Update README.md (#189 )

Add archival notice to README (#188 )
Expose Bandersnatch generators (#184 )
2026-01-27 14:13:46 +01:00 · 2023-12-18 09:24:04 -08:00 · 2023-12-18 08:56:41 -08:00 · 2023-10-14 17:44:58 +02:00 · 2023-09-25 11:28:26 -07:00 · 2023-09-19 04:47:35 -07:00
85 changed files with 1586 additions and 191 deletions
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -50,7 +50,7 @@ jobs:
          toolchain: ${{ matrix.rust }}
          override: true

-      - uses: actions/cache@v2
+      - uses: actions/cache@v3
        with:
          path: |
            ~/.cargo/registry
@@ -104,6 +104,7 @@ jobs:
          - dir: curve-constraint-tests/
          - dir: mnt4_753/
          - dir: mnt6_753/
+          - dir: cp6_782/
    steps:
      - name: Checkout
        uses: actions/checkout@v3
@@ -115,11 +116,34 @@ jobs:
  test-mnt4-753:
    name: Test (mnt4_753/)
    runs-on: macos-latest
-    needs: [directories] # Waits for the directory listing job
    steps:
      - name: Checkout
        uses: actions/checkout@v3
-      - name: Run tests
+
+      - name: Check if source code updated
+        uses: dorny/paths-filter@v2.11.1
+        id: check-diff
+        with:
+          filters: |
+            mnt4_753_is_updated:
+              - 'mnt4_753/**'
+
+      - name: Generate lockfile
+        run: cargo generate-lockfile
+
+      - name: Check if deps updated
+        id: deps-updated
+        uses: actions/cache@v3
+        with:
+          path: |
+            ~/.cargo/registry
+            ~/.cargo/git
+            target
+          key: ${{ runner.os }}-cargo-${{ hashFiles('**/Cargo.lock') }}
+
+      - name: Conditionally run the tests
+        # if source code updated OR dependencies updated
+        if: ${{ steps.check-diff.outputs.mnt4_753_is_updated == 'true' || steps.deps-updated.outputs.cache-hit != 'true' }}
        run: |
          cd mnt4_753/
          cargo test --all-features
@@ -127,15 +151,74 @@ jobs:
  test-mnt6-753:
    name: Test (mnt6_753/)
    runs-on: macos-latest
-    needs: [directories] # Waits for the directory listing job
    steps:
      - name: Checkout
        uses: actions/checkout@v3
-      - name: Run tests
+
+      - name: Check if source code updated
+        uses: dorny/paths-filter@v2.11.1
+        id: check-diff
+        with:
+          filters: |
+            mnt6_753_is_updated:
+              - 'mnt6_753/**'
+
+      - name: Generate lockfile
+        run: cargo generate-lockfile
+
+      - name: Check if deps updated
+        id: deps-updated
+        uses: actions/cache@v3
+        with:
+          path: |
+            ~/.cargo/registry
+            ~/.cargo/git
+            target
+          key: ${{ runner.os }}-cargo-${{ hashFiles('**/Cargo.lock') }}
+
+      - name: Conditionally run the tests
+        # if source code updated OR dependencies updated
+        if: ${{ steps.check-diff.outputs.mnt6_753_is_updated == 'true' || steps.deps-updated.outputs.cache-hit != 'true' }}
        run: |
          cd mnt6_753/
          cargo test --all-features

+  test-cp6_782:
+    name: Test (cp6_782/)
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+
+      - name: Check if source code updated
+        uses: dorny/paths-filter@v2.11.1
+        id: check-diff
+        with:
+          filters: |
+            cp6_782_is_updated:
+              - 'cp6_782/**'
+
+      - name: Generate lockfile
+        run: cargo generate-lockfile
+
+      - name: Check if deps updated
+        id: deps-updated
+        uses: actions/cache@v3
+        with:
+          path: |
+            ~/.cargo/registry
+            ~/.cargo/git
+            target
+          key: ${{ runner.os }}-cargo-${{ hashFiles('**/Cargo.lock') }}
+
+      - name: Conditionally run the tests
+        # if source code updated OR dependencies updated
+        if: ${{ steps.check-diff.outputs.cp6_782_is_updated == 'true' || steps.deps-updated.outputs.cache-hit != 'true' }}
+        run: |
+          cd cp6_782/
+          cargo test --all-features
+
+
  docs:
    name: Check Documentation
    runs-on: ubuntu-latest
@@ -164,14 +247,14 @@ jobs:
      - name: Checkout
        uses: actions/checkout@v3

-      - name: Install Rust (${{ matrix.rust }})
+      - name: Install Rust
        uses: actions-rs/toolchain@v1
        with:
          toolchain: stable
          target: thumbv6m-none-eabi
          override: true

-      - uses: actions/cache@v2
+      - uses: actions/cache@v3
        with:
          path: |
            ~/.cargo/registry
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,10 +6,19 @@

 ### Features

+- [\#156](https://github.com/arkworks-rs/curves/pull/156) Add the bw6-767 curve.
+- [\#174](https://github.com/arkworks-rs/curves/pull/174) Add the "grumpkin" curve.
+
+
 ### 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

+- [\#176](https://github.com/arkworks-rs/curves/pull/176) Non-canonical infinity point and bad flags in BLS12-381 serialization should fail.
+
 ## v0.4.0
 - [\#76](https://github.com/arkworks-rs/curves/pull/76) twisted Edwards parameters for bls12-377
 - Fixed curve benches
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -9,6 +9,8 @@ members = [
    "bw6_761",
    "ed_on_bw6_761",

+    "bw6_767",
+
    "cp6_782",
    "ed_on_cp6_782",

@@ -18,6 +20,7 @@ members = [

    "bn254",
    "ed_on_bn254",
+    "grumpkin",

    "mnt4_298",
    "mnt6_298",
@@ -71,4 +74,5 @@ ark-ec = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-poly = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-serialize = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra/" }
+ark-algebra-bench-templates = { git = "https://github.com/arkworks-rs/algebra/" }
 ark-r1cs-std = { git = "https://github.com/arkworks-rs/r1cs-std/" }
--- a/README.md
+++ b/README.md
@@ -1,4 +1,8 @@
-# Curve implementations
+# Notice
+
+This repository is no longer maintained, and PRs to add or modify curves should instead be made against [arkworks-rs/algebra](https://github.com/arkworks-rs/algebra); all the curves implemented here have moved to the [`curves` folder](https://github.com/arkworks-rs/algebra/tree/master/curves) of that repository.
+
+## Curve implementations

 This repository contains implementations of some popular elliptic curves. The curve API implemented here matches the curve traits defined [here](https://github.com/arkworks-rs/algebra/blob/master/ec/src/lib.rs) in the [arkworks-rs/algebra](https://github.com/arkworks-rs/algebra) repository.

@@ -20,6 +24,7 @@ This repository contains implementations of some popular elliptic curves. The cu
 ### BN254 and related curves
 * [`ark-bn254`](bn254): Implements the BN254 pairing-friendly curve
 * [`ark-ed-on-bn254`](ed_on_bn254): Implements a Twisted Edwards curve atop the scalar field of BN254
+* [`ark-grumpkin`](grumpkin): Implements the Grumpkin curve. A curve that forms a cycle with bn254.

 ### MNT-298 cycle of curves and related curves
 * [`ark-mnt4-298`](mnt4_298): Implements the MNT4-298 pairing-friendly curve. This curve forms a pairing-friendly cycle with MNT6-298
--- a/bls12_377/src/curves/g1.rs
+++ b/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::{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()
--- a/bls12_377/src/curves/g2.rs
+++ b/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, Group,
+    AffineRepr, CurveConfig, CurveGroup, PrimeGroup,
 };

-use ark_ff::{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);

--- a/bls12_377/src/curves/tests/mod.rs
+++ b/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);

--- a/bls12_381/benches/bls12_381.rs
+++ b/bls12_381/benches/bls12_381.rs
@@ -1,5 +1,4 @@
 use ark_algebra_bench_templates::*;
-
 use ark_bls12_381::{
    fq::Fq, fq2::Fq2, fr::Fr, Bls12_381, Fq12, G1Projective as G1, G2Projective as G2,
 };
--- a/bls12_381/src/curves/g1.rs
+++ b/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, Group,
+    AffineRepr, PrimeGroup,
 };
-use ark_ff::{Field, 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
@@ -180,6 +215,7 @@ mod test {

    use super::*;
    use crate::g1;
+    use ark_serialize::CanonicalDeserialize;
    use ark_std::{rand::Rng, UniformRand};

    fn sample_unchecked() -> Affine<g1::Config> {
@@ -204,4 +240,55 @@ mod test {
            assert!(p.is_in_correct_subgroup_assuming_on_curve());
        }
    }
+
+    #[test]
+    fn non_canonical_identity_point() {
+        let non_canonical_hex = "c01000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000";
+        let non_canonical_bytes = hex::decode(non_canonical_hex).unwrap();
+        assert_eq!(non_canonical_bytes.len(), 48);
+
+        let maybe_affine_point: Result<G1Affine, ark_serialize::SerializationError> =
+            CanonicalDeserialize::deserialize_compressed(&non_canonical_bytes[..]);
+
+        assert!(maybe_affine_point.is_err());
+
+        let non_canonical_hex_uncompressed = "c00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001";
+        let non_canonical_bytes = hex::decode(non_canonical_hex_uncompressed).unwrap();
+        assert_eq!(non_canonical_bytes.len(), 96);
+
+        let maybe_affine_point: Result<G1Affine, ark_serialize::SerializationError> =
+            CanonicalDeserialize::deserialize_uncompressed(&non_canonical_bytes[..]);
+
+        assert!(maybe_affine_point.is_err())
+    }
+
+    #[test]
+    fn bad_flag_combination() {
+        // See https://github.com/zkcrypto/pairing/tree/fa8103764a07bd273927447d434de18aace252d3/src/bls12_381#serialization
+        // - Bit 1 is compressed/uncompressed
+        // - Bit 2 is infinity
+        // - Bit 3 is lexicographical order for compressed point deserialization
+        // Hence `0b1110` ("e" in hex) or `0b0110` ("6" in hex") are both nonsensical.
+
+        // uncompressed, but lexicographically largest flag is set
+        let non_canonical_hex = "600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000";
+        let non_canonical_bytes = hex::decode(non_canonical_hex).unwrap();
+        assert_eq!(non_canonical_bytes.len(), 48);
+
+        let maybe_affine_point: Result<G1Affine, ark_serialize::SerializationError> =
+            CanonicalDeserialize::deserialize_compressed(&non_canonical_bytes[..]);
+
+        assert!(maybe_affine_point.is_err());
+
+        // compressed, but infinity flag is set and lexicographically largest flag is
+        // set
+        let non_canonical_hex_2 = "e00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000";
+
+        let non_canonical_bytes = hex::decode(non_canonical_hex_2).unwrap();
+        assert_eq!(non_canonical_bytes.len(), 48);
+
+        let maybe_affine_point: Result<G1Affine, ark_serialize::SerializationError> =
+            CanonicalDeserialize::deserialize_compressed(&non_canonical_bytes[..]);
+        assert!(maybe_affine_point.is_err());
+    }
 }
--- a/bls12_381/src/curves/g2.rs
+++ b/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, Group,
+    AffineRepr, CurveGroup, PrimeGroup,
 };
-use ark_ff::{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);

