missed two dependencies

bump relations & r1cs-std dependency after their alpha version is out
Version 0.4.0-alpha
2026-01-27 14:13:46 +01:00 · 2022-11-19 13:36:02 +01:00 · 2022-11-19 13:28:57 +01:00 · 2022-11-12 20:14:24 +01:00 · 2022-10-31 17:12:52 -07:00 · 2022-10-29 19:55:35 -07:00
359 changed files with 5605 additions and 9496 deletions
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -14,7 +14,7 @@ jobs:
    steps:

    - name: Checkout
-      uses: actions/checkout@v1
+      uses: actions/checkout@v3
    - name: Install Rust
      uses: actions-rs/toolchain@v1
      with:
@@ -41,7 +41,7 @@ jobs:
          - nightly
    steps:
      - name: Checkout
-        uses: actions/checkout@v2
+        uses: actions/checkout@v3

      - name: Install Rust (${{ matrix.rust }})
        uses: actions-rs/toolchain@v1
@@ -79,14 +79,13 @@ jobs:
        if: matrix.rust == 'nightly'


-
  directories: # Job that list subdirectories
    name: List directories for parallelizing tests
    runs-on: ubuntu-latest
    outputs:
      dir: ${{ steps.set-dirs.outputs.dir }} # generate output name dir by using inner step output
    steps:
-      - uses: actions/checkout@v2
+      - uses: actions/checkout@v3
      - id: set-dirs # Give it an id to handle to get step outputs in the outputs key above
        run: echo "::set-output name=dir::$(ls -d */ | jq -R -s -c 'split("\n")[:-1]')"
        # Define step output named dir base on ls command transformed to JSON thanks to jq
@@ -103,22 +102,47 @@ jobs:
        exclude:
          - dir: scripts/
          - dir: curve-constraint-tests/
-          - dir: curve-benches/
+          - dir: mnt4_753/
+          - dir: mnt6_753/
    steps:
      - name: Checkout
-        uses: actions/checkout@v2
+        uses: actions/checkout@v3
      - name: Run tests
        run: |
          cd ${{matrix.dir}}
          cargo test --all-features

+  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
+        run: |
+          cd mnt4_753/
+          cargo test --all-features
+
+  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
+        run: |
+          cd mnt6_753/
+          cargo test --all-features
+
  docs:
    name: Check Documentation
    runs-on: ubuntu-latest
    steps:

    - name: Checkout
-      uses: actions/checkout@v1
+      uses: actions/checkout@v3
    - name: Install Rust
      uses: actions-rs/toolchain@v1
      with:
@@ -138,7 +162,7 @@ jobs:
    runs-on: ubuntu-latest
    steps:
      - name: Checkout
-        uses: actions/checkout@v2
+        uses: actions/checkout@v3

      - name: Install Rust (${{ matrix.rust }})
        uses: actions-rs/toolchain@v1
@@ -159,10 +183,10 @@ jobs:
        uses: actions-rs/cargo@v1
        with:
            command: check
-            args: --examples --workspace --exclude ark-curve-constraint-tests --exclude ark-curve-benches --target aarch64-unknown-none
+            args: --examples --workspace --exclude ark-curve-constraint-tests --target aarch64-unknown-none

      - name: build
        uses: actions-rs/cargo@v1
        with:
            command: build
-            args: --workspace --exclude ark-curve-constraint-tests --exclude ark-curve-benches --target aarch64-unknown-none
+            args: --workspace --exclude ark-curve-constraint-tests --target aarch64-unknown-none
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -3,14 +3,25 @@
 ## Pending

 - [\#76](https://github.com/arkworks-rs/curves/pull/76) twisted Edwards parameters for bls12-377
+- Fixed curve benches

 ### Breaking changes

+- [\#104](https://github.com/arkworks-rs/curves/pull/104) Remove `QUADRATIC_NONRESIDUE` parameter from implementors of `Fp2Config`.
+- [\#129](https://github.com/arkworks-rs/curves/pull/129) Implement custom serialization for BLS12-381 for compatibility with the [Zcash lib](https://github.com/zkcrypto/bls12_381).
+ 
 ### Features

+- [\#121](https://github.com/arkworks-rs/curves/pull/121) Add the ed25519 curve.
+- [\#124](https://github.com/arkworks-rs/curves/pull/124) Add the curve25519 curve.
+
 ### Improvements

+- [\#70](https://github.com/arkworks-rs/curves/pull/70) Add prepared G2 pairing consistency test. 
 - [\#74](https://github.com/arkworks-rs/curves/pull/74) Use Scott's subgroup membership tests for `G1` and `G2` of BLS12-381.
+- [\#103](https://github.com/arkworks-rs/curves/pull/103) Faster cofactor clearing for BLS12-381.
+- [\#107](https://github.com/arkworks-rs/curves/pull/107/) Use 2-NAF of `ATE_LOOP_COUNT` to speed up the Miller loop in MNT curves.
+

