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ark-curves-cherry-picked
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Update `MNT6-753`

fq2_neg_nonresidue
Pratyush Mishra 4 years ago
parent
9a97d75149
commit
5f62fab169
6 changed files with 43 additions and 349 deletions
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  1. +7
    -57
      mnt6_753/src/curves/g1.rs
  2. +15
    -151
      mnt6_753/src/curves/g2.rs
  3. +6
    -7
      mnt6_753/src/curves/mod.rs
  4. +2
    -2
      mnt6_753/src/curves/tests.rs
  5. +8
    -61
      mnt6_753/src/fields/fq3.rs
  6. +5
    -71
      mnt6_753/src/fields/fq6.rs

+ 7
- 57
mnt6_753/src/curves/g1.rs
View File

@ -2,7 +2,7 @@ use ark_ec::{
mnt6, mnt6,
models::{ModelParameters, SWModelParameters}, models::{ModelParameters, SWModelParameters},
}; };
use ark_ff::{biginteger::BigInteger768, field_new};
use ark_ff::{field_new};
use crate::{Fq, Fr, FR_ONE}; use crate::{Fq, Fr, FR_ONE};
@ -21,37 +21,11 @@ impl ModelParameters for Parameters {
impl SWModelParameters for Parameters { impl SWModelParameters for Parameters {
/// COEFF_A = 11 /// COEFF_A = 11
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_A: Fq = field_new!(Fq, BigInteger768([
5145524327033718740,
14149824967095184544,
5159730833497260295,
3902941467692815387,
15830098551216085679,
8665641533746801158,
17502192300007146323,
14483698255198590748,
546300946688995976,
4331975528992054828,
5311428878520309260,
495362057711802,
]));
const COEFF_A: Fq = field_new!(Fq, "11");
/// COEFF_B = 0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A /// COEFF_B = 0x7DA285E70863C79D56446237CE2E1468D14AE9BB64B2BB01B10E60A5D5DFE0A25714B7985993F62F03B22A9A3C737A1A1E0FCF2C43D7BF847957C34CCA1E3585F9A80A95F401867C4E80F4747FDE5ABA7505BA6FCF2485540B13DFC8468A
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_B: Fq = field_new!(Fq, BigInteger768([
8828711393625909642,
12722539140758597443,
2303826860244282256,
8063890988281098391,
6269149169423748670,
3425772737529456013,
1457017085322601211,
5177155908178255133,
18057960053344868113,
10481469207136524576,
17888199912367160320,
290288558853910,
]));
const COEFF_B: Fq = field_new!(Fq, "11625908999541321152027340224010374716841167701783584648338908235410859267060079819722747939267925389062611062156601938166010098747920378738927832658133625454260115409075816187555055859490253375704728027944315501122723426879114");
/// COFACTOR = 1 /// COFACTOR = 1
const COFACTOR: &'static [u64] = &[1]; const COFACTOR: &'static [u64] = &[1];
@ -70,35 +44,11 @@ impl SWModelParameters for Parameters {
// X = 3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728, // X = 3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728,
// Y = 27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569, // Y = 27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569,
/// G1_GENERATOR_X = /// G1_GENERATOR_X =
/// 3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728,
#[rustfmt::skip] #[rustfmt::skip]
pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
16404456614462158210,
16873534995404346316,
29580875041164893,
12740551787746921884,
16087583716780115490,
15096170813200936110,
930080103225705610,
660122182606823185,
5211213138865083410,
15466479635231681544,
11783401481713071326,
20214808394592
]));
pub const G1_GENERATOR_X: Fq = field_new!(Fq, "3458420969484235708806261200128850544017070333833944116801482064540723268149235477762870414664917360605949659630933184751526227993647030875167687492714052872195770088225183259051403087906158701786758441889742618916006546636728");
/// G1_GENERATOR_Y = /// G1_GENERATOR_Y =
/// 27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569,
#[rustfmt::skip] #[rustfmt::skip]
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
11636140615878154554,
15149343852908177063,
14426639389651280896,
12711360703798958610,
3787948290527586979,
7628180411662927078,
17195203689728925717,
6800476327444280291,
2228796880865780105,
15627033749683396124,
13783535191786892346,
61400438920476
]));
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "27460508402331965149626600224382137254502975979168371111640924721589127725376473514838234361114855175488242007431439074223827742813911899817930728112297763448010814764117701403540298764970469500339646563344680868495474127850569");

