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GLV implementation for BLS12_377, BLS12_381 and BN254 (#158)

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This commit is contained in:
mmagician
2023-09-11 15:29:38 -06:00
committed by GitHub
parent 8765798eb0
commit 72a18b6ecf
17 changed files with 377 additions and 15 deletions
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1
CHANGELOG.md
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@@ -11,6 +11,7 @@
### Improvements
- [\#156](https://github.com/arkworks-rs/curves/pull/156) The hard part of the final exponentiation for bw6-761 relocated from arkworks/algebra.
- [\#158](https://github.com/arkworks-rs/curves/pull/158) Enabled GLV as the default scalar multiplication for BLS12-377, BLS12-381 and BN254.
### Bugfixes

39
bls12_377/src/curves/g1.rs
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@@ -3,14 +3,15 @@ use ark_ec::{
bls12::Bls12Config,
hashing::curve_maps::wb::{IsogenyMap, WBConfig},
models::{
short_weierstrass::{Affine as SWAffine, SWCurveConfig},
short_weierstrass::{Affine as SWAffine, Projective as SWProjective, SWCurveConfig},
twisted_edwards::{
Affine as TEAffine, MontCurveConfig, Projective as TEProjective, TECurveConfig,
},
},
scalar_mul::glv::GLVConfig,
CurveConfig,
};
use ark_ff::{AdditiveGroup, Field, MontFp, PrimeField, Zero};
use ark_ff::{AdditiveGroup, BigInt, Field, MontFp, PrimeField, Zero};
use ark_std::{ops::Neg, One};
use super::g1_swu_iso::{SwuIsoConfig, ISOGENY_MAP_TO_G1};
@@ -49,6 +50,12 @@ impl SWCurveConfig for Config {
Self::BaseField::zero()
}
#[inline]
fn mul_projective(p: &G1Projective, scalar: &[u64]) -> G1Projective {
let s = Self::ScalarField::from_sign_and_limbs(true, scalar);
GLVConfig::glv_mul_projective(*p, s)
}
#[inline]
fn clear_cofactor(p: &G1SWAffine) -> G1SWAffine {
// Using the effective cofactor.
@@ -59,6 +66,34 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static[Self::BaseField] = &[
MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231")
];
const LAMBDA: Self::ScalarField =
MontFp!("8444461749428370424248824938781546531284005582649182570233710176290576793600");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(true, BigInt!("91893752504881257701523279626832445441")),
(true, BigInt!("1")),
(false, BigInt!("1")),
(true, BigInt!("91893752504881257701523279626832445440")),
];
fn endomorphism(p: &SWProjective<Self>) -> SWProjective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &SWAffine<Self>) -> SWAffine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
fn x_minus_one() -> Fr {
const X: Fr = Fr::from_sign_and_limbs(!crate::Config::X_IS_NEGATIVE, crate::Config::X);
X - Fr::one()

36
bls12_377/src/curves/g2.rs
View File

@@ -2,12 +2,12 @@ use ark_ec::{
bls12,
bls12::Bls12Config,
hashing::curve_maps::wb::{IsogenyMap, WBConfig},
models::CurveConfig,
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, Projective, SWCurveConfig},
AffineRepr, CurveGroup, PrimeGroup,
AffineRepr, CurveConfig, CurveGroup, PrimeGroup,
};
use ark_ff::{AdditiveGroup, Field, MontFp, Zero};
use ark_ff::{AdditiveGroup, BigInt, Field, MontFp, PrimeField, Zero};
use ark_std::ops::Neg;
use crate::*;
@@ -98,6 +98,36 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static[Self::BaseField] = &[
Fq2::new(
MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
Fq::ZERO
)
];
const LAMBDA: Self::ScalarField = MontFp!("91893752504881257701523279626832445440");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(false, BigInt!("91893752504881257701523279626832445440")),
(true, BigInt!("1")),
(false, BigInt!("1")),
(false, BigInt!("91893752504881257701523279626832445441")),
];
fn endomorphism(p: &Projective<Self>) -> Projective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);

2
bls12_377/src/curves/tests/mod.rs
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@@ -5,6 +5,8 @@ test_group!(g1; G1Projective; sw);
test_group!(g2; G2Projective; sw);
test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bls12_377>; msm);
test_pairing!(pairing; crate::Bls12_377);
test_group!(g1_glv; G1Projective; glv);
test_group!(g2_glv; G2Projective; glv);
test_h2c!(g1_h2c; "./src/curves/tests"; "BLS12377G1"; crate::g1::Config; crate::Fq; crate::Fq; 1);
test_h2c!(g2_hc2; "./src/curves/tests"; "BLS12377G2"; crate::g2::Config; crate::Fq2; crate::Fq; 2);