 ### Bug fixes

--- a/Cargo.toml
+++ b/Cargo.toml
@@ -1,7 +1,6 @@
 [workspace]

 members = [
-    "curve-benches",
    "curve-constraint-tests",

    "bls12_377",
@@ -30,7 +29,11 @@ members = [

    "pallas",
    "vesta",
+
+    "curve25519",
+    "ed25519",
 ]
+resolver = "2"

 [profile.release]
 opt-level = 3
@@ -56,9 +59,3 @@ lto = "thin"
 incremental = true
 debug-assertions = true
 debug = true
-
-# To be removed in the new release.
-[patch.crates-io]
-ark-ec = { git = "https://github.com/arkworks-rs/algebra" }
-ark-ff = { git = "https://github.com/arkworks-rs/algebra" }
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra" }
--- a/bls12_377/Cargo.toml
+++ b/bls12_377/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "ark-bls12-377"
-version = "0.3.0"
+version = "0.4.0-alpha.1"
 authors = [ "arkworks contributors" ]
 description = "The BLS12-377 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
@@ -10,18 +10,19 @@ keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"

 [dependencies]
-ark-ff = { version="^0.3.0", default-features = false }
-ark-ec = { version="^0.3.0", default-features = false }
-ark-r1cs-std = { version="^0.3.0", default-features = false, optional = true }
-ark-std = { version="^0.3.0", default-features = false }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-r1cs-std = { version="0.4.0-alpha", default-features = false, optional = true }
+ark-std = { version = "0.4.0-alpha", default-features = false }

 [dev-dependencies]
-ark-relations = { version="^0.3.0", default-features = false }
-ark-serialize = { version="^0.3.0", default-features = false }
-ark-algebra-test-templates = { version="^0.3.0", default-features = false }
+ark-relations = { version="0.4.0-alpha", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
@@ -32,3 +33,8 @@ curve = [ "scalar_field", "base_field" ]
 scalar_field = []
 base_field = []
 r1cs = [ "base_field", "ark-r1cs-std" ]
+
+[[bench]]
+name = "bls12_377"
+path = "benches/bls12_377.rs"
+harness = false
--- a/bls12_377/benches/bls12_377.rs
+++ b/bls12_377/benches/bls12_377.rs
@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bls12_377::{
+    fq::Fq, fq2::Fq2, fr::Fr, Bls12_377, Fq12, G1Projective as G1, G2Projective as G2,
+};
+
+bench!(
+    Name = "Bls12_377",
+    Pairing = Bls12_377,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq2,
+    TargetField = Fq12,
+);
--- a/bls12_377/scripts/base_field.sage
+++ b/bls12_377/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+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/bls12_377/scripts/scalar_field.sage
+++ b/bls12_377/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 8444461749428370424248824938781546531375899335154063827935233455917409239041
+
+assert(modulus.is_prime())
+
+Fp = GF(modulus)
+
+generator = Fp(0);
+for i in range(0, 30):
+    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/bls12_377/src/constraints/curves.rs
+++ b/bls12_377/src/constraints/curves.rs
@@ -1,11 +1,11 @@
-use crate::Parameters;
-use ark_ec::bls12::Bls12Parameters;
-use ark_ec::ModelParameters;
+use ark_ec::{bls12::Bls12Parameters, CurveConfig};
 use ark_r1cs_std::{
    fields::fp::FpVar,
    groups::{bls12, curves::twisted_edwards::AffineVar as TEAffineVar},
 };

+use crate::Parameters;
+
 /// An element of G1 in the BLS12-377 bilinear group.
 pub type G1Var = bls12::G1Var<Parameters>;
 /// An element of G2 in the BLS12-377 bilinear group.
@@ -14,7 +14,7 @@ pub type G2Var = bls12::G2Var<Parameters>;
 /// An element of G1 (in TE Affine form) in the BLS12-377 bilinear group.
 pub type G1TEAffineVar = TEAffineVar<
    <Parameters as Bls12Parameters>::G1Parameters,
-    FpVar<<<Parameters as Bls12Parameters>::G1Parameters as ModelParameters>::BaseField>,
+    FpVar<<<Parameters as Bls12Parameters>::G1Parameters as CurveConfig>::BaseField>,
 >;