+ 15
- 151
mnt6_753/src/curves/g2.rs
View File

@ -3,7 +3,7 @@ use ark_ec::{
mnt6::MNT6Parameters, mnt6::MNT6Parameters,
models::{ModelParameters, SWModelParameters}, models::{ModelParameters, SWModelParameters},
}; };
use ark_ff::{biginteger::BigInteger768, field_new};
use ark_ff::{field_new};
use crate::{g1, Fq, Fq3, Fr, FQ_ZERO}; use crate::{g1, Fq, Fq3, Fr, FQ_ZERO};
@ -20,38 +20,16 @@ impl ModelParameters for Parameters {
} }
/// MUL_BY_A_C0 = NONRESIDUE * COEFF_A /// MUL_BY_A_C0 = NONRESIDUE * COEFF_A
/// = 11 * 11
/// = 121
#[rustfmt::skip] #[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
]));
pub const MUL_BY_A_C0: Fq = field_new!(Fq, "121");
/// MUL_BY_A_C1 = NONRESIDUE * COEFF_A /// MUL_BY_A_C1 = NONRESIDUE * COEFF_A
/// = 11 * 11
/// = 121
#[rustfmt::skip] #[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
]));
pub const MUL_BY_A_C1: Fq = field_new!(Fq, "121");
/// MUL_BY_A_C2 = COEFF_A /// MUL_BY_A_C2 = COEFF_A
pub const MUL_BY_A_C2: Fq = g1::Parameters::COEFF_A; pub const MUL_BY_A_C2: Fq = g1::Parameters::COEFF_A;
@ -71,20 +49,7 @@ impl SWModelParameters for Parameters {
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_B: Fq3 = field_new!( const COEFF_B: Fq3 = field_new!(
Fq3, Fq3,
field_new!(Fq, BigInteger768([
3284231658830416104,
13720030246451177991,
6276939417009443243,
8340612253649729185,
4863511590806861670,
15883218135158530927,
4865336109262680856,
16600307443495218926,
10112528487499131659,
17308657107605697754,
5326857497786417651,
206191604157846
])),
field_new!(Fq, "2189526091197672465268098090392210500740714959757583916377481826443393499947557697773546040576162515434508768057245887856591913752342600919117433675080691499697020523783784738694360040853591723916201150207746019687604267190251"),
FQ_ZERO, FQ_ZERO,
FQ_ZERO, FQ_ZERO,
); );
@ -122,20 +87,7 @@ impl SWModelParameters for Parameters {
/// COFACTOR^(-1) mod r = /// COFACTOR^(-1) mod r =
/// 6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200 /// 6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200
#[rustfmt::skip] #[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger768([
9418103049026957703,
3464743017686961509,
7872172759259099794,
17514322419398292337,
1496353716802911167,
16961719271566193274,
15426671498718617736,
9230857178223113223,
11731938389074297274,
16450973680014766981,
431917267220694852,
94637508603012
]));
const COFACTOR_INV: Fr = field_new!(Fr, "6983081827986492233724035798540106188028451653325658178630583820170892135428517795509815627298389820236345161981341515817589065927929152555581161598204976128690232061758269440757592419606754539638220064054062394397574161203200");
/// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y) /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -165,98 +117,10 @@ const G2_GENERATOR_Y: Fq3 =
// Y = 2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615, // Y = 2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615,
// 7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497, // 7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497,
// 21014872727619291834131369222699267167761185012487859171850226473555446863681002782100371394603357586906967186931035615146288030444598977758226767063525819170917389755555854704165900869058188909090444447822088242504281789869689, // 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
]));
pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "27250797394340459586637772414334383652934225310678303542554641987990991970766156209996739240400887081904395745019996048910447071686918567661896491214767494514394154061111870331668445455228882471000120574964265209669155206168252");
pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "35762481056967998715733586393399457882827322353696313323665483142561285210083843314423554450886956650265947502285422529615273790981238406393402603210224104850580302463396274854098657541573494421834514772635884262388058080180368");
pub const G2_GENERATOR_X_C2: Fq = field_new!(Fq, "36955296703808958167583270646821654948157955258947892285629161090141878438357164213613114995903637211606408001037026832604054121847388692538440756596264746452765613740820430501353237866984394057660379098674983614861254438847846");
#[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
]));
pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "2540920530670785421282147216459500299597350984927286541981768941513322907384197363939300669100157141915897390694710534916701460991329498878429407641200901974650893207493883271892985923686300670742888673128384350189165542294615");
pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "7768974215205248225654340523113146529854477025417883273460270519532499370133542215655437897583245920162220909271982265882784840026754554720358946490360213245668334549692889019612343620295335698052097726325099648573158597797497");
pub const G2_GENERATOR_Y_C2: Fq = field_new!(Fq, "21014872727619291834131369222699267167761185012487859171850226473555446863681002782100371394603357586906967186931035615146288030444598977758226767063525819170917389755555854704165900869058188909090444447822088242504281789869689");

