Initial commit

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,
+    ]);
+}

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
+            ])
+        ),
+    ];
+}

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,
+        ])),
+    ];
+}

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,
+    ]);
+}

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;

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);
+}