Initial commit

mnt6_753/src/curves/g1.rs

@@ -0,0 +1,104 @@
+use ark_ec::{
+    mnt6,
+    models::{ModelParameters, SWModelParameters},
+};
+use ark_ff::{biginteger::BigInteger768, field_new};
+
+use crate::{Fq, Fr, FR_ONE};
+
+pub type G1Affine = mnt6::G1Affine<crate::Parameters>;
+pub type G1Projective = mnt6::G1Projective<crate::Parameters>;
+pub type G1Prepared = mnt6::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 = 11
+    #[rustfmt::skip]
+    const COEFF_A: Fq = field_new!(Fq, BigInteger768([
+        5145524327033718740,
+        14149824967095184544,
+        5159730833497260295,
+        3902941467692815387,
+        15830098551216085679,
+        8665641533746801158,
+        17502192300007146323,
+        14483698255198590748,
+        546300946688995976,
+        4331975528992054828,
+        5311428878520309260,
+        495362057711802,
+    ]));
+
+    /// COEFF_B = 0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A
+    #[rustfmt::skip]
+    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
+        8828711393625909642,
+        12722539140758597443,
+        2303826860244282256,
+        8063890988281098391,
+        6269149169423748670,
+        3425772737529456013,
+        1457017085322601211,
+        5177155908178255133,
+        18057960053344868113,
+        10481469207136524576,
+        17888199912367160320,
+        290288558853910,
+    ]));
+
+    /// 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 = 3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728,
+// Y = 27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569,
+/// G1_GENERATOR_X =
+#[rustfmt::skip]
+pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
+    16404456614462158210,
+    16873534995404346316,
+    29580875041164893,
+    12740551787746921884,
+    16087583716780115490,
+    15096170813200936110,
+    930080103225705610,
+    660122182606823185,
+    5211213138865083410,
+    15466479635231681544,
+    11783401481713071326,
+    20214808394592
+]));
+
+/// G1_GENERATOR_Y =
+#[rustfmt::skip]
+pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
+    11636140615878154554,
+    15149343852908177063,
+    14426639389651280896,
+    12711360703798958610,
+    3787948290527586979,
+    7628180411662927078,
+    17195203689728925717,
+    6800476327444280291,
+    2228796880865780105,
+    15627033749683396124,
+    13783535191786892346,
+    61400438920476
+]));

