+
+    const NONRESIDUE: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ONE);
+
+    // Coefficients for the Frobenius automorphism.
+    // c1[0] = 1,
+    // c1[1] = 18691656569803771296244054523431852464958959799019013859007259692542121208304602539555350517075508287829753932558576476751900235650227380562700444433662761577027341858128610410779088384480737679672900770810745291515010467307990
+    // c1[2] = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600
+    // c1[3] = 23206834398115182106100160267808784663211750120934935212776243228483231604266504233503543246714830633588317039329677309362453490879357004638891167538350364891904062489821230132228897943262725174047727280881395973788104254381611
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP4_C1: &'static [Fq] = &[
+        FQ_ONE,
+        field_new!(Fq, BigInteger([
+            2732208433323581659,
+            2172983777736624684,
+            14351170316343013496,
+            6345300643186282385,
+            3197292113538174065,
+            1887663496013421009,
+            16627860175048929982,
+            1842296636815120666,
+            13463717484107308085,
+            721000253033730237,
+            1214767992212094798,
+            163570781165682,
+         ])),
+        field_new!(Fq, BigInteger([
+            14260497802974073023,
+            5895249896161266456,
+            14682908860938702530,
+            17222385991615618722,
+            14621060510943733448,
+            10594887362868996148,
+            7477357615964975684,
+            12570239403004322603,
+            2180620924574446161,
+            12129628062772479841,
+            8853285699251153944,
+            362282887012814,
+        ])),
+        field_new!(Fq, BigInteger([
+            4081847608632041254,
+            14228374352133326707,
+            11267574244067947896,
+            1174247187748832530,
+            10065542319823237575,
+            10873259071217986508,
+            12902564573729719519,
+            17180267336735511666,
+            11808206507871910973,
+            12535793096497356591,
+            18394626215023595103,
+            334259642706846,
+        ])),
+    ];
+}
--- a/mnt4_753/src/fields/fr.rs
+++ b/mnt4_753/src/fields/fr.rs
@@ -0,0 +1,151 @@
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
+};
+
+pub type Fr = Fp768<FrParameters>;
+
+pub struct FrParameters;
+
+impl Fp768Parameters for FrParameters {}
+impl FftParameters for FrParameters {
+    type BigInt = BigInteger;
+
+    const TWO_ADICITY: u32 = 30;
+
+    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
+        0x307f66b297671883,
+        0xd72a7f2b1e645f4e,
+        0x67079daa9a902283,
+        0xf33f7620a86c668b,
+        0x8878570d66464c12,
+        0xa557af5b524f522b,
+        0x5fafa3f6ef19319d,
+        0x1eb9e04110a65629,
+        0x3f96feb3c639a0b0,
+        0x4d4fe37df3ffd732,
+        0xadc831bd55bcf3e9,
+        0x1b9f32a8bd6ab,
+    ]);
+}
+impl FpParameters for FrParameters {
+    /// MODULUS = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160001
+    const MODULUS: BigInteger = BigInteger([
+        0xd90776e240000001,
+        0x4ea099170fa13a4f,
+        0xd6c381bc3f005797,
+        0xb9dff97634993aa4,
+        0x3eebca9429212636,
+        0xb26c5c28c859a99b,
+        0x99d124d9a15af79d,
+        0x7fdb925e8a0ed8d,
+        0x5eb7e8f96c97d873,
+        0xb7f997505b8fafed,
+        0x10229022eee2cdad,
+        0x1c4c62d92c411,
+    ]);
+
+    const MODULUS_BITS: u32 = 753;
+
+    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
+
+    const REPR_SHAVE_BITS: u32 = 15;
+
+    const R: BigInteger = BigInteger([
+        0xb99680147fff6f42,
+        0x4eb16817b589cea8,
+        0xa1ebd2d90c79e179,
+        0xf725caec549c0da,
+        0xab0c4ee6d3e6dad4,
+        0x9fbca908de0ccb62,
+        0x320c3bb713338498,
+        0x598b4302d2f00a62,
+        0x4074c9cbfd8ca621,
+        0xfa47edb3865e88c,
+        0x95455fb31ff9a195,
+        0x7b479ec8e242,
+    ]);
+
+    const R2: BigInteger = BigInteger([
+        0x3f9c69c7b7f4c8d1,
+        0x70a50fa9ee48d127,
+        0xcdbe6702009569cb,
+        0x6bd8c6c6c49edc38,
+        0x7955876cc35ee94e,
+        0xc7285529be54a3f4,
+        0xded52121ecec77cf,
+        0x99be80f2ee12ee8e,
+        0xc8a0ff01493bdcef,
+        0xacc27988f3d9a316,
+        0xd9e817a8fb44b3c9,
+        0x5b58037e0e4,
+    ]);
+
+    const INV: u64 = 0xc90776e23fffffff;
+
+    const GENERATOR: BigInteger = BigInteger([
+        0xeee0a5d37ff6635e,
+        0xff458536cfa1cff4,
+        0x659af978d8169ab0,
+        0x1f1841c24780e3f1,
+        0x602213036dcfef3a,