 /// Represents the cached precomputation that can be performed on a G1 element
--- a/bls12_377/src/constraints/fields.rs
+++ b/bls12_377/src/constraints/fields.rs
@@ -1,16 +1,16 @@
-use crate::{Fq, Fq12Parameters, Fq2Parameters, Fq6Parameters};
-
 use ark_r1cs_std::fields::{fp::FpVar, fp12::Fp12Var, fp2::Fp2Var, fp6_3over2::Fp6Var};

+use crate::{Fq, Fq12Config, Fq2Config, Fq6Config};
+
 /// A variable that is the R1CS equivalent of `crate::Fq`.
 pub type FqVar = FpVar<Fq>;

 /// A variable that is the R1CS equivalent of `crate::Fq2`.
-pub type Fq2Var = Fp2Var<Fq2Parameters>;
+pub type Fq2Var = Fp2Var<Fq2Config>;
 /// A variable that is the R1CS equivalent of `crate::Fq6`.
-pub type Fq6Var = Fp6Var<Fq6Parameters>;
+pub type Fq6Var = Fp6Var<Fq6Config>;
 /// A variable that is the R1CS equivalent of `crate::Fq12`.
-pub type Fq12Var = Fp12Var<Fq12Parameters>;
+pub type Fq12Var = Fp12Var<Fq12Config>;

 #[test]
 fn bls12_377_field_test() {
--- a/bls12_377/src/constraints/mod.rs
+++ b/bls12_377/src/constraints/mod.rs
@@ -106,7 +106,7 @@
 //! ```
 //! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
 //! # use ark_std::UniformRand;
-//! # use ark_ec::PairingEngine;
+//! # use ark_ec::pairing::Pairing;
 //! # use ark_relations::r1cs::*;
 //! # use ark_r1cs_std::prelude::*;
 //! # use ark_bls12_377::{*, constraints::*};
@@ -135,7 +135,7 @@
 //! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
 //!
 //! // Check that the value of &a + &b is correct.
-//! assert_eq!(pairing_result.value()?, pairing_result_native);
+//! assert_eq!(pairing_result.value()?, pairing_result_native.0);
 //!
 //! // Check that operations on variables and constants are equivalent.
 //! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
--- a/bls12_377/src/constraints/pairing.rs
+++ b/bls12_377/src/constraints/pairing.rs
@@ -1,10 +1,13 @@
 use crate::Parameters;

-/// Specifies the constraints for computing a pairing in the BLS12-377 bilinear group.
+/// Specifies the constraints for computing a pairing in the BLS12-377 bilinear
+/// group.
 pub type PairingVar = ark_r1cs_std::pairing::bls12::PairingVar<Parameters>;

 #[test]
 fn test() {
    use crate::Bls12_377;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<Bls12_377, PairingVar>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<Bls12_377, PairingVar>().unwrap();
+    ark_curve_constraint_tests::pairing::g2_prepare_consistency_test::<Bls12_377, PairingVar>()
+        .unwrap();
 }
--- a/bls12_377/src/curves/g1.rs
+++ b/bls12_377/src/curves/g1.rs
@@ -1,60 +1,55 @@
 use ark_ec::models::{
-    twisted_edwards_extended::{
-        GroupAffine as TEGroupAffine, GroupProjective as TEGroupProjective,
+    short_weierstrass::{Affine as SWAffine, SWCurveConfig},
+    twisted_edwards::{
+        Affine as TEAffine, MontCurveConfig, Projective as TEProjective, TECurveConfig,
    },
-    ModelParameters, MontgomeryModelParameters, SWModelParameters, TEModelParameters,
+    CurveConfig,
 };
-use ark_ff::{field_new, Zero};
+use ark_ff::{Field, MontFp, Zero};
 use core::ops::Neg;

-use crate::{
-    fields::{FQ_ONE, FQ_ZERO},
-    Fq, Fr,
-};
+use crate::{Fq, Fr};

 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    const COEFF_A: Fq = FQ_ZERO;
-
-    /// COEFF_B = 1
-    #[rustfmt::skip]
-    const COEFF_B: Fq = FQ_ONE;

    /// COFACTOR = (x - 1)^2 / 3  = 30631250834960419227450344600217059328
    const COFACTOR: &'static [u64] = &[0x0, 0x170b5d4430000000];

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// = 5285428838741532253824584287042945485047145357130994810877
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "5285428838741532253824584287042945485047145357130994810877");
+    const COFACTOR_INV: Fr = MontFp!("5285428838741532253824584287042945485047145357130994810877");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 1
+    const COEFF_B: Fq = Fq::ONE;

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1SWAffine = G1SWAffine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);