37
bls12_381/src/curves/g1.rs
View File

@@ -3,10 +3,11 @@ use ark_ec::{
bls12::Bls12Config,
hashing::curve_maps::wb::{IsogenyMap, WBConfig},
models::CurveConfig,
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, SWCurveConfig},
AffineRepr, PrimeGroup,
};
use ark_ff::{AdditiveGroup, MontFp, PrimeField, Zero};
use ark_ff::{AdditiveGroup, BigInt, MontFp, PrimeField, Zero};
use ark_serialize::{Compress, SerializationError};
use ark_std::{ops::Neg, One};
@@ -52,6 +53,12 @@ impl SWCurveConfig for Config {
Self::BaseField::zero()
}
#[inline]
fn mul_projective(p: &G1Projective, scalar: &[u64]) -> G1Projective {
let s = Self::ScalarField::from_sign_and_limbs(true, scalar);
GLVConfig::glv_mul_projective(*p, s)
}
#[inline]
fn is_in_correct_subgroup_assuming_on_curve(p: &G1Affine) -> bool {
// Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
@@ -142,6 +149,34 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static[Self::BaseField] = &[
MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350")
];
const LAMBDA: Self::ScalarField =
MontFp!("52435875175126190479447740508185965837461563690374988244538805122978187051009");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(true, BigInt!("228988810152649578064853576960394133504")),
(true, BigInt!("1")),
(false, BigInt!("1")),
(true, BigInt!("228988810152649578064853576960394133503")),
];
fn endomorphism(p: &G1Projective) -> G1Projective {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
fn one_minus_x() -> Fr {
const X: Fr = Fr::from_sign_and_limbs(!crate::Config::X_IS_NEGATIVE, crate::Config::X);
Fr::one() - X

33
bls12_381/src/curves/g2.rs
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@@ -5,10 +5,11 @@ use ark_ec::{
bls12::Bls12Config,
hashing::curve_maps::wb::{IsogenyMap, WBConfig},
models::CurveConfig,
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, Projective, SWCurveConfig},
AffineRepr, CurveGroup, PrimeGroup,
};
use ark_ff::{AdditiveGroup, Field, MontFp, Zero};
use ark_ff::{AdditiveGroup, BigInt, Field, MontFp, PrimeField, Zero};
use ark_serialize::{Compress, SerializationError};
use super::{
@@ -185,6 +186,36 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static[Self::BaseField] = &[
Fq2::new(
MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
Fq::ZERO
)
];
const LAMBDA: Self::ScalarField = MontFp!("228988810152649578064853576960394133503");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(false, BigInt!("228988810152649578064853576960394133503")),
(true, BigInt!("1")),
(false, BigInt!("1")),
(false, BigInt!("228988810152649578064853576960394133504")),
];
fn endomorphism(p: &Projective<Self>) -> Projective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);

2
bls12_381/src/curves/tests/mod.rs
View File

@@ -8,6 +8,8 @@ use crate::{Bls12_381, Fq, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projecti
test_group!(g1; G1Projective; sw);
test_group!(g2; G2Projective; sw);
test_group!(g1_glv; G1Projective; glv);
test_group!(g2_glv; G2Projective; glv);
test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bls12_381>; msm);
test_pairing!(pairing; crate::Bls12_381);
test_h2c!(g1_h2c; "./src/curves/tests"; "BLS12381G1"; crate::g1::Config; crate::Fq; crate::Fq; 1);

42
bn254/src/curves/g1.rs
View File

@@ -1,8 +1,10 @@
use ark_ec::{
bn,
models::{short_weierstrass::SWCurveConfig, CurveConfig},
short_weierstrass::Affine,
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, Projective},
};
use ark_ff::{AdditiveGroup, Field, MontFp, Zero};
use ark_ff::{AdditiveGroup, BigInt, Field, MontFp, PrimeField, Zero};
use crate::{Fq, Fr};
@@ -36,6 +38,42 @@ impl SWCurveConfig for Config {
fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
Self::BaseField::zero()
}
#[inline]
fn mul_projective(
p: &bn::G1Projective<crate::Config>,
scalar: &[u64],
) -> bn::G1Projective<crate::Config> {
let s = Self::ScalarField::from_sign_and_limbs(true, scalar);
GLVConfig::glv_mul_projective(*p, s)
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static [Self::BaseField] = &[MontFp!(
"21888242871839275220042445260109153167277707414472061641714758635765020556616"
)];
const LAMBDA: Self::ScalarField =
MontFp!("21888242871839275217838484774961031246154997185409878258781734729429964517155");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(false, BigInt!("147946756881789319000765030803803410728")),
(true, BigInt!("9931322734385697763")),
(false, BigInt!("9931322734385697763")),
(false, BigInt!("147946756881789319010696353538189108491")),
];
fn endomorphism(p: &Projective<Self>) -> Projective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
/// G1_GENERATOR_X = 1