mnt6_753/src/curves/g2.rs

@@ -0,0 +1,262 @@
+use ark_ec::{
+    mnt6,
+    mnt6::MNT6Parameters,
+    models::{ModelParameters, SWModelParameters},
+};
+use ark_ff::{biginteger::BigInteger768, field_new};
+
+use crate::{g1, Fq, Fq3, Fr, FQ_ZERO};
+
+pub type G2Affine = mnt6::G2Affine<crate::Parameters>;
+pub type G2Projective = mnt6::G2Projective<crate::Parameters>;
+pub type G2Prepared = mnt6::G2Prepared<crate::Parameters>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Parameters;
+
+impl ModelParameters for Parameters {
+    type BaseField = Fq3;
+    type ScalarField = Fr;
+}
+
+/// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
+#[rustfmt::skip]
+pub const MUL_BY_A_C0: Fq = field_new!(Fq, BigInteger768([
+    10895242587870565906,
+    6757387713923212228,
+    12683949709867392876,
+    1229095484098138811,
+    18111217745394181988,
+    3648021353977015866,
+    7900332254549424237,
+    5988529219097278134,
+    11544487525720487778,
+    7317517692149492894,
+    9905728181042915773,
+    470678396104534
+]));
+
+/// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
+#[rustfmt::skip]
+pub const MUL_BY_A_C1: Fq = field_new!(Fq, BigInteger768([
+    10895242587870565906,
+    6757387713923212228,
+    12683949709867392876,
+    1229095484098138811,
+    18111217745394181988,
+    3648021353977015866,
+    7900332254549424237,
+    5988529219097278134,
+    11544487525720487778,
+    7317517692149492894,
+    9905728181042915773,
+    470678396104534
+]));
+
+/// MUL_BY_A_C2 = COEFF_A
+pub const MUL_BY_A_C2: Fq = g1::Parameters::COEFF_A;
+
+impl SWModelParameters for Parameters {
+    const COEFF_A: Fq3 = crate::Parameters::TWIST_COEFF_A;
+    // B coefficient of MNT6-753 G2 =
+    // ```
+    // mnt6753_twist_coeff_b = mnt6753_Fq3(mnt6753_G1::coeff_b * mnt6753_Fq3::non_residue,
+    //                                  mnt6753_Fq::zero(), mnt6753_Fq::zero());
+    // non_residue = mnt6753_Fq3::non_residue = mnt6753_Fq("11");
+    //  = (G1_B_COEFF * NON_RESIDUE, ZERO, ZERO);
+    //  =
+    //  (2189526091197672465268098090392210500740714959757583916377481826443393499947557697773546040576162515434508768057245887856591913752342600919117433675080691499697020523783784738694360040853591723916201150207746019687604267190251,
+    //  0, 0)
+    // ```
+    #[rustfmt::skip]
+    const COEFF_B: Fq3 = field_new!(
+        Fq3,
+        field_new!(Fq, BigInteger768([
+                3284231658830416104,
+                13720030246451177991,
+                6276939417009443243,
+                8340612253649729185,
+                4863511590806861670,
+                15883218135158530927,
+                4865336109262680856,
+                16600307443495218926,
+                10112528487499131659,
+                17308657107605697754,
+                5326857497786417651,
+                206191604157846
+        ])),
+        FQ_ZERO,
+        FQ_ZERO,
+    );
+
+    /// COFACTOR =
+    /// 1755483545388786116744270475466687259186947712032004459714210070280389500116987496124098574823389466285978151140155508638765729019174599527183600372094760023144398285325863550664578643924584541949466179502227232245309952839189635010671372908411609248348904807785904229403747495114436660255866932060472369629692502198423138429922875792635236729929780298333055698257230963645509826963717287902205842627121011526048163097042046361575549171961352924692480000
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        17839255819456086016,
+        500623104730997740,
+        2110252009236161768,
+        1500878543414750896,
+        12839751506594314239,
+        8978537329634833065,
+        13830010955957826199,
+        7626514311663165506,
+        14876243211944528805,
+        2316601947950921451,
+        2601177562497904269,
+        18300670698693155036,
+        17321427554953155530,
+        12586270719596716948,
+        807965545138267130,
+        13086323046094411844,
+        16597411233431396880,
+        5578519820383338987,
+        16478065054289650824,
+        12110148809888520863,
+        5901144846689643164,
+        3407195776166256068,
+        14663852814447346059,
+        13435169368,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200
+    #[rustfmt::skip]
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger768([
+            9418103049026957703,
+            3464743017686961509,
+            7872172759259099794,
+            17514322419398292337,
+            1496353716802911167,
+            16961719271566193274,
+            15426671498718617736,
+            9230857178223113223,
+            11731938389074297274,
+            16450973680014766981,
+            431917267220694852,
+            94637508603012
+    ]));
+
+    /// 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: &Fq3) -> Fq3 {
+        field_new!(
+            Fq3,
+            MUL_BY_A_C0 * &elt.c1,
+            MUL_BY_A_C1 * &elt.c2,
+            MUL_BY_A_C2 * &elt.c0,
+        )
+    }
+}
+
+const G2_GENERATOR_X: Fq3 =
+    field_new!(Fq3, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
+const G2_GENERATOR_Y: Fq3 =
+    field_new!(Fq3, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
+
+// Generator of G2
+// These are three Fq elements each because X and Y (and Z) are elements of Fq^3
+// X = 27250797394340459586637772414334383652934225310678303542554641987990991970766156209996739240400887081904395745019996048910447071686918567661896491214767494514394154061111870331668445455228882471000120574964265209669155206168252,
+// 35762481056967998715733586393399457882827322353696313323665483142561285210083843314423554450886956650265947502285422529615273790981238406393402603210224104850580302463396274854098657541573494421834514772635884262388058080180368,
+// 36955296703808958167583270646821654948157955258947892285629161090141878438357164213613114995903637211606408001037026832604054121847388692538440756596264746452765613740820430501353237866984394057660379098674983614861254438847846,
+// Y = 2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615,
+// 7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497,
+// 21014872727619291834131369222699267167761185012487859171850226473555446863681002782100371394603357586906967186931035615146288030444598977758226767063525819170917389755555854704165900869058188909090444447822088242504281789869689,
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, BigInteger768([
+    12772807549130126376,
+    2873211972983293592,
+    15999100872160401842,
+    5277158980096688998,
+    12258756012310206056,
+    11885883517271414939,
+    6373672746025419911,
+    13662747456330091710,
+    11960680427306056040,
+    15150766304321120168,
+    9480712498131729809,
+    413066879180657
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, BigInteger768([
+    10478274013728260378,
+    15392361149861123784,
+    17610084573134912261,
+    14474130264887792371,
+    16754378329454263996,
+    3186303078832273968,
+    7143189323629797683,
+    897486443141339765,
+    3675579496642106405,
+    4429391539758461550,
+    18414257413872084180,
+    331209511183940
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_X_C2: Fq = field_new!(Fq, BigInteger768([
+    5133712986240959624,
+    10763134357204872827,
+    8672341403101541980,
+    18084133226637702602,
+    4689040548070804594,
+    7352115990101270007,
+    14358820512747653623,
+    10167201669589504005,
+    3117673189936726036,
+    9407838052466059644,
+    7246385421116647671,
+    464288782946273
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, BigInteger768([
+    710862246533630948,
+    9314168172257972041,
+    4722111556929662508,
+    4408676313209842703,
+    10491088158750500898,
+    13211840969745661306,
+    13985341743807087374,
+    7111198859398088665,
+    158194789363472891,
+    7682183069894584797,
+    9510326135325230913,
+    338826428359581
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, BigInteger768([
+    10889422482835557076,
+    6073207585023077555,
+    16059368148547235058,
+    14871121891082823821,
+    15156344465408677175,
+    12695157488434086405,
+    7840105431702704631,
+    4763759818130023465,
+    12295696339556388640,
+    352741974984397506,
+    10581333776569094279,
+    204002329498100
+]));
+
+#[rustfmt::skip]
+pub const G2_GENERATOR_Y_C2: Fq = field_new!(Fq, BigInteger768([
+    11263496889641203707,
+    16306762242042931049,
+    8275973312257833978,
+    12034012818098316014,
+    5392903691498465561,
+    4572635011530974247,
+    696221667645211601,
+    11098678912660456319,
+    5477755854538915619,
+    11442390115310629698,
+    10262065045802790037,
+    17901561410539
+]));