    #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }
 }

-pub type G1TEAffine = TEGroupAffine<Parameters>;
-pub type G1TEProjective = TEGroupProjective<Parameters>;
+pub type G1SWAffine = SWAffine<Parameters>;
+pub type G1TEAffine = TEAffine<Parameters>;
+pub type G1TEProjective = TEProjective<Parameters>;

 /// Bls12_377::G1 also has a twisted Edwards form.
 /// It can be obtained via the following script, implementing
 /// 1. SW -> Montgomery -> TE1 transformation: <https://en.wikipedia.org/wiki/Montgomery_curve>
 /// 2. TE1 -> TE2 normalization (enforcing `a = -1`)
 /// ``` sage
-///
 /// # modulus
 /// p = 0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001
 /// Fp = Zmod(p)
@@ -96,33 +91,22 @@ pub type G1TEProjective = TEGroupProjective<Parameters>;
 /// TE2a = Fp(-1)
 /// # b = -TE1d/TE1a
 /// TE2d = Fp(122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179)
-///
 /// ```
-impl TEModelParameters for Parameters {
+impl TECurveConfig for Parameters {
    /// COEFF_A = -1
-    const COEFF_A: Fq = field_new!(Fq, "-1");
+    const COEFF_A: Fq = MontFp!("-1");

    /// COEFF_D = 122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179 mod q
-    #[rustfmt::skip]
-    const COEFF_D: Fq = field_new!(Fq, "122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179");
-
-    /// COFACTOR = (x - 1)^2 / 3  = 30631250834960419227450344600217059328
-    const COFACTOR: &'static [u64] = &[0x0, 0x170b5d4430000000];
-
-    /// COFACTOR_INV = COFACTOR^{-1} mod r
-    /// = 5285428838741532253824584287042945485047145357130994810877
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "5285428838741532253824584287042945485047145357130994810877");
+    const COEFF_D: Fq = MontFp!("122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179");

    /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (TE_GENERATOR_X, TE_GENERATOR_Y);
+    const GENERATOR: G1TEAffine = G1TEAffine::new_unchecked(TE_GENERATOR_X, TE_GENERATOR_Y);

-    type MontgomeryModelParameters = Parameters;
+    type MontCurveConfig = Parameters;

    /// Multiplication by `a` is multiply by `-1`.
    #[inline(always)]
-    fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(elem: Self::BaseField) -> Self::BaseField {
        elem.neg()
    }
 }
@@ -132,7 +116,6 @@ impl TEModelParameters for Parameters {
 // It can be obtained via the following script, implementing
 // SW -> Montgomery transformation: <https://en.wikipedia.org/wiki/Montgomery_curve>
 // ``` sage
-//
 // # modulus
 // p=0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001
 // Fp=Zmod(p)
@@ -157,29 +140,26 @@ impl TEModelParameters for Parameters {
 // # MB = s
 // MB=Fp(10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931)
 // ```
-impl MontgomeryModelParameters for Parameters {
+impl MontCurveConfig for Parameters {
    /// COEFF_A = 228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384");
+    const COEFF_A: Fq = MontFp!("228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384");

    /// COEFF_B = 10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931");
+    const COEFF_B: Fq = MontFp!("10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931");

-    type TEModelParameters = Parameters;
+    type TECurveConfig = Parameters;
 }

 /// G1_GENERATOR_X =
 /// 81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, "81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695");
+pub const G1_GENERATOR_X: Fq = MontFp!("81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695");

 /// G1_GENERATOR_Y =
 /// 241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");
+pub const G1_GENERATOR_Y: Fq = MontFp!("241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");

-// The generator for twisted Edward form is the same SW generator converted into the normalized TE form (TE2).
+// The generator for twisted Edward form is the same SW generator converted into
+// the normalized TE form (TE2).
 //``` sage
 // # following scripts in previous section
 // #####################################################
@@ -224,10 +204,8 @@ pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "241266749859715473739788878240585
 // ```
 /// TE_GENERATOR_X =
 /// 71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393
-#[rustfmt::skip]
-pub const TE_GENERATOR_X: Fq = field_new!(Fq, "71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393");
+pub const TE_GENERATOR_X: Fq = MontFp!("71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393");

 /// TE_GENERATOR_Y =
 /// 6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235
-#[rustfmt::skip]
-pub const TE_GENERATOR_Y: Fq = field_new!(Fq, "6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");
+pub const TE_GENERATOR_Y: Fq = MontFp!("6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");
--- a/bls12_377/src/curves/g2.rs
+++ b/bls12_377/src/curves/g2.rs
@@ -1,35 +1,18 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{field_new, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};

-use crate::{fields::FQ_ZERO, g1, Fq, Fq2, Fr};
+use crate::{g1, Fq, Fq2, Fr};