--- a/bls12_381/src/curves/tests/mod.rs
+++ b/bls12_381/src/curves/tests/mod.rs
@@ -1,5 +1,5 @@
 use ark_algebra_test_templates::*;
-use ark_ec::{AffineRepr, CurveGroup, Group};
+use ark_ec::{AffineRepr, CurveGroup, PrimeGroup};
 use ark_ff::{fields::Field, One, UniformRand, Zero};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Compress, Validate};
 use ark_std::{rand::Rng, test_rng, vec};
@@ -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);
--- a/bls12_381/src/curves/util.rs
+++ b/bls12_381/src/curves/util.rs
@@ -14,17 +14,28 @@ pub struct EncodingFlags {
 }

 impl EncodingFlags {
-    pub fn get_flags(bytes: &[u8]) -> Self {
+    /// Fetches the flags from the byte-string
+    pub fn get_flags(bytes: &[u8]) -> Result<Self, SerializationError> {
        let compression_flag_set = (bytes[0] >> 7) & 1;
        let infinity_flag_set = (bytes[0] >> 6) & 1;
        let sort_flag_set = (bytes[0] >> 5) & 1;

-        Self {
-            is_compressed: compression_flag_set == 1,
-            is_infinity: infinity_flag_set == 1,
-            is_lexographically_largest: sort_flag_set == 1,
+        let is_compressed = compression_flag_set == 1;
+        let is_infinity = infinity_flag_set == 1;
+        let is_lexographically_largest = sort_flag_set == 1;
+
+        if is_lexographically_largest && (!is_compressed || is_infinity) {
+            return Err(SerializationError::InvalidData);
        }
+
+        Ok(Self {
+            is_compressed,
+            is_infinity,
+            is_lexographically_largest,
+        })
    }
+
+    /// Encodes the flags into the byte-string
    pub fn encode_flags(&self, bytes: &mut [u8]) {
        if self.is_compressed {
            bytes[0] |= 1 << 7;
@@ -38,6 +49,13 @@ impl EncodingFlags {
            bytes[0] |= 1 << 5;
        }
    }
+
+    /// Removes the flags from the byte-string.
+    ///
+    /// This reverses the effects of `encode_flags`.
+    pub fn remove_flags(bytes: &mut [u8]) {
+        bytes[0] &= 0b0001_1111;
+    }
 }

 pub(crate) fn deserialize_fq(bytes: [u8; 48]) -> Option<Fq> {
@@ -71,20 +89,15 @@ pub(crate) fn serialize_fq(field: Fq) -> [u8; 48] {
    result
 }

-pub(crate) fn read_fq_with_offset(
-    bytes: &[u8],
-    offset: usize,
-    mask: bool,
-) -> Result<Fq, ark_serialize::SerializationError> {
+fn read_bytes_with_offset(bytes: &[u8], offset: usize, mask: bool) -> [u8; G1_SERIALIZED_SIZE] {
    let mut tmp = [0; G1_SERIALIZED_SIZE];
    // read `G1_SERIALIZED_SIZE` bytes
    tmp.copy_from_slice(&bytes[offset * G1_SERIALIZED_SIZE..G1_SERIALIZED_SIZE * (offset + 1)]);

    if mask {
-        // Mask away the flag bits
-        tmp[0] &= 0b0001_1111;
+        EncodingFlags::remove_flags(&mut tmp);
    }
-    deserialize_fq(tmp).ok_or(SerializationError::InvalidData)
+    tmp
 }

 pub(crate) fn read_g1_compressed<R: ark_serialize::Read>(
@@ -97,20 +110,26 @@ pub(crate) fn read_g1_compressed<R: ark_serialize::Read>(
        .ok_or(SerializationError::InvalidData)?;

    // Obtain the three flags from the start of the byte sequence
-    let flags = EncodingFlags::get_flags(&bytes[..]);
+    let flags = EncodingFlags::get_flags(&bytes[..])?;

-    // we expect to be deserializing a compressed point
+    // We expect to be deserializing a compressed point
    if !flags.is_compressed {
        return Err(SerializationError::UnexpectedFlags);
    }

+    // Attempt to obtain the x-coordinate
+    let x_bytes = read_bytes_with_offset(&bytes, 0, true);
+
    if flags.is_infinity {
+        // Check that the `x` co-ordinate was `0`
+        if x_bytes != [0u8; 48] {
+            return Err(SerializationError::InvalidData);
+        }
+
        return Ok(G1Affine::zero());
    }

-    // Attempt to obtain the x-coordinate
-    let x = read_fq_with_offset(&bytes, 0, true)?;
-
+    let x = deserialize_fq(x_bytes).ok_or(SerializationError::InvalidData)?;
    let p = G1Affine::get_point_from_x_unchecked(x, flags.is_lexographically_largest)
        .ok_or(SerializationError::InvalidData)?;

@@ -126,22 +145,27 @@ pub(crate) fn read_g1_uncompressed<R: ark_serialize::Read>(
        .map_err(|_| SerializationError::InvalidData)?;

    // Obtain the three flags from the start of the byte sequence
-    let flags = EncodingFlags::get_flags(&bytes[..]);
+    let flags = EncodingFlags::get_flags(&bytes[..])?;

    // we expect to be deserializing an uncompressed point
    if flags.is_compressed {
        return Err(SerializationError::UnexpectedFlags);
    }

+    let x_bytes = read_bytes_with_offset(&bytes, 0, true);
+    let y_bytes = read_bytes_with_offset(&bytes, 1, false);
+
    if flags.is_infinity {
+        if x_bytes != [0u8; 48] || y_bytes != [0u8; 48] {
+            return Err(SerializationError::InvalidData);
+        }
        return Ok(G1Affine::zero());
    }

    // Attempt to obtain the x-coordinate
-    let x = read_fq_with_offset(&bytes, 0, true)?;
+    let x = deserialize_fq(x_bytes).ok_or(SerializationError::InvalidData)?;
    // Attempt to obtain the y-coordinate
-    let y = read_fq_with_offset(&bytes, 1, false)?;
-
+    let y = deserialize_fq(y_bytes).ok_or(SerializationError::InvalidData)?;
    let p = G1Affine::new_unchecked(x, y);

    Ok(p)
@@ -156,21 +180,26 @@ pub(crate) fn read_g2_compressed<R: ark_serialize::Read>(
        .map_err(|_| SerializationError::InvalidData)?;

    // Obtain the three flags from the start of the byte sequence
-    let flags = EncodingFlags::get_flags(&bytes);
+    let flags = EncodingFlags::get_flags(&bytes)?;

    // we expect to be deserializing a compressed point
    if !flags.is_compressed {
        return Err(SerializationError::UnexpectedFlags);
    }

+    let xc1_bytes = read_bytes_with_offset(&bytes, 0, true);
+    let xc0_bytes = read_bytes_with_offset(&bytes, 1, false);
+
    if flags.is_infinity {
+        if xc1_bytes != [0u8; 48] || xc0_bytes != [0u8; 48] {
+            return Err(SerializationError::InvalidData);
+        }
        return Ok(G2Affine::zero());
    }

    // Attempt to obtain the x-coordinate
-    let xc1 = read_fq_with_offset(&bytes, 0, true)?;
-    let xc0 = read_fq_with_offset(&bytes, 1, false)?;
-
+    let xc1 = deserialize_fq(xc1_bytes).ok_or(SerializationError::InvalidData)?;
+    let xc0 = deserialize_fq(xc0_bytes).ok_or(SerializationError::InvalidData)?;
    let x = Fq2::new(xc0, xc1);

    let p = G2Affine::get_point_from_x_unchecked(x, flags.is_lexographically_largest)
@@ -188,25 +217,39 @@ pub(crate) fn read_g2_uncompressed<R: ark_serialize::Read>(
        .map_err(|_| SerializationError::InvalidData)?;

    // Obtain the three flags from the start of the byte sequence
-    let flags = EncodingFlags::get_flags(&bytes);
+    let flags = EncodingFlags::get_flags(&bytes)?;

    // we expect to be deserializing an uncompressed point
    if flags.is_compressed {
        return Err(SerializationError::UnexpectedFlags);
    }

+    let xc1_bytes = read_bytes_with_offset(&bytes, 0, true);
+    let xc0_bytes = read_bytes_with_offset(&bytes, 1, false);
+
+    let yc1_bytes = read_bytes_with_offset(&bytes, 2, false);
+    let yc0_bytes = read_bytes_with_offset(&bytes, 3, false);
+
    if flags.is_infinity {
+        if xc1_bytes != [0u8; 48]
+            || xc0_bytes != [0u8; 48]
+            || yc1_bytes != [0u8; 48]
+            || yc0_bytes != [0u8; 48]
+        {
+            return Err(SerializationError::InvalidData);
+        }
        return Ok(G2Affine::zero());
    }

+    let xc1 = deserialize_fq(xc1_bytes).ok_or(SerializationError::InvalidData)?;
+    let xc0 = deserialize_fq(xc0_bytes).ok_or(SerializationError::InvalidData)?;
+    let yc1 = deserialize_fq(yc1_bytes).ok_or(SerializationError::InvalidData)?;
+    let yc0 = deserialize_fq(yc0_bytes).ok_or(SerializationError::InvalidData)?;
+
    // Attempt to obtain the x-coordinate
-    let xc1 = read_fq_with_offset(&bytes, 0, true)?;
-    let xc0 = read_fq_with_offset(&bytes, 1, false)?;
    let x = Fq2::new(xc0, xc1);