mnt6_753/src/curves/mod.rs

@@ -0,0 +1,77 @@
+use ark_ff::{biginteger::BigInteger768, field_new, fields::FpParameters, Fp3};
+
+use ark_ec::models::{
+    mnt6::{MNT6Parameters, MNT6},
+    SWModelParameters,
+};
+
+use crate::{Fq, Fq3, Fq3Parameters, Fq6Parameters, 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 MNT6_753 = MNT6<Parameters>;
+
+pub struct Parameters;
+
+impl MNT6Parameters for Parameters {
+    const TWIST: Fp3<Self::Fp3Params> = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+    // A coefficient of MNT6-753 G2 =
+    // ```
+    // mnt6753_twist_coeff_a = mnt6753_Fq3(mnt6753_Fq::zero(), mnt6753_Fq::zero(),
+    //                                  mnt6753_G1::coeff_a);
+    //  = (ZERO, ZERO, A_COEFF);
+    // ```
+    #[rustfmt::skip]
+    const TWIST_COEFF_A: Fp3<Self::Fp3Params> = field_new!(Fq3,
+        FQ_ZERO,
+        FQ_ZERO,
+        g1::Parameters::COEFF_A,
+    );
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt6753.ml
+    const ATE_LOOP_COUNT: &'static [u64] = &[
+        8824542903220142080,
+        7711082599397206192,
+        8303354903384568230,
+        5874150271971943936,
+        9717849827920685054,
+        95829799234282493,
+    ];
+    const ATE_IS_LOOP_COUNT_NEG: bool = false;
+    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 = false;
+    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger768 = BigInteger768([
+        8824542903220142080,
+        7711082599397206192,
+        8303354903384568230,
+        5874150271971943936,
+        9717849827920685054,
+        95829799234282493,
+        0,
+        0,
+        0,
+        0,
+        0,
+        0,
+    ]);
+    type Fp = Fq;
+    type Fr = Fr;
+    type Fp3Params = Fq3Parameters;
+    type Fp6Params = Fq6Parameters;
+    type G1Parameters = self::g1::Parameters;
+    type G2Parameters = self::g2::Parameters;
+}
+
+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);