+pub type G2Affine = Affine<Parameters>;
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq2;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = [0, 0]
-    #[rustfmt::skip]
-    const COEFF_A: Fq2 = field_new!(Fq2,
-        g1::Parameters::COEFF_A,
-        g1::Parameters::COEFF_A,
-    );
-
-    // As per https://eprint.iacr.org/2012/072.pdf,
-    // this curve has b' = b/i, where b is the COEFF_B of G1, and x^6 -i is
-    // the irreducible poly used to extend from Fp2 to Fp12.
-    // In our case, i = u (App A.3, T_6).
-    /// COEFF_B = [0,
-    /// 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906]
-    #[rustfmt::skip]
-    const COEFF_B: Fq2 = field_new!(Fq2,
-        FQ_ZERO,
-        field_new!(Fq, "155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906"),
-    );

    /// COFACTOR =
    /// 7923214915284317143930293550643874566881017850177945424769256759165301436616933228209277966774092486467289478618404761412630691835764674559376407658497
@@ -47,40 +30,49 @@ impl SWModelParameters for Parameters {

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// = 6764900296503390671038341982857278410319949526107311149686707033187604810669
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "6764900296503390671038341982857278410319949526107311149686707033187604810669");
+    const COFACTOR_INV: Fr =
+        MontFp!("6764900296503390671038341982857278410319949526107311149686707033187604810669");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = [0, 0]
+    const COEFF_A: Fq2 = Fq2::new(g1::Parameters::COEFF_A, g1::Parameters::COEFF_A);
+
+    // As per https://eprint.iacr.org/2012/072.pdf,
+    // this curve has b' = b/i, where b is the COEFF_B of G1, and x^6 -i is
+    // the irreducible poly used to extend from Fp2 to Fp12.
+    // In our case, i = u (App A.3, T_6).
+    /// COEFF_B = [0,
+    /// 155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906]
+    const COEFF_B: Fq2 = Fq2::new(
+        Fq::ZERO,
+        MontFp!("155198655607781456406391640216936120121836107652948796323930557600032281009004493664981332883744016074664192874906"),
+    );

    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);

    #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }
 }

-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+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);

 /// G2_GENERATOR_X_C0 =
 /// 233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("233578398248691099356572568220835526895379068987715365179118596935057653620464273615301663571204657964920925606294");

 /// G2_GENERATOR_X_C1 =
 /// 140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("140913150380207355837477652521042157274541796891053068589147167627541651775299824604154852141315666357241556069118");

 /// G2_GENERATOR_Y_C0 =
 /// 63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("63160294768292073209381361943935198908131692476676907196754037919244929611450776219210369229519898517858833747423");

 /// G2_GENERATOR_Y_C1 =
 /// 149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("149157405641012693445398062341192467754805999074082136895788947234480009303640899064710353187729182149407503257491");
--- a/bls12_377/src/curves/mod.rs
+++ b/bls12_377/src/curves/mod.rs
@@ -1,9 +1,10 @@
-use crate::*;
 use ark_ec::{
    bls12,
    bls12::{Bls12, Bls12Parameters, TwistType},
 };

+use crate::*;
+
 pub mod g1;
 pub mod g2;

@@ -18,9 +19,9 @@ impl Bls12Parameters for Parameters {
    const X_IS_NEGATIVE: bool = false;
    const TWIST_TYPE: TwistType = TwistType::D;
    type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
    type G1Parameters = g1::Parameters;
    type G2Parameters = g2::Parameters;
 }
--- a/bls12_377/src/curves/tests.rs
+++ b/bls12_377/src/curves/tests.rs
@@ -1,130 +1,7 @@
-#![allow(unused_imports)]
-use crate::{
-    g1, g2, Bls12_377, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G1TEProjective, G2Affine,
-    G2Projective,
-};
-use ark_ec::{
-    models::SWModelParameters, short_weierstrass_jacobian, AffineCurve, PairingEngine,
-    ProjectiveCurve,
-};
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    One, Zero,
-};
-use ark_serialize::CanonicalSerialize;
-use ark_std::{rand::Rng, test_rng};
-use core::ops::{AddAssign, MulAssign};
+use crate::{Bls12_377, G1Projective, G2Projective};
+use ark_algebra_test_templates::*;

