GLV implementation for BLS12_377, BLS12_381 and BN254

CHANGELOG.md

@@ -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
 

bls12_377/src/curves/g1.rs

@@ -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()

bls12_377/src/curves/g2.rs

@@ -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);
 

bls12_377/src/curves/tests/mod.rs

@@ -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);
 

bls12_381/src/curves/g1.rs

@@ -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

bls12_381/src/curves/g2.rs

@@ -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);
 

bls12_381/src/curves/tests/mod.rs

@@ -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);

bn254/src/curves/g1.rs

@@ -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

bn254/src/curves/g2.rs

@@ -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);
 

bn254/src/curves/tests.rs

@@ -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);