    // Attempt to obtain the y-coordinate
-    let yc1 = read_fq_with_offset(&bytes, 2, false)?;
-    let yc0 = read_fq_with_offset(&bytes, 3, false)?;
    let y = Fq2::new(yc0, yc1);

    let p = G2Affine::new_unchecked(x, y);
--- a/bls12_381/src/fields/tests.rs
+++ b/bls12_381/src/fields/tests.rs
@@ -2,7 +2,7 @@ use ark_algebra_test_templates::*;
 use ark_ff::{
    biginteger::{BigInt, BigInteger, BigInteger384},
    fields::{FftField, Field, Fp12Config, Fp2Config, Fp6Config, PrimeField},
-    One, UniformRand, Zero,
+    AdditiveGroup, One, UniformRand, Zero,
 };
 use ark_std::{
    cmp::Ordering,
--- a/bn254/src/curves/g1.rs
+++ b/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::{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
--- a/bn254/src/curves/g2.rs
+++ b/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::{Field, 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);

--- a/bn254/src/curves/tests.rs
+++ b/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);
--- a/bn254/src/fields/fr.rs
+++ b/bn254/src/fields/fr.rs
@@ -3,5 +3,7 @@ use ark_ff::fields::{Fp256, MontBackend, MontConfig};
 #[derive(MontConfig)]
 #[modulus = "21888242871839275222246405745257275088548364400416034343698204186575808495617"]
 #[generator = "5"]
+#[small_subgroup_base = "3"]
+#[small_subgroup_power = "2"]
 pub struct FrConfig;
 pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
--- a/bw6_761/src/curves/g1.rs
+++ b/bw6_761/src/curves/g1.rs
@@ -1,8 +1,9 @@
 use ark_ec::{
    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    scalar_mul::glv::GLVConfig,
    short_weierstrass::{Affine, Projective},
 };
-use ark_ff::{Field, 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");
--- a/bw6_761/src/curves/g2.rs
+++ b/bw6_761/src/curves/g2.rs
@@ -1,8 +1,9 @@
 use ark_ec::{
    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    scalar_mul::glv::GLVConfig,
    short_weierstrass::{Affine, Projective},
 };
-use ark_ff::{Field, 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");
--- a/bw6_761/src/curves/mod.rs
+++ b/bw6_761/src/curves/mod.rs
@@ -2,7 +2,9 @@ use ark_ec::{
    bw6,
    bw6::{BW6Config, TwistType, BW6},
 };
-use ark_ff::{biginteger::BigInteger768 as BigInteger, BigInt};
+use ark_ff::{
+    biginteger::BigInteger768 as BigInteger, fp6_2over3::Fp6, BigInt, CyclotomicMultSubgroup, Field,
+};

 use crate::*;

@@ -16,42 +18,141 @@ mod tests;
 pub struct Config;

 impl BW6Config for Config {
-    const X: BigInteger = BigInt::new([
-        0x8508c00000000001,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-        0x0,
-    ]);
+    const X: BigInteger = BigInt!("0x8508c00000000001");
    /// `x` is positive.
    const X_IS_NEGATIVE: bool = false;
+    // X
+    const ATE_LOOP_COUNT_1: &'static [u64] = &[0x8508c00000000001];
+    // (X-1)/3
+    const X_MINUS_1_DIV_3: BigInteger = BigInt!("0x2c58400000000000");
    // X+1
-    const ATE_LOOP_COUNT_1: &'static [u64] = &[0x8508c00000000002];
    const ATE_LOOP_COUNT_1_IS_NEGATIVE: bool = false;
-    // X^3-X^2-X
+    // X^2-X-1
    const ATE_LOOP_COUNT_2: &'static [i8] = &[
        -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
-        0, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1,
-        0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, -1, 0, 0,
-        1, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, 1,
-        0, -1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 0, 1,
+        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0,
+        0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0,
+        0, 1, 0, 1, 0, 0, 0, 1,
    ];
    const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
    const TWIST_TYPE: TwistType = TwistType::M;
+    const H_T: i64 = 13;
+    const H_Y: i64 = 9;
+    const T_MOD_R_IS_ZERO: bool = false;
    type Fp = Fq;
    type Fp3Config = Fq3Config;
    type Fp6Config = Fq6Config;
    type G1Config = g1::Config;
    type G2Config = g2::Config;
+
+    fn final_exponentiation_hard_part(f: &Fp6<Self::Fp6Config>) -> Fp6<Self::Fp6Config> {
+        // hard_part
+        // From https://eprint.iacr.org/2020/351.pdf, Alg.6
+
+        #[rustfmt::skip]
+        // R0(x) := (-103*x^7 + 70*x^6 + 269*x^5 - 197*x^4 - 314*x^3 - 73*x^2 - 263*x - 220)
+        // R1(x) := (103*x^9 - 276*x^8 + 77*x^7 + 492*x^6 - 445*x^5 - 65*x^4 + 452*x^3 - 181*x^2 + 34*x + 229)
+        // f ^ R0(u) * (f ^ q) ^ R1(u) in a 2-NAF multi-exp fashion.
+
+        // steps 1,2,3
+        let f0 = *f;
+        let mut f0p = f0;
+        f0p.frobenius_map_in_place(1);
+        let f1 = Self::exp_by_x(&f0);
+        let mut f1p = f1;
+        f1p.frobenius_map_in_place(1);
+        let f2 = Self::exp_by_x(&f1);
+        let mut f2p = f2;
+        f2p.frobenius_map_in_place(1);
+        let f3 = Self::exp_by_x(&f2);
+        let mut f3p = f3;
+        f3p.frobenius_map_in_place(1);
+        let f4 = Self::exp_by_x(&f3);
+        let mut f4p = f4;
+        f4p.frobenius_map_in_place(1);
+        let f5 = Self::exp_by_x(&f4);
+        let mut f5p = f5;
+        f5p.frobenius_map_in_place(1);
+        let f6 = Self::exp_by_x(&f5);
+        let mut f6p = f6;
+        f6p.frobenius_map_in_place(1);
+        let f7 = Self::exp_by_x(&f6);
+        let mut f7p = f7;
+        f7p.frobenius_map_in_place(1);
+
+        // step 4
+        let f8p = Self::exp_by_x(&f7p);
+        let f9p = Self::exp_by_x(&f8p);
+
+        // step 5
+        let mut f5p_p3 = f5p;
+        f5p_p3.cyclotomic_inverse_in_place();
+        let result1 = f3p * &f6p * &f5p_p3;
+
+        // step 6
+        let result2 = result1.square();
+        let f4_2p = f4 * &f2p;
+        let mut tmp1_p3 = f0 * &f1 * &f3 * &f4_2p * &f8p;
+        tmp1_p3.cyclotomic_inverse_in_place();
+        let result3 = result2 * &f5 * &f0p * &tmp1_p3;
+
+        // step 7
+        let result4 = result3.square();
+        let mut f7_p3 = f7;
+        f7_p3.cyclotomic_inverse_in_place();
+        let result5 = result4 * &f9p * &f7_p3;
+
+        // step 8
+        let result6 = result5.square();
+        let f2_4p = f2 * &f4p;
+        let f4_2p_5p = f4_2p * &f5p;
+        let mut tmp2_p3 = f2_4p * &f3 * &f3p;
+        tmp2_p3.cyclotomic_inverse_in_place();
+        let result7 = result6 * &f4_2p_5p * &f6 * &f7p * &tmp2_p3;
+
+        // step 9
+        let result8 = result7.square();
+        let mut tmp3_p3 = f0p * &f9p;
+        tmp3_p3.cyclotomic_inverse_in_place();
+        let result9 = result8 * &f0 * &f7 * &f1p * &tmp3_p3;
+
+        // step 10
+        let result10 = result9.square();
+        let f6p_8p = f6p * &f8p;
+        let f5_7p = f5 * &f7p;
+        let mut tmp4_p3 = f6p_8p;
+        tmp4_p3.cyclotomic_inverse_in_place();
+        let result11 = result10 * &f5_7p * &f2p * &tmp4_p3;
+
+        // step 11
+        let result12 = result11.square();
+        let f3_6 = f3 * &f6;
+        let f1_7 = f1 * &f7;
+        let mut tmp5_p3 = f1_7 * &f2;
+        tmp5_p3.cyclotomic_inverse_in_place();
+        let result13 = result12 * &f3_6 * &f9p * &tmp5_p3;
+
+        // step 12
+        let result14 = result13.square();
+        let mut tmp6_p3 = f4_2p * &f5_7p * &f6p_8p;
+        tmp6_p3.cyclotomic_inverse_in_place();
+        let result15 = result14 * &f0 * &f0p * &f3p * &f5p * &tmp6_p3;
+
+        // step 13
+        let result16 = result15.square();
+        let mut tmp7_p3 = f3_6;
+        tmp7_p3.cyclotomic_inverse_in_place();
+        let result17 = result16 * &f1p * &tmp7_p3;
+
+        // step 14
+        let result18 = result17.square();
+        let mut tmp8_p3 = f2_4p * &f4_2p_5p * &f9p;
+        tmp8_p3.cyclotomic_inverse_in_place();
+        let result19 = result18 * &f1_7 * &f5_7p * &f0p * &tmp8_p3;
+
+        result19
+    }
 }