-use ark_algebra_test_templates::{
-    curves::{curve_tests, edwards_tests, sw_tests},
-    groups::group_test,
-};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-    edwards_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-
-    let c = rng.gen();
-    let d = rng.gen();
-    group_test::<G1TEProjective>(c, d);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let mut sa = a;
-    sa.mul_assign(s);
-    let mut sb = b;
-    sb.mul_assign(s);
-
-    let ans1 = Bls12_377::pairing(sa, b);
-    let ans2 = Bls12_377::pairing(a, sb);
-    let ans3 = Bls12_377::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq12::one());
-    assert_ne!(ans2, Fq12::one());
-    assert_ne!(ans3, Fq12::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq12::one());
-}
-
-#[test]
-fn test_g1_generator_raw() {
-    let mut x = Fq::zero();
-    let mut i = 0;
-    loop {
-        // y^2 = x^3 + b
-        let mut rhs = x;
-        rhs.square_in_place();
-        rhs.mul_assign(&x);
-        rhs.add_assign(&g1::Parameters::COEFF_B);
-
-        if let Some(y) = rhs.sqrt() {
-            let p = G1Affine::new(x, if y < -y { y } else { -y }, false);
-            assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-
-            let g1 = p.scale_by_cofactor();
-            if !g1.is_zero() {
-                assert_eq!(i, 1);
-                let g1 = G1Affine::from(g1);
-
-                assert!(g1.is_in_correct_subgroup_assuming_on_curve());
-
-                assert_eq!(g1, G1Affine::prime_subgroup_generator());
-                break;
-            }
-        }
-
-        i += 1;
-        x.add_assign(&Fq::one());
-    }
-}
+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);
--- a/bls12_377/src/fields/fq.rs
+++ b/bls12_377/src/fields/fq.rs
@@ -1,118 +1,7 @@
-use ark_ff::{biginteger::BigInteger384 as BigInteger, fields::*};
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};

-pub type Fq = Fp384<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp384Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 46u32;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        2022196864061697551u64,
-        17419102863309525423u64,
-        8564289679875062096u64,
-        17152078065055548215u64,
-        17966377291017729567u64,
-        68610905582439508u64,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0x8508c00000000001,
-        0x170b5d4430000000,
-        0x1ef3622fba094800,
-        0x1a22d9f300f5138f,
-        0xc63b05c06ca1493b,
-        0x1ae3a4617c510ea,
-    ]);
-
-    const MODULUS_BITS: u32 = 377;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 7;
-
-    /// R = 85013442423176922659824578519796707547925331718418265885885478904210582549405549618995257669764901891699128663912
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        202099033278250856u64,
-        5854854902718660529u64,
-        11492539364873682930u64,
-        8885205928937022213u64,
-        5545221690922665192u64,
-        39800542322357402u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xb786686c9400cd22,
-        0x329fcaab00431b1,
-        0x22a5f11162d6b46d,
-        0xbfdf7d03827dc3ac,
-        0x837e92f041790bf9,
-        0x6dfccb1e914b88,
-    ]);
-
-    const INV: u64 = 9586122913090633727u64;
-
-    /// GENERATOR = -5
-    /// Encoded in Montgomery form, so the value here is
-    /// (-5 * R) % q = 92261639910053574722182574790803529333160366917737991650341130812388023949653897454961487930322210790384999596794
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0xfc0b8000000002fa,
-        0x97d39cf6e000018b,
-        0x2072420fbfa05044,
-        0xcbbcbd50d97c3802,
-        0xbaf1ec35813f9eb,
-        0x9974a2c0945ad2,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x4284600000000000,
-        0xb85aea218000000,
-        0x8f79b117dd04a400,
-        0x8d116cf9807a89c7,
-        0x631d82e03650a49d,
-        0xd71d230be28875,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-    // For T coprime to 2
-
-    // T = (MODULUS - 1) // 2^S =
-    // 3675842578061421676390135839012792950148785745837396071634149488243117337281387659330802195819009059
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x7510c00000021423,
-        0x88bee82520005c2d,
-        0x67cc03d44e3c7bcd,
-        0x1701b28524ec688b,
-        0xe9185f1443ab18ec,
-        0x6b8,
-    ]);
-
-    // (T - 1) // 2 =
-    // 1837921289030710838195067919506396475074392872918698035817074744121558668640693829665401097909504529
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xba88600000010a11,
-        0xc45f741290002e16,
-        0xb3e601ea271e3de6,
-        0xb80d94292763445,
-        0x748c2f8a21d58c76,
-        0x35c,
-    ]);
-}
-
-#[allow(dead_code)]
-pub const FQ_ONE: Fq = Fq::new(FqParameters::R);
-#[allow(dead_code)]
-pub const FQ_ZERO: Fq = Fq::new(BigInteger([0, 0, 0, 0, 0, 0]));
+#[derive(MontConfig)]
+#[modulus = "258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177"]
+#[generator = "15"]
+pub struct FqConfig;
+pub type Fq = Fp384<MontBackend<FqConfig, 6>>;
--- a/bls12_377/src/fields/fq12.rs
+++ b/bls12_377/src/fields/fq12.rs
@@ -1,74 +1,74 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;

