Update `MNT4-753`

4 years ago · 4b050b1aae
6 changed files with 30 additions and 264 deletions
--- a/mnt4_753/src/curves/g1.rs
+++ b/mnt4_753/src/curves/g1.rs
@ -2,7 +2,7 @@ use ark_ec::{
    mnt4,
    models::{ModelParameters, SWModelParameters},
 };
 use ark_ff::{biginteger::BigInteger768, field_new};
 use ark_ff::field_new;

 use crate::{Fq, Fr, FR_ONE};

@ -21,37 +21,11 @@ impl ModelParameters for Parameters {
 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,
    ]));
    const COEFF_A: Fq = field_new!(Fq, "2");

    /// 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,
    ]));
    const COEFF_B: Fq = field_new!(Fq, "28798803903456388891410036793299405764940372360099938340752576406393880372126970068421383312482853541572780087363938442377933706865252053507077543420534380486492786626556269083255657125025963825610840222568694137138741554679540");

    /// COFACTOR = 1
    const COFACTOR: &'static [u64] = &[1];
@ -69,36 +43,10 @@ impl SWModelParameters for Parameters {
 // Generator of G1
 // X = 7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569,
 // Y = 6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648,
 /// G1_GENERATOR_X =
 /// G1_GENERATOR_X = 7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569
 #[rustfmt::skip]
 pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
    9433494781491502420,
    373642694095780604,
    7974079134466535382,
    15325904219470166885,
    16825705122208020751,
    898733863352481713,
    3802318585082797759,
    14417069684372068941,
    4332882897981414838,
    15138727514183191816,
    16850594895992448907,
    30598511593902
 ]));
 pub const G1_GENERATOR_X: Fq = field_new!(Fq, "7790163481385331313124631546957228376128961350185262705123068027727518350362064426002432450801002268747950550964579198552865939244360469674540925037890082678099826733417900510086646711680891516503232107232083181010099241949569");

 /// G1_GENERATOR_Y =
 /// G1_GENERATOR_Y = 6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648
 #[rustfmt::skip]
 pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
    15710199097794077134,
    3645667958306606136,
    8298269426007169475,
    5277073422205725562,
    10451808582969862130,
    14392820246664025579,
    4365987620174557815,
    14007263953321073101,
    1355600847400958219,
    3872959105252355444,
    18016882244107198324,
    424779036457857
 ]));
 pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "6913648190367314284606685101150155872986263667483624713540251048208073654617802840433842931301128643140890502238233930290161632176167186761333725658542781350626799660920481723757654531036893265359076440986158843531053720994648");
--- a/mnt4_753/src/curves/g2.rs
+++ b/mnt4_753/src/curves/g2.rs
@ -3,7 +3,7 @@ use ark_ec::{
    mnt4::MNT4Parameters,
    models::{ModelParameters, SWModelParameters},
 };
 use ark_ff::{biginteger::BigInteger768, field_new};
 use ark_ff::field_new;

 use crate::{Fq, Fq2, Fr, FQ_ZERO, G1_COEFF_A_NON_RESIDUE};

@ -41,20 +41,7 @@ impl SWModelParameters for Parameters {
    #[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,
        ])),
        field_new!(Fq, "39196523001581428369576759982967177918859161321667605855515469914917622337081756705006832951954384669101573360625169461998308377011601613979275218690841934572954991361632773738259652003389826903175898479855893660378722437317212")
    );

    /// COFACTOR =
@ -78,20 +65,7 @@ impl SWModelParameters for Parameters {
    /// 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,
    ]));
    const COFACTOR_INV: Fr = field_new!(Fr, "102345604409665481004734934052318066391634848395005988700111949231215905051467807945653833683883449458834877235200");

    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -113,65 +87,13 @@ const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1
 // 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
 ]));
 pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "29483965110843144675703364744708836524643960105538608078862508397502447349913068434941060515343254862580437318493682762113105361632548148204806052114008731372757389645383891982211245013965175213456066452587869519098351487925167");

 #[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
 ]));
 pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "19706011319630172391076079624799753948158506771222147486237995321925443331396169656568431378974558350664383559981183980668976846806019030432389169137953988990802000581078994008283967768348275973921598166274857631001635633631000");