 pub type BW6_761 = BW6<Config>;
--- a/bw6_761/src/curves/tests.rs
+++ b/bw6_761/src/curves/tests.rs
@@ -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);
--- a/bw6_761/src/fields/fq3.rs
+++ b/bw6_761/src/fields/fq3.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp3::{Fp3, Fp3Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::Fq;
--- a/bw6_761/src/fields/fq6.rs
+++ b/bw6_761/src/fields/fq6.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp6_2over3::{Fp6, Fp6Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::{Fq, Fq3, Fq3Config};
--- a/bw6_767/Cargo.toml
+++ b/bw6_767/Cargo.toml
@@ -0,0 +1,33 @@
+[package]
+name = "ark-bw6-767"
+version = "0.4.0"
+authors = [ "arkworks contributors" ]
+description = "The BW6-767 pairing-friendly elliptic curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-bw6-767/"
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
+license = "MIT/Apache-2.0"
+edition = "2021"
+
+[dependencies]
+ark-ff = { version= "0.4.0", default-features = false }
+ark-ec = { version= "0.4.0", default-features = false }
+ark-std = { version = "0.4.0", default-features = false }
+ark-bls12-381 = { version = "0.4.0", path = "../bls12_381", default-features = false, features = [ "curve" ] }
+
+[dev-dependencies]
+ark-serialize = { version = "0.4.0", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0", default-features = false }
+
+[features]
+default = []
+std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bls12-381/std" ]
+
+[[bench]]
+name = "bw6_767"
+path = "benches/bw6_767.rs"
+harness = false
--- a/bw6_767/LICENSE-APACHE
+++ b/bw6_767/LICENSE-APACHE
@@ -0,0 +1 @@
+../LICENSE-APACHE
--- a/bw6_767/LICENSE-MIT
+++ b/bw6_767/LICENSE-MIT
@@ -0,0 +1 @@
+../LICENSE-MIT
--- a/bw6_767/benches/bw6_767.rs
+++ b/bw6_767/benches/bw6_767.rs
@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bw6_767::{
+    fq::Fq, fq3::Fq3, fq6::Fq6, fr::Fr, g1::G1Projective as G1, g2::G2Projective as G2, BW6_767,
+};
+
+bench!(
+    Name = "BW6_767",
+    Pairing = BW6_767,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq3,
+    TargetField = Fq6,
+);
--- a/bw6_767/scripts/base_field.sage
+++ b/bw6_767/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 496597749679620867773432037469214230242402307330180853437434581099336634619713640485778675608223760166307530047354464605410050411581079376994803852937842168733702867087556948851016246640584660942486895230518034810309227309966899431
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/bw6_767/scripts/scalar_field.sage
+++ b/bw6_767/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/bw6_767/src/curves/g1.rs
+++ b/bw6_767/src/curves/g1.rs
@@ -0,0 +1,59 @@
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
+};
+use ark_ff::{AdditiveGroup, MontFp};
+
+use crate::{Fq, Fr};
+
+pub type G1Affine = Affine<Config>;
+pub type G1Projective = Projective<Config>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR =
+    /// 124074696211871689196744963988542244365937182994917792082847997279938522233341057826255097957635256182243502012934844
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        0x9fed0006fffaaabc,
+        0xfae29bffb34d7c0d,
+        0xc51e35fba8145036,
+        0x58c9927410ca3a62,
+        0x7772b64205a0bc67,
+        0x26212b5cf67cecaf,
+        0x3,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 1707860402533867312515920333330662452399178546610458136488910471176197226039103222144872611321997303708365553992812
+    const COFACTOR_INV: Fr = MontFp!("1707860402533867312515920333330662452399178546610458136488910471176197226039103222144872611321997303708365553992812");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 1
+    const COEFF_B: Fq = MontFp!("1");
+
+    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
+    #[inline(always)]
+    fn mul_by_a(_elem: Self::BaseField) -> Self::BaseField {
+        use ark_ff::Zero;
+        Self::BaseField::zero()
+    }
+}
+
+/// G1_GENERATOR_X =
+/// 127687253511432941835499154999732953539969793860764514205013635996439242747457934431893570832266740963864950713809357287070846939000367049554519743864924323440810949629217677483481194663331926309250818003412838087592587472550707218
+pub const G1_GENERATOR_X: Fq = MontFp!("127687253511432941835499154999732953539969793860764514205013635996439242747457934431893570832266740963864950713809357287070846939000367049554519743864924323440810949629217677483481194663331926309250818003412838087592587472550707218");
+
+/// G1_GENERATOR_Y =
+/// 415570529523170147223250223671601071129165798689804006717876771297003017718159840368703823786319144396618898691682149260290217115399107531975419658973137909698922937988511368601419289861827304905241655385035120916874417442125721204
+pub const G1_GENERATOR_Y: Fq = MontFp!("415570529523170147223250223671601071129165798689804006717876771297003017718159840368703823786319144396618898691682149260290217115399107531975419658973137909698922937988511368601419289861827304905241655385035120916874417442125721204");
--- a/bw6_767/src/curves/g2.rs
+++ b/bw6_767/src/curves/g2.rs
@@ -0,0 +1,60 @@
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
+};
+use ark_ff::{AdditiveGroup, MontFp};
+
+use crate::{Fq, Fr};
+
+pub type G2Affine = Affine<Config>;
+pub type G2Projective = Projective<Config>;
+
+#[derive(Clone, Default, PartialEq, Eq)]
+pub struct Config;
+
+impl CurveConfig for Config {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR =
+    /// 124074696211871689196744963988542244365937182994917792082847997279938522233341057826255097957635256182243502012934833
+    #[rustfmt::skip]
+    const COFACTOR: &'static [u64] = &[
+        0x9fed0006fffaaab1,
+        0xfae29bffb34d7c0d,
+        0xc51e35fba8145036,
+        0x58c9927410ca3a62,
+        0x7772b64205a0bc67,
+        0x26212b5cf67cecaf,
+        0x3,
+    ];
+
+    /// COFACTOR^(-1) mod r =
+    /// 1034808299677096100380606582404873291173913026971901593767142419502683535585229274705219741821274468081298550569313
+    const COFACTOR_INV: Fr = MontFp!("1034808299677096100380606582404873291173913026971901593767142419502683535585229274705219741821274468081298550569313");
+}
+
+impl SWCurveConfig for Config {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 4
+    const COEFF_B: Fq = MontFp!("3");
+
+    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
+
+    #[inline(always)]
+    fn mul_by_a(_elem: Self::BaseField) -> Self::BaseField {
+        use ark_ff::Zero;
+        Self::BaseField::zero()
+    }
+}
+
+/// G2_GENERATOR_X =
+///  370611171465172359348863648443534520144617072349884185652206813771489664034831143983178049920510836078361116088420840622225267322852644540540617123958979924966938307707664543525950567252218300954395355151658118858470703533448342222
+pub const G2_GENERATOR_X: Fq = MontFp!("370611171465172359348863648443534520144617072349884185652206813771489664034831143983178049920510836078361116088420840622225267322852644540540617123958979924966938307707664543525950567252218300954395355151658118858470703533448342222");
+
+/// G2_GENERATOR_Y =
+/// 455144308204607096185992716699045373884508292978508084510087807751472279103896568109582325400258900176330927780121791269969939391813736974371796892558810828460226121428602798229282770695472612961143258458821149661074127679136388603
+pub const G2_GENERATOR_Y: Fq = MontFp!("455144308204607096185992716699045373884508292978508084510087807751472279103896568109582325400258900176330927780121791269969939391813736974371796892558810828460226121428602798229282770695472612961143258458821149661074127679136388603");
--- a/bw6_767/src/curves/mod.rs
+++ b/bw6_767/src/curves/mod.rs
@@ -0,0 +1,51 @@
+use ark_ec::{
+    bw6,
+    bw6::{BW6Config, TwistType, BW6},
+};
+use ark_ff::{biginteger::BigInteger768 as BigInteger, BigInt};
+
+use crate::*;
+
+pub mod g1;
+pub mod g2;
+
+#[cfg(test)]
+mod tests;
+
+#[derive(PartialEq, Eq)]
+pub struct Config;
+
+impl BW6Config for Config {
+    // X is the same as in bls12_381
+    const X: BigInteger = BigInt!("0xd201000000010000");
+    const X_IS_NEGATIVE: bool = true;
+    // X
+    const ATE_LOOP_COUNT_1: &'static [u64] = &[0xd201000000010000];
+    const X_MINUS_1_DIV_3: BigInteger = BigInt!("0x460055555555aaab");
+    const ATE_LOOP_COUNT_1_IS_NEGATIVE: bool = true;
+    // X^2-X-1
+    const ATE_LOOP_COUNT_2: &'static [i8] = &[
+        -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0,
+        1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0,
+        0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, -1, 0, 1, 0, 0, 1,
+        0, 0, 0, -1, 0, -1, 0, -1, 0, 1,
+    ];
+    const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
+    const TWIST_TYPE: TwistType = TwistType::M;
+    const H_T: i64 = -4;
+    const H_Y: i64 = -6;
+    const T_MOD_R_IS_ZERO: bool = true;
+    type Fp = Fq;
+    type Fp3Config = Fq3Config;
+    type Fp6Config = Fq6Config;
+    type G1Config = g1::Config;
+    type G2Config = g2::Config;
+}
+
+pub type BW6_767 = BW6<Config>;
+
+pub type G1Affine = bw6::G1Affine<Config>;
+pub type G1Projective = bw6::G1Projective<Config>;
+pub type G2Affine = bw6::G2Affine<Config>;
+pub type G2Projective = bw6::G2Projective<Config>;
--- a/bw6_767/src/curves/tests.rs
+++ b/bw6_767/src/curves/tests.rs
@@ -0,0 +1,8 @@
+use crate::*;
+use ark_algebra_test_templates::*;
+use ark_ff::Field;
+
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<BW6_767>; msm);
+test_pairing!(pairing; crate::BW6_767);
--- a/bw6_767/src/fields/fq.rs
+++ b/bw6_767/src/fields/fq.rs
@@ -0,0 +1,7 @@
+use ark_ff::fields::{Fp768, MontBackend, MontConfig};
+
+#[derive(MontConfig)]
+#[modulus = "496597749679620867773432037469214230242402307330180853437434581099336634619713640485778675608223760166307530047354464605410050411581079376994803852937842168733702867087556948851016246640584660942486895230518034810309227309966899431"]
+#[generator = "3"]
+pub struct FqConfig;
+pub type Fq = Fp768<MontBackend<FqConfig, 12>>;
--- a/bw6_767/src/fields/fq3.rs
+++ b/bw6_767/src/fields/fq3.rs
@@ -0,0 +1,79 @@
+use ark_ff::{
+    fields::fp3::{Fp3, Fp3Config},
+    AdditiveGroup, Field, MontFp,
+};
+
+use crate::Fq;
+
+pub type Fq3 = Fp3<Fq3Config>;
+
+pub struct Fq3Config;
+
+impl Fp3Config for Fq3Config {
+    type Fp = Fq;
+
+    /// NONRESIDUE = 3
+    // Fq3 = Fq\[u\]/u^3-3
+    const NONRESIDUE: Fq = MontFp!("3");
+
+    // (MODULUS^3 - 1) % 2^TWO_ADICITY == 0
+    const TWO_ADICITY: u32 = 1;
+
+    // (T-1)/2 with T = (MODULUS^3-1) / 2^TWO_ADICITY
+    #[rustfmt::skip]
+    const TRACE_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+        0x22d18a101ce54f7d,
+        0x354335b0e7c460e8,
+        0x8014efd2b7ade04d,
+        0x3a3c62ab52e0a2c1,
+        0x79ce8405b95dd2ee,
+        0x24f75cbd8559a2b6,
+        0x2519d1267e548214,
+        0xea0034421965f6c8,
+        0xbbaa92b6aca7d134,
+        0x9ec0892af11e70cc,
+        0x06e6ab40a2fd09ec,
+        0xd333987617c1542a,
+        0xdcb52167b1f0ae0f,
+        0xeffa098d77a86e52,
+        0x9fe0d744c24ed062,
+        0x7df249c9ef981da1,
+        0x01337d754cef36fa,
+        0xf84c4f79c259bd8b,
+        0x6552e19d7dc57335,
+        0x9f2cab11727d9c89,
+        0xe5cc4da17a684263,
+        0xaab0632027470c14,
+        0xb841a2fe447f48a3,
+        0x6e705db09cb2c6c9,
+        0x51d3c82bd5de018d,
+        0xf0bb21ffbef26bd1,
+        0x294ce678e6a4c0ff,
+        0x130ad731f57d4c85,
+        0xa1e367e5eb70a85b,
+        0xd1b2d73d567515cd,
+        0x0527dddbc3e9f165,
+        0x1d9c04e0098344e7,
+        0x5db616f391729475,
+        0xd2834b1fae1c2c1b,
+        0x7cf1b8c728557851,
+        0x218325db61d6ebd,
+    ];
+
+    // NONRESIDUE^T % q
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(Fq::ONE, Fq::ZERO, Fq::ZERO);
+
+    // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
+    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
+        Fq::ONE,
+        MontFp!("451452499708746243421442696394275804592767119751118962106882058158528025766103643615697202253207413006991058800455542766924935899310685166148099708594514571753800103096705086912881023032622324847956780035251378028187894066092550170"),
+        MontFp!("45145249970874624351989341074938425649635187579061891330552522940808608853609996870081473355016347159316471246898921838485114512270394210846704144343327596979902763990851861938135223607962336094530115195266656782121333243874349260"),
+    ];
+
+    // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
+    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
+        Fq::ONE,
+        MontFp!("45145249970874624351989341074938425649635187579061891330552522940808608853609996870081473355016347159316471246898921838485114512270394210846704144343327596979902763990851861938135223607962336094530115195266656782121333243874349260"),
+        MontFp!("451452499708746243421442696394275804592767119751118962106882058158528025766103643615697202253207413006991058800455542766924935899310685166148099708594514571753800103096705086912881023032622324847956780035251378028187894066092550170"),
+    ];
+}
--- a/bw6_767/src/fields/fq6.rs
+++ b/bw6_767/src/fields/fq6.rs
@@ -0,0 +1,26 @@
+use ark_ff::{
+    fields::fp6_2over3::{Fp6, Fp6Config},
+    AdditiveGroup, Field, MontFp,
+};
+
+use crate::{Fq, Fq3, Fq3Config};
+
+pub type Fq6 = Fp6<Fq6Config>;
+
+pub struct Fq6Config;
+
+impl Fp6Config for Fq6Config {
+    type Fp3Config = Fq3Config;
+
+    /// NONRESIDUE = (0, 1, 0)
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);
+
+    const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
+        Fq::ONE,
+        MontFp!("451452499708746243421442696394275804592767119751118962106882058158528025766103643615697202253207413006991058800455542766924935899310685166148099708594514571753800103096705086912881023032622324847956780035251378028187894066092550171"),
+        MontFp!("451452499708746243421442696394275804592767119751118962106882058158528025766103643615697202253207413006991058800455542766924935899310685166148099708594514571753800103096705086912881023032622324847956780035251378028187894066092550170"),
+        MontFp!("-1"),
+        MontFp!("45145249970874624351989341074938425649635187579061891330552522940808608853609996870081473355016347159316471246898921838485114512270394210846704144343327596979902763990851861938135223607962336094530115195266656782121333243874349260"),
+        MontFp!("45145249970874624351989341074938425649635187579061891330552522940808608853609996870081473355016347159316471246898921838485114512270394210846704144343327596979902763990851861938135223607962336094530115195266656782121333243874349261"),
+    ];
+}
--- a/bw6_767/src/fields/fr.rs
+++ b/bw6_767/src/fields/fr.rs
@@ -0,0 +1 @@
+pub use ark_bls12_381::{Fq as Fr, FqConfig as FrConfig};
--- a/bw6_767/src/fields/mod.rs
+++ b/bw6_767/src/fields/mod.rs
@@ -0,0 +1,14 @@
+pub mod fr;
+pub use self::fr::*;
+
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fq3;
+pub use self::fq3::*;
+
+pub mod fq6;
+pub use self::fq6::*;
+
+#[cfg(test)]
+mod tests;
--- a/bw6_767/src/fields/tests.rs
+++ b/bw6_767/src/fields/tests.rs
@@ -0,0 +1,7 @@
+use crate::*;
+use ark_algebra_test_templates::*;
+
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq3; Fq3);
+test_field!(fq6; Fq6);
--- a/bw6_767/src/lib.rs
+++ b/bw6_767/src/lib.rs
@@ -0,0 +1,36 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This module implements the BW6_767 curve generated by [\[El Housni and Guillevic\]](https://hackmd.io/@gnark/bw6_bls12381),
+//! using their generic approach described in [\[HG21\]](https://eprint.iacr.org/2021/1359).
+//! The name denotes that it is a curve generated using the Brezing--Weng
+//! method, and that its embedding degree is 6.
+//! The main feature of this curve is that the scalar field equals the base
+//! field of the BLS12_381 curve.
+//!
+//! Curve information:
+//! * Base field: q = 496597749679620867773432037469214230242402307330180853437434581099336634619713640485778675608223760166307530047354464605410050411581079376994803852937842168733702867087556948851016246640584660942486895230518034810309227309966899431
+//! * Scalar field: r = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
+//! * valuation(q - 1, 2) = 1
+//! * valuation(r - 1, 2) = 1
+//!
+//! G1 curve equation: y^2 = x^3 + Ax + B, where
+//! * A = 0,
+//! * B = 1
+//!
+//! G2 curve equation: y^2 = x^3 + Ax + B, where
+//! * A = 0
+//! * B = 3
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;
--- a/cp6_782/src/curves/g2.rs
+++ b/cp6_782/src/curves/g2.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    short_weierstrass::{Affine, Projective, SWCurveConfig},
    AffineRepr, CurveGroup,
 };
-use ark_ff::{Field, MontFp};
+use ark_ff::{AdditiveGroup, MontFp};
 use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
 use ark_std::vec::Vec;