mnt6_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 = MNT6_753::pairing(sa, b);
+    let ans2 = MNT6_753::pairing(a, sb);
+    let ans3 = MNT6_753::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());
+}
+
+#[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 = MNT6_753::pairing(a, b) * &MNT6_753::pairing(c, d);
+    let ans2 = MNT6_753::product_of_pairings(&[(a.into(), b.into()), (c.into(), d.into())]);
+    assert_eq!(ans1, ans2);
+}

mnt6_753/src/fields/fq.rs

@@ -0,0 +1 @@
+pub use ark_mnt4_753::{Fr as Fq, FrParameters as FqParameters};

mnt6_753/src/fields/fq3.rs

@@ -0,0 +1,137 @@
+use crate::{fq::Fq, FQ_ONE};
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger,
+    field_new,
+    fields::fp3::{Fp3, Fp3Parameters},
+};
+
+pub type Fq3 = Fp3<Fq3Parameters>;
+
+pub struct Fq3Parameters;
+
+impl Fp3Parameters for Fq3Parameters {
+    type Fp = Fq;
+
+    #[rustfmt::skip]
+    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
+        5145524327033718740,
+        14149824967095184544,
+        5159730833497260295,
+        3902941467692815387,
+        15830098551216085679,
+        8665641533746801158,
+        17502192300007146323,
+        14483698255198590748,
+        546300946688995976,
+        4331975528992054828,
+        5311428878520309260,
+        495362057711802,
+    ]));
+
+    const TWO_ADICITY: u32 = 30;
+
+    #[rustfmt::skip]
+    const T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+        15439605736802142541,
+        18190868848461853149,
+        6220121510046940818,
+        10310485528612680366,
+        5032137869959796540,
+        3943048799800510054,
+        1971151279016362045,
+        6096644900171872841,
+        12908407994230849218,
+        4163225373804228290,
+        10382959950522770522,
+        9008828410264446883,
+        18411821899404157689,
+        12386199240837247984,
+        13370099281150720481,
+        11909278545073807560,
+        5964354403900302648,
+        15347506722065009035,
+        7045354120681109597,
+        14294096902719509929,
+        6180325033003959541,
+        14381489272445870003,
+        18159920240207503954,
+        17487026929061632528,
+        12314108197538755669,
+        12116872703077811769,
+        3401400733784294722,
+        13905351619889935522,
+        10972472942574358218,
+        6104159581753028261,
+        4690139121547787552,
+        4880965491878697414,
+        1926648890365125214,
+        13532564555356297305,
+        3114545746551080,
+        0,
+    ];
+
+    #[rustfmt::skip]
+    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
+        field_new!(Fq, BigInteger([
+            2456656400918202012,
+            7503386575313625620,
+            1014314685003569848,
+            10473903647598823719,
+            15893393002146336511,
+            8418203974290622500,
+            9017296731996077946,
+            2923126592994124774,
+            9368756030960215800,
+            17344552888362241070,
+            10938255746876359306,
+            107029542386399,
+        ])),
+        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])),
+    );
+
+    // Coefficients for the Frobenius automorphism.
+    // c1[0] = 1,
+    // c1[1] = 24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132
+    // c1[2] = 17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868,
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
+        FQ_ONE,
+        field_new!(Fq, BigInteger([
+            7739145380395648640,
+            1403348385939055902,
+            11220424057264707228,
+            4567962295300549271,
+            5929583493640677751,
+            17618207486530478833,
+            16600462137977359741,
+            16551719371247820635,
+            12057922785354578416,
+            13022559182829558162,
+            13308285686168533250,
+            313705269181021,
+        ])),
+        field_new!(Fq, BigInteger([
+            12973180669431253567,
+            17038664486452692616,
+            11034024317238370177,
+            7712681843988565810,
+            4725787734130647531,
+            2175028350442404679,
+            9323639551697167751,
+            14465264105466053583,
+            8569442212929419360,
+            17553812953652473294,
+            13991744086792172309,
+            48577617831792,
+        ])),
+    ];
+
+    // c2 = {c1[0], c1[2], c1[1]}
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
+        FQ_ONE,
+        Self::FROBENIUS_COEFF_FP3_C1[2],
+        Self::FROBENIUS_COEFF_FP3_C1[1],
+    ];
+}