 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;

-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;

-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        field_new!(Fq2, FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "92949345220277864758624960506473182677953048909283248980960104381795901929519566951595905490535835115111760994353"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("92949345220277864758624960506473182677953048909283248980960104381795901929519566951595905490535835115111760994353"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "216465761340224619389371505802605247630151569547285782856803747159100223055385581585702401816380679166954762214499"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("216465761340224619389371505802605247630151569547285782856803747159100223055385581585702401816380679166954762214499"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "123516416119946754630746545296132064952198520638002533875843642777304321125866014634106496325844844051843001220146"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("123516416119946754630746545296132064952198520638002533875843642777304321125866014634106496325844844051843001220146"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "-1"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "165715080792691229252027773188420350858440463845631411558924158284924566418821255823372982649037525009328560463824"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("165715080792691229252027773188420350858440463845631411558924158284924566418821255823372982649037525009328560463824"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "42198664672744474621281227892288285906241943207628877683080515507620245292955241189266486323192680957485559243678"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("42198664672744474621281227892288285906241943207628877683080515507620245292955241189266486323192680957485559243678"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "135148009893022339379906188398761468584194992116912126664040619889416147222474808140862391813728516072597320238031"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("135148009893022339379906188398761468584194992116912126664040619889416147222474808140862391813728516072597320238031"),
+            Fq::ZERO,
        ),
    ];
 }
--- a/bls12_377/src/fields/fq2.rs
+++ b/bls12_377/src/fields/fq2.rs
@@ -1,38 +1,51 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq2 = Fp2<Fq2Parameters>;
+use crate::*;

-pub struct Fq2Parameters;
+pub type Fq2 = Fp2<Fq2Config>;

-impl Fp2Parameters for Fq2Parameters {
+pub struct Fq2Config;
+
+impl Fp2Config for Fq2Config {
    type Fp = Fq;

    /// NONRESIDUE = -5
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, "-5");
-
-    /// QUADRATIC_NONRESIDUE = U
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (FQ_ZERO, FQ_ONE);
+    const NONRESIDUE: Fq = MontFp!("-5");

    /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
        // NONRESIDUE**(((q^0) - 1) / 2)
-        FQ_ONE,
+        Fq::ONE,
        // NONRESIDUE**(((q^1) - 1) / 2)
-        field_new!(Fq, "-1"),
+        MontFp!("-1"),
    ];

    #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
-        let original = fe;
-        let mut fe = -fe.double();
-        fe.double_in_place();
-        fe - original
-    }
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
+        fe.neg_in_place();
+        *fe = *fe + fe.double_in_place().double_in_place();
+        fe
    }

-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(y: &mut Self::Fp, x: &Self::Fp) {
+        let mut original = *y;
+        original += x;
+        y.double_in_place().double_in_place();
+        *y += original;
+    }
+
+    #[inline(always)]
+    fn mul_fp_by_nonresidue_plus_one_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        y.double_in_place().double_in_place().neg_in_place();
+        *y += x;
+    }
+
+    fn mul_fp_by_nonresidue_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        let mut original = *y;
+        original.double_in_place().double_in_place();
+        original += &*y;
+        *y = *x;
+        *y -= original;
+    }
+}
--- a/bls12_377/src/fields/fq6.rs
+++ b/bls12_377/src/fields/fq6.rs
@@ -1,78 +1,79 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;

 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;

-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;

    /// NONRESIDUE = U
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ONE);
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ZERO, Fq::ONE);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        field_new!(Fq2, FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410946"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        field_new!(Fq2, field_new!(Fq, "-1"), FQ_ZERO),
+        Fq2::new(MontFp!("-1"), Fq::ZERO),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047232"),
+            Fq::ZERO,
        ),
    ];
-    #[rustfmt::skip]
+
    const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        field_new!(Fq2, FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO
        ),
        // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        field_new!(Fq2, FQ_ONE, FQ_ZERO),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("80949648264912719408558363140637477264845294720710499478137287262712535938301461879813459410945"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
-            FQ_ZERO,
+        Fq2::new(
+            MontFp!("258664426012969093929703085429980814127835149614277183275038967946009968870203535512256352201271898244626862047231"),
+            Fq::ZERO,
        ),
    ];