--- a/cp6_782/src/curves/mod.rs
+++ b/cp6_782/src/curves/mod.rs
@@ -3,7 +3,8 @@ use ark_ec::{
    pairing::{MillerLoopOutput, Pairing, PairingOutput},
 };
 use ark_ff::{
-    biginteger::BigInteger832, BigInt, BitIteratorBE, CyclotomicMultSubgroup, Field, One,
+    biginteger::BigInteger832, AdditiveGroup, BigInt, BitIteratorBE, CyclotomicMultSubgroup, Field,
+    One,
 };
 use itertools::Itertools;

@@ -181,38 +182,6 @@ pub const ATE_LOOP_COUNT: [u64; 13] = [
 /// FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG = true
 pub const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = true;

-/// FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0 =
-/// 7000705447348627246181409558336018323010329260726930841638672011287206690002601216854775649561085256265269640040570922609783227469279331691880282815325569032149343779036142830666859805506518426649197067288711084398033
-pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInt::new([
-    0xb62ef36af72855d1,
-    0x676b5cef49d290fa,
-    0xd17fcf3c60947427,
-    0x5b93d992bc1b2849,
-    0x2171887cecd072cb,
-    0x879a2873f1516f4a,
-    0x8cc6856bd2cdf24e,
-    0xbff4fb6644d01993,
-    0x5dcbeea3e31ea667,
-    0x5f256f47681649f3,
-    0x2355a2b0839967fe,
-    0x144ed,
-    0x0,
-]);
+pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInt!("7000705447348627246181409558336018323010329260726930841638672011287206690002601216854775649561085256265269640040570922609783227469279331691880282815325569032149343779036142830666859805506518426649197067288711084398033");

-/// FINAL_EXPONENT_LAST_CHUNK_W1 =
-/// 86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951562986
-pub const FINAL_EXPONENT_LAST_CHUNK_W1: BigInteger832 = BigInt::new([
-    0x5657b9b57b942aea,
-    0x84f9a65f3bd54eaf,
-    0x5ea4214e35cd127,
-    0xe3cbcbc14ec1501d,
-    0xf196cb845a3092ab,
-    0x7e14627ad0e19017,
-    0x217db4,
-    0x0,
-    0x0,
-    0x0,
-    0x0,
-    0x0,
-    0x0,
-]);
+pub const FINAL_EXPONENT_LAST_CHUNK_W1: BigInteger832 = BigInt!("86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951562986");
--- a/cp6_782/src/fields/fq3.rs
+++ b/cp6_782/src/fields/fq3.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp3::{Fp3, Fp3Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::Fq;
--- a/cp6_782/src/fields/fq6.rs
+++ b/cp6_782/src/fields/fq6.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp6_2over3::{Fp6, Fp6Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::{Fq, Fq3, Fq3Config};
--- a/curve-constraint-tests/src/lib.rs
+++ b/curve-constraint-tests/src/lib.rs
@@ -225,7 +225,7 @@ pub mod fields {
 pub mod curves {
    use ark_ec::{
        short_weierstrass::Projective as SWProjective, twisted_edwards::Projective as TEProjective,
-        CurveGroup, Group,
+        AdditiveGroup, CurveGroup,
    };
    use ark_ff::{BitIteratorLE, Field, One, PrimeField};
    use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
@@ -315,12 +315,14 @@ pub mod curves {
            }
            assert!(cs.is_satisfied().unwrap());