34
bn254/src/curves/g2.rs
View File

@@ -1,8 +1,9 @@
use ark_ec::{
models::{short_weierstrass::SWCurveConfig, CurveConfig},
short_weierstrass::Affine,
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, Projective},
};
use ark_ff::{AdditiveGroup, MontFp, Zero};
use ark_ff::{AdditiveGroup, BigInt, MontFp, PrimeField, Zero};
use crate::{Fq, Fq2, Fr};
@@ -50,6 +51,35 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static [Self::BaseField] = &[Fq2::new(
MontFp!("21888242871839275220042445260109153167277707414472061641714758635765020556616"),
Fq::ZERO,
)];
const LAMBDA: Self::ScalarField =
MontFp!("4407920970296243842393367215006156084916469457145843978461");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(false, BigInt!("147946756881789319010696353538189108491")),
(false, BigInt!("9931322734385697763")),
(true, BigInt!("9931322734385697763")),
(false, BigInt!("147946756881789319000765030803803410728")),
];
fn endomorphism(p: &Projective<Self>) -> Projective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
pub const G2_GENERATOR_X: Fq2 = Fq2::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
pub const G2_GENERATOR_Y: Fq2 = Fq2::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);

2
bn254/src/curves/tests.rs
View File

@@ -7,3 +7,5 @@ test_group!(g1; G1Projective; sw);
test_group!(g2; G2Projective; sw);
test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bn254>; msm);
test_pairing!(pairing; crate::Bn254);
test_group!(g1_glv; G1Projective; glv);
test_group!(g2_glv; G2Projective; glv);

43
bw6_761/src/curves/g1.rs
View File

@@ -1,8 +1,9 @@
use ark_ec::{
models::{short_weierstrass::SWCurveConfig, CurveConfig},
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, Projective},
};
use ark_ff::{AdditiveGroup, MontFp};
use ark_ff::{AdditiveGroup, BigInt, MontFp, PrimeField};
use crate::{Fq, Fr};
@@ -49,6 +50,46 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static [Self::BaseField] = &[MontFp!(
"4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"
)];
const LAMBDA: Self::ScalarField =
MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(
true,
BigInt!("293634935485640680722085584138834120324914961969255022593"),
),
(
false,
BigInt!("293634935485640680722085584138834120315328839056164388863"),
),
(
true,
BigInt!("293634935485640680722085584138834120315328839056164388863"),
),
(
true,
BigInt!("587269870971281361444171168277668240640243801025419411456"),
),
];
fn endomorphism(p: &Projective<Self>) -> Projective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
/// G1_GENERATOR_X =
/// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237
pub const G1_GENERATOR_X: Fq = MontFp!("6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");

43
bw6_761/src/curves/g2.rs
View File

@@ -1,8 +1,9 @@
use ark_ec::{
models::{short_weierstrass::SWCurveConfig, CurveConfig},
scalar_mul::glv::GLVConfig,
short_weierstrass::{Affine, Projective},
};
use ark_ff::{AdditiveGroup, MontFp};
use ark_ff::{AdditiveGroup, BigInt, MontFp, PrimeField};
use crate::{Fq, Fr};
@@ -50,6 +51,46 @@ impl SWCurveConfig for Config {
}
}
impl GLVConfig for Config {
const ENDO_COEFFS: &'static [Self::BaseField] = &[
MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
];
const LAMBDA: Self::ScalarField =
MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(
true,
BigInt!("293634935485640680722085584138834120315328839056164388863"),
),
(
false,
BigInt!("293634935485640680722085584138834120324914961969255022593"),
),
(
true,
BigInt!("293634935485640680722085584138834120324914961969255022593"),
),
(
true,
BigInt!("587269870971281361444171168277668240640243801025419411456"),
),
];
fn endomorphism(p: &Projective<Self>) -> Projective<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine<Self>) -> Affine<Self> {
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
/// G2_GENERATOR_X =
/// 6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428
pub const G2_GENERATOR_X: Fq = MontFp!("6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");

