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Update BW6-761

fq2_neg_nonresidue
Pratyush Mishra 4 years ago
parent
31664a0e2e
commit
6a6b3711c6
5 changed files with 31 additions and 314 deletions
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  1. +6
    -55
      bw6_761/src/curves/g1.rs
  2. +6
    -55
      bw6_761/src/curves/g2.rs
  3. +2
    -2
      bw6_761/src/fields/fq.rs
  4. +11
    -117
      bw6_761/src/fields/fq3.rs
  5. +6
    -85
      bw6_761/src/fields/fq6.rs

+ 6
- 55
bw6_761/src/curves/g1.rs
View File

@ -3,10 +3,7 @@ use ark_ec::{
models::{ModelParameters, SWModelParameters}, models::{ModelParameters, SWModelParameters},
short_weierstrass_jacobian::{GroupAffine, GroupProjective}, short_weierstrass_jacobian::{GroupAffine, GroupProjective},
}; };
use ark_ff::{
biginteger::{BigInteger384, BigInteger768},
field_new,
};
use ark_ff::field_new;
pub type G1Affine = GroupAffine<Parameters>; pub type G1Affine = GroupAffine<Parameters>;
pub type G1Projective = GroupProjective<Parameters>; pub type G1Projective = GroupProjective<Parameters>;
@ -23,24 +20,11 @@ impl SWModelParameters for Parameters {
/// COEFF_A = 0 /// COEFF_A = 0
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_A: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
const COEFF_A: Fq = field_new!(Fq, "0");
/// COEFF_B = -1 /// COEFF_B = -1
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_B: Fq = field_new!(Fq, BigInteger768([
0xf29a000000007ab6,
0x8c391832e000739b,
0x77738a6b6870f959,
0xbe36179047832b03,
0x84f3089e56574722,
0xc5a3614ac0b1d984,
0x5c81153f4906e9fe,
0x4d28be3a9f55c815,
0xd72c1d6f77d5f5c5,
0x73a18e069ac04458,
0xf9dfaa846595555f,
0xd0f0a60a5be58c,
]));
const COEFF_B: Fq = field_new!(Fq, "-1");
/// COFACTOR = /// COFACTOR =
/// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194876 /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194876
@ -57,14 +41,7 @@ impl SWModelParameters for Parameters {
/// COFACTOR^(-1) mod r = /// COFACTOR^(-1) mod r =
/// 91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804 /// 91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804
#[rustfmt::skip] #[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
489703175600125849,
3883341943836920852,
1678256062427438196,
5848789333018172718,
7127967896440782320,
71512347676739162,
]));
const COFACTOR_INV: Fr = field_new!(Fr, "91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804");
/// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y) /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
@ -79,35 +56,9 @@ impl SWModelParameters for Parameters {
/// G1_GENERATOR_X = /// G1_GENERATOR_X =
/// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237 /// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237
#[rustfmt::skip] #[rustfmt::skip]
pub const G1_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
0xd6e42d7614c2d770,
0x4bb886eddbc3fc21,
0x64648b044098b4d2,
0x1a585c895a422985,
0xf1a9ac17cf8685c9,
0x352785830727aea5,
0xddf8cb12306266fe,
0x6913b4bfbc9e949a,
0x3a4b78d67ba5f6ab,
0x0f481c06a8d02a04,
0x91d4e7365c43edac,
0xf4d17cd48beca5,
]));
pub const G1_GENERATOR_X: Fq = field_new!(Fq, "6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");
/// G1_GENERATOR_Y = /// G1_GENERATOR_Y =
/// 2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099 /// 2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099
#[rustfmt::skip] #[rustfmt::skip]
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
0x97e805c4bd16411f,
0x870d844e1ee6dd08,
0x1eba7a37cb9eab4d,
0xd544c4df10b9889a,
0x8fe37f21a33897be,
0xe9bf99a43a0885d2,
0xd7ee0c9e273de139,
0xaa6a9ec7a38dd791,
0x8f95d3fcf765da8e,
0x42326e7db7357c99,
0xe217e407e218695f,
0x9d1eb23b7cf684,
]));
pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099");