-            let modulus = <C::ScalarField as PrimeField>::MODULUS.as_ref().to_vec();
+            let modulus = C::ScalarField::MODULUS.as_ref().to_vec();
            let mut max = modulus.clone();
            for limb in &mut max {
                *limb = u64::MAX;
            }

+            let num_limbs = max.len();
+
            let modulus_num_bits_mod_64 = <C::ScalarField as PrimeField>::MODULUS_BIT_SIZE % 64;
            if modulus_num_bits_mod_64 != 0 {
                *max.last_mut().unwrap() >>= 64 - modulus_num_bits_mod_64;
@@ -332,10 +334,10 @@ pub mod curves {
                    .to_vec(),
                vec![u64::rand(&mut rng)],
                (-C::ScalarField::one()).into_bigint().as_ref().to_vec(),
-                <C::ScalarField as PrimeField>::MODULUS.as_ref().to_vec(),
+                modulus,
                max,
-                vec![0; 50],
-                vec![1000012341233u64; 36],
+                vec![0u64; num_limbs],
+                vec![1000012341233u64; num_limbs],
            ];

            let mut input = vec![];
--- a/ed_on_bls12_381/src/fields/tests.rs
+++ b/ed_on_bls12_381/src/fields/tests.rs
@@ -3,7 +3,7 @@ use ark_algebra_test_templates::*;
 use ark_ff::{
    biginteger::BigInteger256 as BigInteger,
    fields::{Field, LegendreSymbol::*},
-    One, Zero,
+    AdditiveGroup, One, Zero,
 };
 use ark_std::str::FromStr;

--- a/ed_on_bls12_381_bandersnatch/src/curves/mod.rs
+++ b/ed_on_bls12_381_bandersnatch/src/curves/mod.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    short_weierstrass::{self, SWCurveConfig},
    twisted_edwards::{Affine, MontCurveConfig, Projective, TECurveConfig},
 };
-use ark_ff::{Field, MontFp};
+use ark_ff::{AdditiveGroup, MontFp};

 use crate::{Fq, Fr};

@@ -110,19 +110,19 @@ impl MontCurveConfig for BandersnatchConfig {
 //   <https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/bandersnatch.sage>

 /// x coordinate for TE curve generator
-const TE_GENERATOR_X: Fq =
+pub const TE_GENERATOR_X: Fq =
    MontFp!("18886178867200960497001835917649091219057080094937609519140440539760939937304");

 /// y coordinate for TE curve generator
-const TE_GENERATOR_Y: Fq =
+pub const TE_GENERATOR_Y: Fq =
    MontFp!("19188667384257783945677642223292697773471335439753913231509108946878080696678");

 /// x coordinate for SW curve generator
-const SW_GENERATOR_X: Fq =
+pub const SW_GENERATOR_X: Fq =
    MontFp!("30900340493481298850216505686589334086208278925799850409469406976849338430199");

 /// y coordinate for SW curve generator
-const SW_GENERATOR_Y: Fq =
+pub const SW_GENERATOR_Y: Fq =
    MontFp!("12663882780877899054958035777720958383845500985908634476792678820121468453298");

 impl SWCurveConfig for BandersnatchConfig {
--- a/ed_on_bls12_381_bandersnatch/src/fields/tests.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/tests.rs
@@ -3,7 +3,7 @@ use ark_algebra_test_templates::*;
 use ark_ff::{
    biginteger::BigInteger256 as BigInteger,
    fields::{Field, LegendreSymbol::*},
-    One, Zero,
+    AdditiveGroup, One, Zero,
 };
 use ark_std::str::FromStr;

--- a/ed_on_bn254/src/fields/tests.rs
+++ b/ed_on_bn254/src/fields/tests.rs
@@ -2,7 +2,7 @@ use ark_algebra_test_templates::*;
 use ark_ff::{
    biginteger::BigInteger256 as BigInteger,
    fields::{Field, LegendreSymbol::*},
-    One, Zero,
+    AdditiveGroup, One, Zero,
 };
 use ark_std::str::FromStr;

--- a/grumpkin/Cargo.toml
+++ b/grumpkin/Cargo.toml
@@ -0,0 +1,37 @@
+[package]
+name = "ark-grumpkin"
+version = "0.4.0"
+authors = [ "CPerezz", "arkworks contributors" ]
+description = "The Grumpkin prime-order elliptic curve"
+homepage = "https://arkworks.rs"
+repository = "https://github.com/arkworks-rs/curves"
+documentation = "https://docs.rs/ark-grumpkin/"
+keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+categories = ["cryptography"]
+include = ["Cargo.toml", "src"]
+license = "MIT/Apache-2.0"
+edition = "2021"
+
+[dependencies]
+ark-ff = { version = "0.4.0", default-features = false }
+ark-ec = { version = "0.4.0", default-features = false }
+ark-r1cs-std = { version = "0.4.0", default-features = false, optional = true }
+ark-std = { version = "0.4.0", default-features = false }
+ark-bn254 = { version = "0.4.0", path = "../bn254", default-features = false, features = [ "scalar_field", "curve" ] }
+
+[dev-dependencies]
+ark-relations = { version = "0.4.0", default-features = false }
+ark-serialize = { version = "0.4.0", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0", default-features = false }
+ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
+
+[features]
+default = []
+std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
+r1cs = [ "ark-r1cs-std" ]
+
+[[bench]]
+name = "grumpkin"
+path = "benches/grumpkin.rs"
+harness = false
--- a/grumpkin/LICENSE-APACHE
+++ b/grumpkin/LICENSE-APACHE
@@ -0,0 +1 @@
+../LICENSE-APACHE
--- a/grumpkin/LICENSE-MIT
+++ b/grumpkin/LICENSE-MIT
@@ -0,0 +1 @@
+../LICENSE-MIT
--- a/grumpkin/benches/grumpkin.rs
+++ b/grumpkin/benches/grumpkin.rs
@@ -0,0 +1,9 @@
+use ark_algebra_bench_templates::*;
+use ark_grumpkin::{fq::Fq, fr::Fr, Projective as G};
+
+bench!(
+    Name = "Grumpkin",
+    Group = G,
+    ScalarField = Fr,
+    PrimeBaseField = Fq,
+);
--- a/grumpkin/scripts/base_field.sage
+++ b/grumpkin/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/grumpkin/scripts/scalar_field.sage
+++ b/grumpkin/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 21888242871839275222246405745257275088696311157297823662689037894645226208583
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 20):
+    i = Fp(i);
+    neg_i = Fp(-i)
+    if not(i.is_primitive_root() or neg_i.is_primitive_root()):
+        continue
+    elif i.is_primitive_root():
+        assert(i.is_primitive_root());
+        print("Generator: %d" % i)
+        generator = i
+        break
+    else:
+        assert(neg_i.is_primitive_root());
+        print("Generator: %d" % neg_i)
+        generator = neg_i
+        break
+
+
+two_adicity = valuation(modulus - 1, 2);
+trace = (modulus - 1) / 2**two_adicity;
+two_adic_root_of_unity = generator^trace
+print("2-adic Root of Unity: %d " % two_adic_root_of_unity)
--- a/grumpkin/src/constraints/curves.rs
+++ b/grumpkin/src/constraints/curves.rs
@@ -0,0 +1,11 @@
+use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;
+
+use crate::{constraints::FBaseVar, *};
+
+/// A group element in the Grumpkin prime-order group.
+pub type GVar = ProjectiveVar<GrumpkinConfig, FBaseVar>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::curves::sw_test::<GrumpkinConfig, GVar>().unwrap();
+}
--- a/grumpkin/src/constraints/fields.rs
+++ b/grumpkin/src/constraints/fields.rs
@@ -0,0 +1,11 @@
+use ark_r1cs_std::fields::fp::FpVar;
+
+use crate::fq::Fq;
+
+/// A variable that is the R1CS equivalent of `crate::Fq`.
+pub type FBaseVar = FpVar<Fq>;
+
+#[test]
+fn test() {
+    ark_curve_constraint_tests::fields::field_test::<_, _, FBaseVar>().unwrap();
+}
--- a/grumpkin/src/constraints/mod.rs
+++ b/grumpkin/src/constraints/mod.rs
@@ -0,0 +1,107 @@
+//! This module implements the R1CS equivalent of `ark_grumpkin`.
+//!
+//! It implements field variables for `crate::Fq`,
+//! and group variables for `crate::Projective`.
+//!
+//! The field underlying these constraints is `crate::Fq`.
+//!
+//! # Examples
+//!
+//! One can perform standard algebraic operations on `FBaseVar`:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! use ark_std::UniformRand;
+//! use ark_relations::r1cs::*;
+//! use ark_r1cs_std::prelude::*;
+//! use ark_grumpkin::{*, constraints::*};
+//!
+//! let cs = ConstraintSystem::<Fq>::new_ref();
+//! // This rng is just for test purposes; do not use it
+//! // in real applications.
+//! let mut rng = ark_std::test_rng();
+//!
+//! // Generate some random `Fq` elements.
+//! let a_native = Fq::rand(&mut rng);
+//! let b_native = Fq::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = FBaseVar::new_witness(ark_relations::ns!(cs, "generate_a"), || Ok(a_native))?;
+//! let b = FBaseVar::new_witness(ark_relations::ns!(cs, "generate_b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = FBaseVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = FBaseVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! let one = FBaseVar::one();
+//! let zero = FBaseVar::zero();
+//!
+//! // Sanity check one + one = two
+//! let two = &one + &one + &zero;
+//! two.enforce_equal(&one.double()?)?;
+//!
+//! assert!(cs.is_satisfied()?);
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!((&a + &b).value()?, a_native + &b_native);
+//!
+//! // Check that the value of &a * &b is correct.
+//! assert_eq!((&a * &b).value()?, a_native * &b_native);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+//!
+//! One can also perform standard algebraic operations on `GVar`:
+//!
+//! ```
+//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
+//! # use ark_std::UniformRand;
+//! # use ark_relations::r1cs::*;
+//! # use ark_r1cs_std::prelude::*;
+//! # use ark_grumpkin::{*, constraints::*};
+//!
+//! # let cs = ConstraintSystem::<Fq>::new_ref();
+//! # let mut rng = ark_std::test_rng();
+//!
+//! // Generate some random `Projective` elements.
+//! let a_native = Projective::rand(&mut rng);
+//! let b_native = Projective::rand(&mut rng);
+//!
+//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
+//! let a = GVar::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?;
+//! let b = GVar::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?;
+//!
+//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
+//! // constraints or variables.
+//! let a_const = GVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
+//! let b_const = GVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
+//!
+//! // This returns the identity.
+//! let zero = GVar::zero();
+//!
+//! // Sanity check one + one = two
+//! let two_a = &a + &a + &zero;
+//! two_a.enforce_equal(&a.double()?)?;
+//!
+//! assert!(cs.is_satisfied()?);
+//!
+//! // Check that the value of &a + &b is correct.
+//! assert_eq!((&a + &b).value()?, a_native + &b_native);
+//!
+//! // Check that operations on variables and constants are equivalent.
+//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
+//! assert!(cs.is_satisfied()?);
+//! # Ok(())
+//! # }
+//! ```
+
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;
--- a/grumpkin/src/curves/mod.rs
+++ b/grumpkin/src/curves/mod.rs
@@ -0,0 +1,52 @@
+// The parameters for the curve have been taken from
+// https://github.com/AztecProtocol/barretenberg/blob/97ccf76c42db581a8b8f8bfbcffe8ca015a3dd22/cpp/src/barretenberg/ecc/curves/grumpkin/grumpkin.hpp
+
+use crate::{fq::Fq, fr::Fr};
+use ark_ec::{
+    models::CurveConfig,
+    short_weierstrass::{self as sw, SWCurveConfig},
+};
+use ark_ff::{AdditiveGroup, Field, MontFp, Zero};
+
+#[cfg(test)]
+mod tests;
+
+#[derive(Copy, Clone, Default, PartialEq, Eq)]
+pub struct GrumpkinConfig;
+
+impl CurveConfig for GrumpkinConfig {
+    type BaseField = Fq;
+    type ScalarField = Fr;
+
+    /// COFACTOR = 1
+    const COFACTOR: &'static [u64] = &[0x1];
+
+    /// COFACTOR_INV = 1
+    const COFACTOR_INV: Fr = Fr::ONE;
+}
+
+pub type Affine = sw::Affine<GrumpkinConfig>;
+pub type Projective = sw::Projective<GrumpkinConfig>;
+
+impl SWCurveConfig for GrumpkinConfig {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = -17
+    const COEFF_B: Fq = MontFp!("-17");
+
+    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
+    const GENERATOR: Affine = Affine::new_unchecked(G_GENERATOR_X, G_GENERATOR_Y);
+
+    #[inline(always)]
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
+        Self::BaseField::zero()
+    }
+}
+
+/// G_GENERATOR_X = 1
+pub const G_GENERATOR_X: Fq = MontFp!("1");
+
+/// G_GENERATOR_Y = sqrt(-16)
+pub const G_GENERATOR_Y: Fq =
+    MontFp!("17631683881184975370165255887551781615748388533673675138860");
--- a/grumpkin/src/curves/tests.rs
+++ b/grumpkin/src/curves/tests.rs
@@ -0,0 +1,4 @@
+use crate::Projective;
+use ark_algebra_test_templates::*;
+
+test_group!(g1; Projective; sw);
--- a/grumpkin/src/fields/fq.rs
+++ b/grumpkin/src/fields/fq.rs
@@ -0,0 +1 @@
+pub use ark_bn254::{Fr as Fq, FrConfig as FqConfig};
--- a/grumpkin/src/fields/fr.rs
+++ b/grumpkin/src/fields/fr.rs
@@ -0,0 +1 @@
+pub use ark_bn254::{Fq as Fr, FqConfig as FrConfig};
--- a/grumpkin/src/fields/mod.rs
+++ b/grumpkin/src/fields/mod.rs
@@ -0,0 +1,8 @@
+pub mod fq;
+pub use self::fq::*;
+
+pub mod fr;
+pub use self::fr::*;
+
+#[cfg(test)]
+mod tests;
--- a/grumpkin/src/fields/tests.rs
+++ b/grumpkin/src/fields/tests.rs
@@ -0,0 +1,5 @@
+use crate::{Fq, Fr};
+use ark_algebra_test_templates::*;
+
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
--- a/grumpkin/src/lib.rs
+++ b/grumpkin/src/lib.rs
@@ -0,0 +1,33 @@
+#![cfg_attr(not(feature = "std"), no_std)]
+#![deny(
+    warnings,
+    unused,
+    future_incompatible,
+    nonstandard_style,
+    rust_2018_idioms
+)]
+#![forbid(unsafe_code)]
+
+//! This library implements the prime-order curve Grumpkin, generated by
+//! Zachary J. Williamson from Aztec protocol. The main feature of this
+//! curve is that it forms a cycle with bn254, i.e. its scalar field and base
+//! field respectively are the base field and scalar field of bn254.
+//!
+//!
+//! Curve information:
+//! Grumpkin:
+//! * Base field: q =
+//!   21888242871839275222246405745257275088548364400416034343698204186575808495617
+//! * Scalar field: r =
+//!   21888242871839275222246405745257275088696311157297823662689037894645226208583
+//! * Curve equation: y^2 = x^3 - 17
+//! * Valuation(q - 1, 2) = 28
+//! * Valuation(r - 1, 2) = 1
+
+#[cfg(feature = "r1cs")]
+pub mod constraints;
+mod curves;
+mod fields;
+
+pub use curves::*;
+pub use fields::*;
--- a/mnt4_298/src/curves/g2.rs
+++ b/mnt4_298/src/curves/g2.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    mnt4::MNT4Config,
    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{Field, MontFp};
+use ark_ff::{AdditiveGroup, MontFp};