mnt6_753/src/fields/fq6.rs

@@ -0,0 +1,99 @@
+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;
+
+    #[rustfmt::skip]
+    const NONRESIDUE: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+
+    // Coefficients for the Frobenius automorphism.
+    // c1[0] = 1,
+    // c1[1] = 24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052133
+    // c1[2] = 24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132
+    // c1[3] = 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160000
+    // c1[4] = 17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868
+    // c1[5] = 17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107869
+    #[rustfmt::skip]
+    const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
+        FQ_ONE,
+        field_new!(Fq, BigInteger([
+            2665418275744511426,
+            7073776242814464967,
+            4441331072847607829,
+            5681016258918493042,
+            18254896527151449163,
+            10681724016023285331,
+            1760041123371930134,
+            4557299868084578750,
+            16702481779049799698,
+            14149724469588165150,
+            5617650120443517591,
+            449252806040736,
+        ])),
+        field_new!(Fq, BigInteger([
+            7739145380395648640,
+            1403348385939055902,
+            11220424057264707228,
+            4567962295300549271,
+            5929583493640677751,
+            17618207486530478833,
+            16600462137977359741,
+            16551719371247820635,
+            12057922785354578416,
+            13022559182829558162,
+            13308285686168533250,
+            313705269181021,
+        ])),
+        field_new!(Fq, BigInteger([
+            2265581976117350591,
+            18442012872391748519,
+            3807704300793525789,
+            12280644139289115082,
+            10655371227771325282,
+            1346491763263331896,
+            7477357615964975877,
+            12570239403004322603,
+            2180620924574446161,
+            12129628062772479841,
+            8853285699251153944,
+            362282887012814,
+        ])),
+        field_new!(Fq, BigInteger([
+            12973180669431253567,
+            17038664486452692616,
+            11034024317238370177,
+            7712681843988565810,
+            4725787734130647531,
+            2175028350442404679,
+            9323639551697167751,
+            14465264105466053583,
+            8569442212929419360,
+            17553812953652473294,
+            13991744086792172309,
+            48577617831792,
+        ])),
+        field_new!(Fq, BigInteger([
+            7899453564780116353,
+            4262348269618550065,
+            4254931332821270779,
+            8825735807606509581,
+            17051100767641418943,
+            13685288953644762793,
+            12929962610801289759,
+            2470844602302811697,
+            13214001206624640642,
+            234234166701528666,
+            6301108521067156651,
+            184125154691507,
+        ])),
+    ];
+}

mnt6_753/src/fields/fr.rs

@@ -0,0 +1 @@
+pub use ark_mnt4_753::{Fq as Fr, FqParameters as FrParameters};

mnt6_753/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(all(feature = "mnt6_753", test))]
+mod tests;

mnt6_753/src/fields/tests.rs

@@ -0,0 +1,52 @@
+use ark_ff::{
+    fields::{models::fp6_2over3::*, quadratic_extension::QuadExtParameters},
+    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_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);
+    assert_eq!(
+        a * Fq6Parameters::NONRESIDUE,
+        <Fp6ParamsWrapper<Fq6Parameters>>::mul_base_field_by_nonresidue(&a)
+    );
+}
+
+#[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);
+}

mnt6_753/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 MNT6_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 6, 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 MNT4_753.
+//!
+//! Curve information:
+//! * Base field: q = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB26C5C28C859A99B3EEBCA9429212636B9DFF97634993AA4D6C381BC3F0057974EA099170FA13A4FD90776E240000001
+//! * Scalar field: r = 0x01C4C62D92C41110229022EEE2CDADB7F997505B8FAFED5EB7E8F96C97D87307FDB925E8A0ED8D99D124D9A15AF79DB117E776F218059DB80F0DA5CB537E38685ACCE9767254A4638810719AC425F0E39D54522CDD119F5E9063DE245E8001
+//! * valuation(q - 1, 2) = 30
+//! * valuation(r - 1, 2) = 15
+//! * G1 curve equation: y^2 = x^3 + ax + b, where
+//!    * a = 11
+//!    * b = 0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A
+//! * G2 curve equation: y^2 = x^3 + Ax + B, where
+//!    * A = Fq3(0, 0, a)
+//!    * B = Fq3(b * NON_RESIDUE, 0, 0)
+//!    * NON_RESIDUE = 11 is the cubic non-residue used to construct the extension field Fq3
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;