+ 6
- 55
bw6_761/src/curves/g2.rs
View File

@ -3,10 +3,7 @@ use ark_ec::{
models::{ModelParameters, SWModelParameters}, models::{ModelParameters, SWModelParameters},
short_weierstrass_jacobian::{GroupAffine, GroupProjective}, short_weierstrass_jacobian::{GroupAffine, GroupProjective},
}; };
use ark_ff::{
biginteger::{BigInteger384, BigInteger768},
field_new,
};
use ark_ff::field_new;
pub type G2Affine = GroupAffine<Parameters>; pub type G2Affine = GroupAffine<Parameters>;
pub type G2Projective = GroupProjective<Parameters>; pub type G2Projective = GroupProjective<Parameters>;
@ -23,24 +20,11 @@ impl SWModelParameters for Parameters {
/// COEFF_A = 0 /// COEFF_A = 0
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_A: Fq = field_new!(Fq, BigInteger768([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
const COEFF_A: Fq = field_new!(Fq, "0");
/// COEFF_B = 4 /// COEFF_B = 4
#[rustfmt::skip] #[rustfmt::skip]
const COEFF_B: Fq = field_new!(Fq, BigInteger768([
0x136efffffffe16c9,
0x82cf5a6dcffe3319,
0x6458c05f1f0e0741,
0xd10ae605e52a4eda,
0x41ca591c0266e100,
0x7d0fd59c3626929f,
0x9967dc004d00c112,
0x1ccff9c033379af5,
0x9ad6ec10a23f63af,
0x5cec11251a72c235,
0x8d18b1ae789ba83e,
10403402007434220,
]));
const COEFF_B: Fq = field_new!(Fq, "4");
/// COFACTOR = /// COFACTOR =
/// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194869 /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194869
@ -57,14 +41,7 @@ impl SWModelParameters for Parameters {
/// COFACTOR^(-1) mod r = /// COFACTOR^(-1) mod r =
/// 214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124 /// 214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124
#[rustfmt::skip] #[rustfmt::skip]
const COFACTOR_INV: Fr = field_new!(Fr, BigInteger384([
14378295991815829998,
14586153992421458638,
9788477762582722914,
12654821707953664524,
15185631607604703397,
26723985783783076,
]));
const COFACTOR_INV: Fr = field_new!(Fr, "214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124");
/// 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) =
@ -79,35 +56,9 @@ impl SWModelParameters for Parameters {
/// G2_GENERATOR_X = /// G2_GENERATOR_X =
/// 6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428 /// 6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428
#[rustfmt::skip] #[rustfmt::skip]
pub const G2_GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
0x3d902a84cd9f4f78,
0x864e451b8a9c05dd,
0xc2b3c0d6646c5673,
0x17a7682def1ecb9d,
0xbe31a1e0fb768fe3,
0x4df125e09b92d1a6,
0x0943fce635b02ee9,
0xffc8e7ad0605e780,
0x8165c00a39341e95,
0x8ccc2ae90a0f094f,
0x73a8b8cc0ad09e0c,
0x11027e203edd9f4,
]));
pub const G2_GENERATOR_X: Fq = field_new!(Fq, "6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");
/// G2_GENERATOR_Y = /// G2_GENERATOR_Y =
/// 562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041 /// 562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041
#[rustfmt::skip] #[rustfmt::skip]
pub const G2_GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
0x9a159be4e773f67c,
0x6b957244aa8f4e6b,
0xa27b70c9c945a38c,
0xacb6a09fda11d0ab,
0x3abbdaa9bb6b1291,
0xdbdf642af5694c36,
0xb6360bb9560b369f,
0xac0bd1e822b8d6da,
0xfa355d17afe6945f,
0x8d6a0fc1fbcad35e,
0x72a63c7874409840,
0x114976e5b0db280,
]));
pub const G2_GENERATOR_Y: Fq = field_new!(Fq, "562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041");

+ 2
- 2
bw6_761/src/fields/fq.rs
View File

@ -8,8 +8,8 @@ pub type Fq = Fp768;
pub struct FqParameters; pub struct FqParameters;
pub const FQ_ONE: Fq = field_new!(Fq, FqParameters::R);
pub const FQ_ZERO: Fq = field_new!(Fq, BigInteger([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]));
pub const FQ_ONE: Fq = field_new!(Fq, "1");
pub const FQ_ZERO: Fq = field_new!(Fq, "0");
impl Fp768Parameters for FqParameters {} impl Fp768Parameters for FqParameters {}
impl FftParameters for FqParameters { impl FftParameters for FqParameters {