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

--- a/mnt4_298/src/curves/mod.rs
+++ b/mnt4_298/src/curves/mod.rs
@@ -1,5 +1,5 @@
 use ark_ec::models::mnt4::{MNT4Config, MNT4};
-use ark_ff::{biginteger::BigInteger320, BigInt, Field, MontFp};
+use ark_ff::{biginteger::BigInteger320, AdditiveGroup, BigInt, Field, MontFp};

 use crate::{Fq, Fq2, Fq2Config, Fq4Config, Fr};

@@ -38,10 +38,11 @@ impl MNT4Config for Config {
        0, 0, 0, 0, 0, 0,
    ];
    const ATE_IS_LOOP_COUNT_NEG: bool = false;
-    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger320 = BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0]);
+    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger320 = BigInt!("0x1");
    const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = false;
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt4_80.ml#L96
    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger320 =
-        BigInt::new([993502997770534913, 5071219579242586943, 2027349, 0, 0]);
+        BigInt!("689871209842287392837045615510547309923794945");
    type Fp = Fq;
    type Fr = Fr;
    type Fp2Config = Fq2Config;
--- a/mnt4_298/src/fields/fq4.rs
+++ b/mnt4_298/src/fields/fq4.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp4::{Fp4, Fp4Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::{Fq, Fq2, Fq2Config};
--- a/mnt4_753/src/curves/g2.rs
+++ b/mnt4_753/src/curves/g2.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    mnt4::MNT4Config,
    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{Field, MontFp};
+use ark_ff::{AdditiveGroup, MontFp};

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

--- a/mnt4_753/src/curves/mod.rs
+++ b/mnt4_753/src/curves/mod.rs
@@ -1,8 +1,5 @@
 use ark_ec::models::mnt4::{MNT4Config, MNT4};
-use ark_ff::{
-    biginteger::{BigInt, BigInteger768},
-    Field, Fp2, MontFp,
-};
+use ark_ff::{biginteger::BigInteger768, AdditiveGroup, BigInt, Field, Fp2, MontFp};

 use crate::{Fq, Fq2Config, Fq4Config, Fr};

@@ -48,23 +45,10 @@ impl MNT4Config for Config {
        0, 0, 0,
    ];
    const ATE_IS_LOOP_COUNT_NEG: bool = true;
-    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger768 =
-        BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0]);
+    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger768 = BigInt!("0x1");
    const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = true;
-    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger768 = BigInt::new([
-        8824542903220142079,
-        7711082599397206192,
-        8303354903384568230,
-        5874150271971943936,
-        9717849827920685054,
-        95829799234282493,
-        0,
-        0,
-        0,
-        0,
-        0,
-        0,
-    ]);
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt4753.ml#L100
+    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger768 = BigInt!("204691208819330962009469868104636132783269696790011977400223898462431810102935615891307667367766898917669754470399");
    type Fp = Fq;
    type Fr = Fr;
    type Fp2Config = Fq2Config;
--- a/mnt4_753/src/fields/fq4.rs
+++ b/mnt4_753/src/fields/fq4.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp4::{Fp4, Fp4Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::{Fq, Fq2, Fq2Config};
--- a/mnt6_298/src/curves/g2.rs
+++ b/mnt6_298/src/curves/g2.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    mnt6::MNT6Config,
    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{Field, MontFp};
+use ark_ff::{AdditiveGroup, MontFp};

 use crate::{g1, Fq, Fq3, Fr};

--- a/mnt6_298/src/curves/mod.rs
+++ b/mnt6_298/src/curves/mod.rs
@@ -2,7 +2,7 @@ use ark_ec::{
    models::mnt6::{MNT6Config, MNT6},
    short_weierstrass::SWCurveConfig,
 };
-use ark_ff::{biginteger::BigInteger320, BigInt, Field, Fp3};
+use ark_ff::{biginteger::BigInteger320, AdditiveGroup, BigInt, Field, Fp3};

 use crate::{Fq, Fq3Config, Fq6Config, Fr};

@@ -26,7 +26,7 @@ impl MNT6Config for Config {
    const TWIST_COEFF_A: Fp3<Self::Fp3Config> =
        Fp3::<Self::Fp3Config>::new(Fq::ZERO, Fq::ZERO, g1::Config::COEFF_A);