2
bw6_761/src/curves/tests.rs
View File

@@ -6,3 +6,5 @@ test_group!(g1; G1Projective; sw);
test_group!(g2; G2Projective; sw);
test_group!(pairing_output; ark_ec::pairing::PairingOutput<BW6_761>; msm);
test_pairing!(pairing; crate::BW6_761);
test_group!(g1_glv; G1Projective; glv);
test_group!(g2_glv; G2Projective; glv);

37
pallas/src/curves/mod.rs
View File

@@ -1,8 +1,9 @@
use ark_ec::{
models::CurveConfig,
scalar_mul::glv::GLVConfig,
short_weierstrass::{self as sw, SWCurveConfig},
};
use ark_ff::{AdditiveGroup, Field, MontFp, Zero};
use ark_ff::{AdditiveGroup, BigInt, Field, MontFp, PrimeField, Zero};
use crate::{fq::Fq, fr::Fr};
@@ -42,6 +43,40 @@ impl SWCurveConfig for PallasConfig {
}
}
impl GLVConfig for PallasConfig {
const ENDO_COEFFS: &'static [Self::BaseField] = &[MontFp!(
"20444556541222657078399132219657928148671392403212669005631716460534733845831"
)];
const LAMBDA: Self::ScalarField =
MontFp!("26005156700822196841419187675678338661165322343552424574062261873906994770353");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(false, BigInt!("98231058071100081932162823354453065728")),
(true, BigInt!("98231058071186745657228807397848383489")),
(false, BigInt!("196462116142286827589391630752301449217")),
(false, BigInt!("98231058071100081932162823354453065728")),
];
fn endomorphism(p: &Projective) -> Projective {
// Endomorphism of the points on the curve.
// endomorphism_p(x,y) = (BETA * x, y)
// where BETA is a non-trivial cubic root of unity in Fq.
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine) -> Affine {
// Endomorphism of the points on the curve.
// endomorphism_p(x,y) = (BETA * x, y)
// where BETA is a non-trivial cubic root of unity in Fq.
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
/// G_GENERATOR_X = -1
pub const G_GENERATOR_X: Fq = MontFp!("-1");

1
pallas/src/curves/tests.rs
View File

@@ -2,3 +2,4 @@ use crate::Projective;
use ark_algebra_test_templates::*;
test_group!(g1; Projective; sw);
test_group!(g1_glv; Projective; glv);

37
vesta/src/curves/mod.rs
View File

@@ -1,9 +1,10 @@
use crate::{fq::Fq, fr::Fr};
use ark_ec::{
models::CurveConfig,
scalar_mul::glv::GLVConfig,
short_weierstrass::{self as sw, SWCurveConfig},
};
use ark_ff::{AdditiveGroup, Field, MontFp, Zero};
use ark_ff::{AdditiveGroup, BigInt, Field, MontFp, PrimeField, Zero};
#[cfg(test)]
mod tests;
@@ -41,6 +42,40 @@ impl SWCurveConfig for VestaConfig {
}
}
impl GLVConfig for VestaConfig {
const ENDO_COEFFS: &'static [Self::BaseField] = &[MontFp!(
"26005156700822196841419187675678338661165322343552424574062261873906994770353"
)];
const LAMBDA: Self::ScalarField =
MontFp!("20444556541222657078399132219657928148671392403212669005631716460534733845831");
const SCALAR_DECOMP_COEFFS: [(bool, <Self::ScalarField as PrimeField>::BigInt); 4] = [
(false, BigInt!("98231058071100081932162823354453065729")),
(true, BigInt!("98231058071186745657228807397848383488")),
(false, BigInt!("196462116142286827589391630752301449217")),
(false, BigInt!("98231058071100081932162823354453065729")),
];
fn endomorphism(p: &Projective) -> Projective {
// Endomorphism of the points on the curve.
// endomorphism_p(x,y) = (BETA * x, y)
// where BETA is a non-trivial cubic root of unity in Fq.
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
fn endomorphism_affine(p: &Affine) -> Affine {
// Endomorphism of the points on the curve.
// endomorphism_p(x,y) = (BETA * x, y)
// where BETA is a non-trivial cubic root of unity in Fq.
let mut res = (*p).clone();
res.x *= Self::ENDO_COEFFS[0];
res
}
}
/// G_GENERATOR_X = -1
/// Encoded in Montgomery form, so the value here is -R mod p.
pub const G_GENERATOR_X: Fq = MontFp!("-1");

1
vesta/src/curves/tests.rs
View File

@@ -2,3 +2,4 @@ use crate::Projective;
use ark_algebra_test_templates::*;
test_group!(g1; Projective; sw);
test_group!(g1_glv; Projective; glv);