+ 11
- 117
bw6_761/src/fields/fq3.rs
View File

@ -1,10 +1,9 @@
use ark_ff::{ use ark_ff::{
biginteger::BigInteger768 as BigInteger,
field_new, field_new,
fields::fp3::{Fp3, Fp3Parameters}, fields::fp3::{Fp3, Fp3Parameters},
}; };
use crate::Fq;
use crate::{Fq, fields::{FQ_ZERO, FQ_ONE}};
pub type Fq3 = Fp3<Fq3Parameters>; pub type Fq3 = Fp3<Fq3Parameters>;
@ -16,20 +15,7 @@ impl Fp3Parameters for Fq3Parameters {
/// NONRESIDUE = -4 /// NONRESIDUE = -4
// Fq3 = Fq[u]/u^3+4 // Fq3 = Fq[u]/u^3+4
#[rustfmt::skip] #[rustfmt::skip]
const NONRESIDUE: Fq = field_new!(Fq, BigInteger([
0xe12e00000001e9c2,
0x63c1e3faa001cd69,
0xb1b4384fcbe29cf6,
0xc79630bc713d5a1d,
0x30127ac071851e2d,
0x0979f350dcd36af1,
0x6a66defed8b361f2,
0x53abac78b24d4e23,
0xb7ab89dede485a92,
0x5c3a0745675e8452,
0x446f17918c5f5700,
0xfdf24e3267fa1e,
]));
const NONRESIDUE: Fq = field_new!(Fq, "-4");
// (MODULUS^3 - 1) % 2^TWO_ADICITY == 0 // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
const TWO_ADICITY: u32 = 1; const TWO_ADICITY: u32 = 1;
@ -78,117 +64,25 @@ impl Fp3Parameters for Fq3Parameters {
// NONRESIDUE^T % q // NONRESIDUE^T % q
#[rustfmt::skip] #[rustfmt::skip]
const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = ( const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
field_new!(Fq, BigInteger([
0xf29a000000007ab6,
0x8c391832e000739b,
0x77738a6b6870f959,
0xbe36179047832b03,
0x84f3089e56574722,
0xc5a3614ac0b1d984,
0x5c81153f4906e9fe,
0x4d28be3a9f55c815,
0xd72c1d6f77d5f5c5,
0x73a18e069ac04458,
0xf9dfaa846595555f,
0xd0f0a60a5be58c,
])),
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, "6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
FQ_ZERO,
FQ_ZERO,
); );
// NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0) // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[ const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
field_new!(Fq, BigInteger([
0x0202ffffffff85d5,
0x5a5826358fff8ce7,
0x9e996e43827faade,
0xda6aff320ee47df4,
0xece9cb3e1d94b80b,
0xc0e667a25248240b,
0xa74da5bfdcad3905,
0x2352e7fe462f2103,
0x7b56588008b1c87c,
0x45848a63e711022f,
0xd7a81ebb9f65a9df,
0x51f77ef127e87d,
])),
field_new!(Fq, BigInteger([
0x7f96b51bd840c549,
0xd59782096496171f,
0x49b046fd9ce14bbc,
0x4b6163bba7527a56,
0xef6c92fb771d59f1,
0x0425bedbac1dfdc7,
0xd3ac39de759c0ffd,
0x9f43ed0e063a81d0,
0x5bd7d20b4f9a3ce2,
0x0411f03c36cf5c3c,
0x2d658fd49661c472,
0x1100249ae760b93,
])),
field_new!(Fq, BigInteger([
0x67a04ae427bfb5f8,
0x9d32d491eb6a5cff,
0x43d03c1cb68051d4,
0x0b75ca96f69859a5,
0x0763497f5325ec60,
0x48076b5c278dd94d,
0x8ca3965ff91efd06,
0x1e6077657ea02f5d,
0xcdd6c153a8c37724,
0x28b5b634e5c22ea4,
0x9e01e3efd42e902c,
0xe3d6815769a804,
])),
FQ_ONE,
field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
]; ];
// NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0) // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[ const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
field_new!(Fq, BigInteger([
0x0202ffffffff85d5,
0x5a5826358fff8ce7,
0x9e996e43827faade,
0xda6aff320ee47df4,
0xece9cb3e1d94b80b,
0xc0e667a25248240b,
0xa74da5bfdcad3905,
0x2352e7fe462f2103,
0x7b56588008b1c87c,
0x45848a63e711022f,
0xd7a81ebb9f65a9df,
0x51f77ef127e87d,
])),
field_new!(Fq, BigInteger([
0x67a04ae427bfb5f8,
0x9d32d491eb6a5cff,
0x43d03c1cb68051d4,
0x0b75ca96f69859a5,
0x0763497f5325ec60,
0x48076b5c278dd94d,
0x8ca3965ff91efd06,
0x1e6077657ea02f5d,
0xcdd6c153a8c37724,
0x28b5b634e5c22ea4,
0x9e01e3efd42e902c,
0xe3d6815769a804,
])),
field_new!(Fq, BigInteger([
0x7f96b51bd840c549,
0xd59782096496171f,
0x49b046fd9ce14bbc,
0x4b6163bba7527a56,
0xef6c92fb771d59f1,
0x0425bedbac1dfdc7,
0xd3ac39de759c0ffd,
0x9f43ed0e063a81d0,
0x5bd7d20b4f9a3ce2,
0x0411f03c36cf5c3c,
0x2d658fd49661c472,
0x1100249ae760b93,
])),
FQ_ONE,
field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
]; ];
#[inline(always)] #[inline(always)]