 #[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
 ]));
 pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "39940152670760519653940320314827327941993141403708338666925204282084477074754642625849927569427860786384998614863651207257467076192649385174108085803168743803491780568503369317093191101779534035377266300185099318717465441820654");

 #[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
 ]));
 pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "17608637424964395737041291373756657139607306440193731804102457011726690702169238966996114255971643893157857311132388792357391583164125870757541009035041469463366528798593952884745987697403056488744603829437448927398468360797245");
--- a/mnt4_753/src/curves/mod.rs
+++ b/mnt4_753/src/curves/mod.rs
@ -1,7 +1,7 @@
 use ark_ec::models::mnt4::{MNT4Parameters, MNT4};
 use ark_ff::{biginteger::BigInteger768, field_new, fields::FpParameters, Fp2};
 use ark_ff::{biginteger::BigInteger768, field_new, Fp2};

 use crate::{Fq, Fq2, Fq2Parameters, Fq4Parameters, FqParameters, Fr, FrParameters};
 use crate::{Fq, Fq2, Fq2Parameters, Fq4Parameters, Fr};

 pub mod g1;
 pub mod g2;
@ -67,24 +67,9 @@ impl MNT4Parameters for 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);
 pub const G1_COEFF_A_NON_RESIDUE: Fq = field_new!(Fq, "26");

 pub const FQ_ZERO: Fq = field_new!(Fq, "0");
 pub const FQ_ONE: Fq = field_new!(Fq, "1");
 pub const FR_ZERO: Fr = field_new!(Fr, "0");
 pub const FR_ONE: Fr = field_new!(Fr, "1");
--- a/mnt4_753/src/curves/tests.rs
+++ b/mnt4_753/src/curves/tests.rs
@ -57,8 +57,8 @@ fn test_bilinearity() {
    let b: G2Projective = rng.gen();
    let s: Fr = rng.gen();

    let sa = a.mul(s);
    let sb = b.mul(s);
    let sa = a.mul(s.into_repr());
    let sb = b.mul(s.into_repr());

    let ans1 = MNT4_753::pairing(sa, b);
    let ans2 = MNT4_753::pairing(a, sb);
--- a/mnt4_753/src/fields/fq2.rs
+++ b/mnt4_753/src/fields/fq2.rs
@ -1,6 +1,5 @@
 use crate::{Fq, FQ_ONE};
 use ark_ff::{
    biginteger::BigInteger768 as BigInteger,
    field_new,
    fields::fp2::{Fp2, Fp2Parameters},
 };
@ -14,64 +13,16 @@ impl Fp2Parameters for Fq2Parameters {

    // non_residue = 13
    #[rustfmt::skip]
    const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
            11881297496860141143,
            13588356353764843511,
            9969398190777826186,
            17325157081734070311,
            16341533986183788031,
            8322434028726676858,
            13631157743146294957,
            8365783422740577875,
            3010239015809771096,
            11776256826687733591,
            7214251687253691272,
            268626707558702
    ]));
    const NONRESIDUE: Fq = field_new!(Fq, "13");

    // 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,
    );
    const QUADRATIC_NONRESIDUE: (Self::Fp, Self::Fp) = (field_new!(Fq, "8"), 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
            ])
        ),
        field_new!(Fq, "41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600"),
    ];
 }
--- a/mnt4_753/src/fields/fq4.rs
+++ b/mnt4_753/src/fields/fq4.rs
@ -1,6 +1,5 @@
 use crate::{Fq, Fq2, Fq2Parameters, FQ_ONE, FQ_ZERO};
 use ark_ff::{
    biginteger::BigInteger768 as BigInteger,
    field_new,
    fields::fp4::{Fp4, Fp4Parameters},
 };
@ -22,47 +21,8 @@ impl Fp4Parameters for Fq4Parameters {
    #[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,
        ])),
        field_new!(Fq, "18691656569803771296244054523431852464958959799019013859007259692542121208304602539555350517075508287829753932558576476751900235650227380562700444433662761577027341858128610410779088384480737679672900770810745291515010467307990"),
        field_new!(Fq, "41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600"),
        field_new!(Fq, "23206834398115182106100160267808784663211750120934935212776243228483231604266504233503543246714830633588317039329677309362453490879357004638891167538350364891904062489821230132228897943262725174047727280881395973788104254381611"),
    ];
 }