+        0xd1d5c8f39d72db20,
+        0xeb8b63c1c0ffefab,
+        0xd2488e985f6cfa4e,
+        0xcce1c2a623f7a66a,
+        0x2a060f4d5085b19a,
+        0xa9111a596408842f,
+        0x11ca8d50bf627,
+    ]);
+
+    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0xec83bb7120000000,
+        0xa7504c8b87d09d27,
+        0x6b61c0de1f802bcb,
+        0x5ceffcbb1a4c9d52,
+        0x9f75e54a1490931b,
+        0xd9362e14642cd4cd,
+        0xcce8926cd0ad7bce,
+        0x83fedc92f45076c6,
+        0xaf5bf47cb64bec39,
+        0xdbfccba82dc7d7f6,
+        0x88114811777166d6,
+        0xe26316c96208,
+    ]);
+
+    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
+
+    /// T = (MODULUS - 1) / 2^S =
+    /// 39021010480745652133919498688765463538626870065884617224134041854204007249857398469987226430131438115069708760723898631821547688442835449306011425196003537779414482717728302293895201885929702287178426719326440397855625
+    const T: BigInteger = BigInteger([
+        0x3e84e93f641ddb89,
+        0xfc015e5d3a82645c,
+        0xd264ea935b0e06f0,
+        0xa48498dae77fe5d8,
+        0x2166a66cfbaf2a50,
+        0x856bde76c9b170a3,
+        0xa283b63667449366,
+        0xb25f61cc1ff6e497,
+        0x6e3ebfb57adfa3e5,
+        0xbb8b36b6dfe65d41,
+        0xb64b1044408a408b,
+        0x71318,
+    ]);
+
+    /// (T - 1) / 2 =
+    /// 19510505240372826066959749344382731769313435032942308612067020927102003624928699234993613215065719057534854380361949315910773844221417724653005712598001768889707241358864151146947600942964851143589213359663220198927812
+    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
+        0x1f42749fb20eedc4,
+        0x7e00af2e9d41322e,
+        0x69327549ad870378,
+        0x52424c6d73bff2ec,
+        0x90b353367dd79528,
+        0x42b5ef3b64d8b851,
+        0xd141db1b33a249b3,
+        0xd92fb0e60ffb724b,
+        0xb71f5fdabd6fd1f2,
+        0xddc59b5b6ff32ea0,
+        0x5b25882220452045,
+        0x3898c,
+    ]);
+}
--- a/mnt4_753/src/fields/mod.rs
+++ b/mnt4_753/src/fields/mod.rs
@@ -0,0 +1,22 @@
+#[cfg(feature = "scalar_field")]
+pub mod fr;
+#[cfg(feature = "scalar_field")]
+pub use self::fr::*;
+
+#[cfg(feature = "base_field")]
+pub mod fq;
+#[cfg(feature = "base_field")]
+pub use self::fq::*;
+
+#[cfg(feature = "curve")]
+pub mod fq2;
+#[cfg(feature = "curve")]
+pub use self::fq2::*;
+
+#[cfg(feature = "curve")]
+pub mod fq4;
+#[cfg(feature = "curve")]
+pub use self::fq4::*;
+
+#[cfg(all(feature = "curve", test))]
+mod tests;
--- a/mnt4_753/src/fields/tests.rs
+++ b/mnt4_753/src/fields/tests.rs
@@ -0,0 +1,45 @@
+use ark_ff::{test_rng, Field};
+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);
+    sqrt_field_test(a);
+    primefield_test::<Fq>();
+}
+
+#[test]
+fn test_fq2() {
+    let mut rng = test_rng();
+    let a: Fq2 = rng.gen();
+    let b: Fq2 = rng.gen();
+    field_test(a, b);
+    sqrt_field_test(a);
+    frobenius_test::<Fq2, _>(Fq::characteristic(), 13);
+}
+
+#[test]
+fn test_fq4() {
+    let mut rng = test_rng();
+    let a: Fq4 = rng.gen();
+    let b: Fq4 = rng.gen();
+    field_test(a, b);
+    frobenius_test::<Fq4, _>(Fq::characteristic(), 13);
+}
--- a/mnt4_753/src/lib.rs
+++ b/mnt4_753/src/lib.rs
@@ -0,0 +1,38 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the MNT4_753 curve generated in
+//! [[BCTV14]](https://eprint.iacr.org/2014/595). The name denotes that it is a
+//! Miyaji--Nakabayashi--Takano curve of embedding degree 4, defined over a 753-bit (prime) field.
+//! The main feature of this curve is that its scalar field and base field respectively equal the
+//! base field and scalar field of MNT6_753.
+//!
+//! Curve information:
+//! * Base field: q = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
+//! * Scalar field: r = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
+//! * valuation(q - 1, 2) = 15
+//! * valuation(r - 1, 2) = 30
+//! * G1 curve equation: y^2 = x^3 + ax + b, where
+//!    * a = 2
+//!    * b = 0x01373684A8C9DCAE7A016AC5D7748D3313CD8E39051C596560835DF0C9E50A5B59B882A92C78DC537E51A16703EC9855C77FC3D8BB21C8D68BB8CFB9DB4B8C8FBA773111C36C8B1B4E8F1ECE940EF9EAAD265458E06372009C9A0491678EF4
+//! * G2 curve equation: y^2 = x^3 + Ax + B, where
+//!    * A = Fq2 = (a * NON_RESIDUE, 0)
+//!    * B = Fq2(0, b * NON_RESIDUE)
+//!    * NON_RESIDUE = 13 is the quadratic non-residue used to construct the extension field Fq2
+
+#[cfg(feature = "curve")]
+mod curves;
+#[cfg(any(feature = "scalar_field", feature = "base_field"))]
+mod fields;
+
+#[cfg(feature = "curve")]
+pub use curves::*;
+#[cfg(any(feature = "scalar_field", feature = "base_field"))]
+pub use fields::*;