+ 6
- 7
mnt6_753/src/curves/mod.rs
View File

@ -1,11 +1,10 @@
use ark_ff::{biginteger::BigInteger768, field_new, fields::FpParameters, Fp3};
use ark_ff::{biginteger::BigInteger768, field_new, Fp3};
use ark_ec::models::{ use ark_ec::models::{
mnt6::{MNT6Parameters, MNT6}, mnt6::{MNT6Parameters, MNT6},
SWModelParameters, SWModelParameters,
}; };
use crate::{Fq, Fq3, Fq3Parameters, Fq6Parameters, FqParameters, Fr, FrParameters};
use crate::{Fq, Fq3, Fq3Parameters, Fq6Parameters, Fr};
pub mod g1; pub mod g1;
pub mod g2; pub mod g2;
@ -71,7 +70,7 @@ impl MNT6Parameters for Parameters {
type G2Parameters = self::g2::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);
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");

+ 2
- 2
mnt6_753/src/curves/tests.rs
View File

@ -57,8 +57,8 @@ fn test_bilinearity() {
let b: G2Projective = rng.gen(); let b: G2Projective = rng.gen();
let s: Fr = 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 = MNT6_753::pairing(sa, b); let ans1 = MNT6_753::pairing(sa, b);
let ans2 = MNT6_753::pairing(a, sb); let ans2 = MNT6_753::pairing(a, sb);

+ 8
- 61
mnt6_753/src/fields/fq3.rs
View File

@ -1,6 +1,5 @@
use crate::{fq::Fq, FQ_ONE};
use crate::{fq::Fq, FQ_ONE, FQ_ZERO};
use ark_ff::{ use ark_ff::{
biginteger::BigInteger768 as BigInteger,
field_new, field_new,
fields::fp3::{Fp3, Fp3Parameters}, fields::fp3::{Fp3, Fp3Parameters},
}; };
@ -13,20 +12,7 @@ impl Fp3Parameters for Fq3Parameters {
type Fp = Fq; type Fp = Fq;
#[rustfmt::skip] #[rustfmt::skip]
const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
5145524327033718740,
14149824967095184544,
5159730833497260295,
3902941467692815387,
15830098551216085679,
8665641533746801158,
17502192300007146323,
14483698255198590748,
546300946688995976,
4331975528992054828,
5311428878520309260,
495362057711802,
]));
const NONRESIDUE: Fq = field_new!(Fq, "11");
const TWO_ADICITY: u32 = 30; const TWO_ADICITY: u32 = 30;
@ -67,27 +53,14 @@ impl Fp3Parameters for Fq3Parameters {
1926648890365125214, 1926648890365125214,
13532564555356297305, 13532564555356297305,
3114545746551080, 3114545746551080,
0,
]; ];
/// (11^T, 0, 0)
#[rustfmt::skip] #[rustfmt::skip]
const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = ( 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])),
field_new!(Fq, "22168644070733283197994897338612733221095941481265408161807376791727499343083607817089033595478370212662133368413166734396127674284827734481031659015434501966360165723728649019457855887066657739809176476252080335185730833468062"),
FQ_ZERO,
FQ_ZERO,
); );
// Coefficients for the Frobenius automorphism. // Coefficients for the Frobenius automorphism.
@ -97,34 +70,8 @@ impl Fp3Parameters for Fq3Parameters {
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[ const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
FQ_ONE, 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,
])),
field_new!(Fq, "24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132"),
field_new!(Fq, "17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868"),
]; ];
// c2 = {c1[0], c1[2], c1[1]} // c2 = {c1[0], c1[2], c1[1]}

+ 5
- 71
mnt6_753/src/fields/fq6.rs
View File

@ -1,6 +1,5 @@
use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO}; use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO};
use ark_ff::{ use ark_ff::{
biginteger::BigInteger768 as BigInteger,
field_new, field_new,
fields::fp6_2over3::{Fp6, Fp6Parameters}, fields::fp6_2over3::{Fp6, Fp6Parameters},
}; };
@ -25,75 +24,10 @@ impl Fp6Parameters for Fq6Parameters {
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[ const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
FQ_ONE, 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,
])),
field_new!(Fq, "24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052133"),
field_new!(Fq, "24129022407817241407134263419936114379815707076943508280977368156625538709102831814843582780138963119807143081677569721953561801075623741378629346409604471234573396989178424163772589090105392407118197799904755622897541183052132"),
field_new!(Fq, "41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888458477323173057491593855069696241854796396165721416325350064441470418137846398469611935719059908164220784476160000"),
field_new!(Fq, "17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107868"),
field_new!(Fq, "17769468560101711995209951371304522748355002843010440790806134764399814103468274958215310983651375801610927890210888755369611256415970113691066895445191924931148019336171640277697829047741006062493737919155152541323243293107869"),
]; ];
} }

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