-    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt4_80.ml#L88
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt6_80.ml#L118
    const ATE_LOOP_COUNT: &'static [i8] = &[
        1, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, -1,
        0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, -1, 0, -1, 0,
@@ -36,10 +36,11 @@ impl MNT6Config for Config {
        0, 0, 0, 0, 0, 0,
    ];
    const ATE_IS_LOOP_COUNT_NEG: bool = true;
-    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger320 = BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0]);
+    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger320 = BigInt!("0x1");
    const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = true;
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt6_80.ml#L126
    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger320 =
-        BigInt::new([0xdc9a1b671660000, 0x46609756bec2a33f, 0x1eef55, 0x0, 0x0]);
+        BigInt!("689871209842287392837045615510547309923794944");
    type Fp = Fq;
    type Fr = Fr;
    type Fp3Config = Fq3Config;
--- a/mnt6_298/src/fields/fq3.rs
+++ b/mnt6_298/src/fields/fq3.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp3::{Fp3, Fp3Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::fq::Fq;
--- a/mnt6_298/src/fields/fq6.rs
+++ b/mnt6_298/src/fields/fq6.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp6_2over3::{Fp6, Fp6Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::{Fq, Fq3, Fq3Config};
--- a/mnt6_753/src/curves/g2.rs
+++ b/mnt6_753/src/curves/g2.rs
@@ -3,7 +3,7 @@ use ark_ec::{
    mnt6::MNT6Config,
    models::{short_weierstrass::SWCurveConfig, CurveConfig},
 };
-use ark_ff::{Field, MontFp};
+use ark_ff::{AdditiveGroup, MontFp};

 use crate::{g1, Fq, Fq3, Fr};

--- a/mnt6_753/src/curves/mod.rs
+++ b/mnt6_753/src/curves/mod.rs
@@ -2,7 +2,7 @@ use ark_ec::models::{
    mnt6::{MNT6Config, MNT6},
    short_weierstrass::SWCurveConfig,
 };
-use ark_ff::{biginteger::BigInteger768, BigInt, Field, Fp3};
+use ark_ff::{biginteger::BigInteger768, AdditiveGroup, BigInt, Field, Fp3};

 use crate::{Fq, Fq3Config, Fq6Config, Fr};

@@ -49,23 +49,10 @@ impl MNT6Config for Config {
        0, 0, 0,
    ];
    const ATE_IS_LOOP_COUNT_NEG: bool = false;
-    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger768 =
-        BigInt::new([0x1, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0, 0x0]);
+    const FINAL_EXPONENT_LAST_CHUNK_1: BigInteger768 = BigInt!("0x1");
    const FINAL_EXPONENT_LAST_CHUNK_W0_IS_NEG: bool = false;
-    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger768 = BigInt::new([
-        8824542903220142080,
-        7711082599397206192,
-        8303354903384568230,
-        5874150271971943936,
-        9717849827920685054,
-        95829799234282493,
-        0,
-        0,
-        0,
-        0,
-        0,
-        0,
-    ]);
+    // https://github.com/o1-labs/snarky/blob/9c21ab2bb23874604640740d646a932e813432c3/snarkette/mnt6753.ml#L130C1-L130C1
+    const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger768 = BigInt!("204691208819330962009469868104636132783269696790011977400223898462431810102935615891307667367766898917669754470400");
    type Fp = Fq;
    type Fr = Fr;
    type Fp3Config = Fq3Config;
--- a/mnt6_753/src/fields/fq3.rs
+++ b/mnt6_753/src/fields/fq3.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp3::{Fp3, Fp3Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::fq::Fq;
--- a/mnt6_753/src/fields/fq6.rs
+++ b/mnt6_753/src/fields/fq6.rs
@@ -1,6 +1,6 @@
 use ark_ff::{
    fields::fp6_2over3::{Fp6, Fp6Config},
-    Field, MontFp,
+    AdditiveGroup, Field, MontFp,
 };

 use crate::{Fq, Fq3, Fq3Config};
--- a/pallas/src/curves/mod.rs
+++ b/pallas/src/curves/mod.rs
@@ -1,8 +1,9 @@
 use ark_ec::{
    models::CurveConfig,
+    scalar_mul::glv::GLVConfig,
    short_weierstrass::{self as sw, SWCurveConfig},
 };
-use ark_ff::{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");

--- a/pallas/src/curves/tests.rs
+++ b/pallas/src/curves/tests.rs
@@ -2,3 +2,4 @@ use crate::Projective;
 use ark_algebra_test_templates::*;

 test_group!(g1; Projective; sw);
+test_group!(g1_glv; Projective; glv);
--- a/secp256k1/src/curves/mod.rs
+++ b/secp256k1/src/curves/mod.rs
@@ -2,7 +2,7 @@ use ark_ec::{
    models::CurveConfig,
    short_weierstrass::{self as sw, SWCurveConfig},
 };
-use ark_ff::{Field, MontFp, Zero};
+use ark_ff::{AdditiveGroup, Field, MontFp, Zero};

 use crate::{fq::Fq, fr::Fr};

--- a/secq256k1/src/curves/mod.rs
+++ b/secq256k1/src/curves/mod.rs
@@ -2,7 +2,7 @@ use ark_ec::{
    models::CurveConfig,
    short_weierstrass::{self as sw, SWCurveConfig},
 };
-use ark_ff::{Field, MontFp, Zero};
+use ark_ff::{AdditiveGroup, Field, MontFp, Zero};

 use crate::{fq::Fq, fr::Fr};

--- a/vesta/src/curves/mod.rs
+++ b/vesta/src/curves/mod.rs
@@ -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::{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");
--- a/vesta/src/curves/tests.rs
+++ b/vesta/src/curves/tests.rs
@@ -2,3 +2,4 @@ use crate::Projective;
 use ark_algebra_test_templates::*;

 test_group!(g1; Projective; sw);
+test_group!(g1_glv; Projective; glv);
Author	SHA1	Message	Date
Michele Orrù	e2d16a27e2	Update README.md (#189 )	2023-12-18 09:24:04 -08:00
Pratyush Mishra	7854883b47	Add archival notice to README (#188 )	2023-12-18 08:56:41 -08:00
Davide Galassi	ccf83923f8	Expose Bandersnatch generators (#184 )	2023-10-14 17:44:58 +02:00
Andrew Z	0a64024ebc	Fix #178 : Make MNT{4,6}-753, cp6_782 tests run conditionally (#179 )	2023-09-25 11:28:26 -07:00
Pratyush Mishra	8c0256ac9c	Fix comments for Grumpkin curve generator (#175 ) Co-authored-by: Weikeng Chen <w.k@berkeley.edu>	2023-09-19 04:47:35 -07:00
mmagician	72a18b6ecf	GLV implementation for BLS12_377, BLS12_381 and BN254 (#158 )	2023-09-11 17:29:38 -04:00
mmagician	8765798eb0	The scalar to be multiplied by should be at most `num_limbs` long (#171 ) Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2023-09-11 12:44:41 -07:00
mmagician	7e4b4bf027	Non-canonical infinity point & bad flags in BLS12-381 serialization should fail (#176 ) Co-authored-by: Kevaundray Wedderburn <kevtheappdev@gmail.com>	2023-09-11 12:21:37 -07:00
Carlos Pérez	4d1e504025	Add Grumpkin support for arkworks (#174 ) Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2023-09-07 05:15:36 -07:00
Weikeng Chen	fc8379d9ed	Add the small subgroup power for BN254 (#163 ) Co-authored-by: mmagician <marcin.gorny.94@protonmail.com> Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2023-09-05 05:39:34 -07:00
mmagician	a0bd36f781	Revert "temp switch to bw6-optimization branch on algebra" (#172 )	2023-09-04 11:38:00 -04:00
mmagician	1ce1fcf70f	Bw6-761 optimized Miller loop (#155 )	2023-09-03 09:38:44 -04:00
mmagician	379f23070c	Use `BigInt` macro for defining curve config parameters (#170 )	2023-09-01 09:43:12 -07:00
swasilyev	7e58260618	Add BW6-767 curve and update BW6-761 to use the new bw6 model (#156 ) * Rework bw6-761 to bw6-767 use bls12-381 instead of 377 for test imports fix the inline comments with correct name and params Set the right base field Equation for base curve is y2 = x3 + 1 fill in pairing params adapt sage scripts with correct moduli calculate the correct cubic non residue correct the parameter B in the curve equation remove the specialized method for mult by nonresidue nonresidue is two, so default will be doubling calculate more correct parameters for fq3 `TRACE_MINUS_ONE_DIV_TWO` and `QUADRATIC_NONRESIDUE_TO_T` compute the right fq3 & fp6 frobenious coefficients calculate the cofactor for g1 use the g1 generator from gnark's fork use the right g2 equation g2 cofactor is slightly smaller than g1 cofactor get the g2 generators from gnark's fork update g1 and g2 curve info in the comments fill in `COFACTOR_INV` value for g1 fill in `COFACTOR_INV` value for g2 * update module description author information 2-adicity of the scalar field * update changelog * remove trailing comma * remove todo * 2nd loop count is x^3 - x^2 - x * Revert "2nd loop count is x^3 - x^2 - x" This reverts commit 2b323db3baff06a6077fd7505ff489fa31be7282. * fix comment regarding non-residue * first loop count should be X * 1. Generic BW6 params added to BW6-761 2. Curve specific hard part of the final exp moved from algebra * 1. Generic BW6 params added to BW6-767 2. Miller loop params changed to the "unoptimized" version * cargo fmt * changelog updated * X_MINUS_1_DIV_3 added to BW6Config * imports fixed --------- Co-authored-by: mmagician <marcin.gorny.94@protonmail.com>	2023-09-01 10:06:45 +02:00
Chris Sosnin	3fded1fbcc	patch dependencies and fix imports (#167 ) Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2023-08-19 13:13:13 -07:00
Hossein Moghaddas	32b487e7fd	Adding `AdditiveGroup` and `PrimeGroup` (#159 ) Co-authored-by: Michele Orrù <michele.orru@berkeley.edu> Co-authored-by: Weikeng Chen <w.k@berkeley.edu> Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2023-08-19 12:09:04 -07:00
				`@@ -0,0 +1 @@`
				`pub use ark_bls12_381::{Fq as Fr, FqConfig as FrConfig};`
				`@@ -0,0 +1 @@`
				`pub use ark_bn254::{Fr as Fq, FrConfig as FqConfig};`
				`@@ -0,0 +1 @@`
				`pub use ark_bn254::{Fq as Fr, FqConfig as FrConfig};`