+ 6
- 85
bw6_761/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},
}; };
@ -18,89 +17,11 @@ impl Fp6Parameters for Fq6Parameters {
#[rustfmt::skip] #[rustfmt::skip]
const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[ const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
field_new!(Fq, BigInteger([
0x0202ffffffff85d5,
0x5a5826358fff8ce7,
0x9e996e43827faade,
0xda6aff320ee47df4,
0xece9cb3e1d94b80b,
0xc0e667a25248240b,
0xa74da5bfdcad3905,
0x2352e7fe462f2103,
0x7b56588008b1c87c,
0x45848a63e711022f,
0xd7a81ebb9f65a9df,
0x51f77ef127e87d,
])),
field_new!(Fq, BigInteger([
0x8cfcb51bd8404a93,
0x495e69d68495a383,
0xd23cbc9234705263,
0x8d2b4c2b5fcf4f52,
0x6a798a5d20c612ce,
0x3e825d90eb6c2443,
0x772b249f2c9525fe,
0x521b2ed366e4b9bb,
0x84abb49bd7c4471d,
0x907062359c0f17e3,
0x3385e55030cc6f12,
0x3f11a3a41a2606,
])),
field_new!(Fq, BigInteger([
0x7f96b51bd840c549,
0xd59782096496171f,
0x49b046fd9ce14bbc,
0x4b6163bba7527a56,
0xef6c92fb771d59f1,
0x0425bedbac1dfdc7,
0xd3ac39de759c0ffd,
0x9f43ed0e063a81d0,
0x5bd7d20b4f9a3ce2,
0x0411f03c36cf5c3c,
0x2d658fd49661c472,
0x1100249ae760b93,
])),
field_new!(Fq, BigInteger([
0xf29a000000007ab6,
0x8c391832e000739b,
0x77738a6b6870f959,
0xbe36179047832b03,
0x84f3089e56574722,
0xc5a3614ac0b1d984,
0x5c81153f4906e9fe,
0x4d28be3a9f55c815,
0xd72c1d6f77d5f5c5,
0x73a18e069ac04458,
0xf9dfaa846595555f,
0xd0f0a60a5be58c,
])),
field_new!(Fq, BigInteger([
0x67a04ae427bfb5f8,
0x9d32d491eb6a5cff,
0x43d03c1cb68051d4,
0x0b75ca96f69859a5,
0x0763497f5325ec60,
0x48076b5c278dd94d,
0x8ca3965ff91efd06,
0x1e6077657ea02f5d,
0xcdd6c153a8c37724,
0x28b5b634e5c22ea4,
0x9e01e3efd42e902c,
0xe3d6815769a804,
])),
field_new!(Fq, BigInteger([
0x75064ae427bf3b42,
0x10f9bc5f0b69e963,
0xcc5cb1b14e0f587b,
0x4d3fb306af152ea1,
0x827040e0fccea53d,
0x82640a1166dbffc8,
0x30228120b0181307,
0xd137b92adf4a6748,
0xf6aaa3e430ed815e,
0xb514282e4b01ea4b,
0xa422396b6e993acc,
0x12e5db4d0dc277,
])),
field_new!(Fq, "1"),
field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775649"),
field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
field_new!(Fq, "-1"),
field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292651"),
]; ];
} }

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