    #[inline(always)]
-    fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
+    fn mul_fp2_by_nonresidue_in_place(fe: &mut Fq2) -> &mut Fq2 {
        // Karatsuba multiplication with constant other = u.
-        let c0 = Fq2Parameters::mul_fp_by_nonresidue(&fe.c1);
-        let c1 = fe.c0;
-        field_new!(Fq2, c0, c1)
+        let old_c0 = fe.c0;
+        fe.c0 = fe.c1;
+        Fq2Config::mul_fp_by_nonresidue_in_place(&mut fe.c0);
+        fe.c1 = old_c0;
+        fe
    }
 }
--- a/bls12_377/src/fields/fr.rs
+++ b/bls12_377/src/fields/fr.rs
@@ -1,5 +1,4 @@
 //! Bls12-377 scalar field.
-///
 /// Roots of unity computed from modulus and R using this sage code:
 ///
 /// ```ignore
@@ -19,103 +18,10 @@
 /// print("Gen: ", into_chunks(g * R % q, 64, 4))
 /// print("2-adic gen: ", into_chunks(g2 * R % q, 64, 4))
 /// ```
-use ark_ff::{biginteger::BigInteger256 as BigInteger, fields::*};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};

-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 47;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        12646347781564978760u64,
-        6783048705277173164u64,
-        268534165941069093u64,
-        1121515446318641358u64,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 8444461749428370424248824938781546531375899335154063827935233455917409239041
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        725501752471715841u64,
-        6461107452199829505u64,
-        6968279316240510977u64,
-        1345280370688173398u64,
-    ]);
-
-    const MODULUS_BITS: u32 = 253;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 3;
-
-    /// R = 6014086494747379908336260804527802945383293308637734276299549080986809532403
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        9015221291577245683u64,
-        8239323489949974514u64,
-        1646089257421115374u64,
-        958099254763297437u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        2726216793283724667u64,
-        14712177743343147295u64,
-        12091039717619697043u64,
-        81024008013859129u64,
-    ]);
-
-    const INV: u64 = 725501752471715839u64;
-
-    /// GENERATOR = 22
-    /// Encoded in Montgomery form, so the value is
-    /// (22 * R) % q =
-    /// 5642976643016801619665363617888466827793962762719196659561577942948671127251
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        2984901390528151251u64,
-        10561528701063790279u64,
-        5476750214495080041u64,
-        898978044469942640u64,
-    ]);
-
-    /// (r - 1)/2 =
-    /// 4222230874714185212124412469390773265687949667577031913967616727958704619520
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x8508c00000000000,
-        0xacd53b7f68000000,
-        0x305a268f2e1bd800,
-        0x955b2af4d1652ab,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t
-    // For T coprime to 2
-
-    /// t = (r - 1) / 2^s =
-    /// 60001509534603559531609739528203892656505753216962260608619555
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0xedfda00000021423,
-        0x9a3cb86f6002b354,
-        0xcabd34594aacc168,
-        0x2556,
-    ]);
-
-    /// (t - 1) / 2 =
-    /// 30000754767301779765804869764101946328252876608481130304309777
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x76fed00000010a11,
-        0x4d1e5c37b00159aa,
-        0x655e9a2ca55660b4,
-        0x12ab,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "8444461749428370424248824938781546531375899335154063827935233455917409239041"]
+#[generator = "22"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
--- a/bls12_377/src/fields/tests.rs
+++ b/bls12_377/src/fields/tests.rs
@@ -1,127 +1,52 @@
+use ark_algebra_test_templates::*;
 use ark_ff::{
-    biginteger::{BigInteger, BigInteger384},
-    fields::{
-        fp6_3over2::Fp6Parameters, FftField, FftParameters, Field, Fp2Parameters, FpParameters,
-        PrimeField, SquareRootField,
-    },
-    One, UniformRand, Zero,
+    biginteger::{BigInt, BigInteger, BigInteger384},
+    fields::{FftField, Field, Fp6Config, PrimeField},
+    Fp384, One, UniformRand, Zero,
 };
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use ark_std::{rand::Rng, test_rng};
-use core::{
+use ark_std::{
    cmp::Ordering,
-    ops::{AddAssign, MulAssign, SubAssign},
+    ops::{AddAssign, MulAssign},
+    test_rng,
 };

-use crate::{Fq, Fq12, Fq2, Fq2Parameters, Fq6, Fq6Parameters, FqParameters, Fr};
+use crate::{Fq, Fq12, Fq2, Fq6, Fq6Config, Fr};

-use ark_algebra_test_templates::fields::*;
-
-pub(crate) const ITERATIONS: usize = 5;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fr = rng.gen();
-        let b: Fr = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fr>();
-        sqrt_field_test(b);
-        let byte_size = a.serialized_size();
-        field_serialization_test::<Fr>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq = rng.gen();
-        let b: Fq = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fq>();
-        sqrt_field_test(a);
-        let byte_size = a.serialized_size();
-        let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-        assert_eq!(byte_size, buffer_size);
-        field_serialization_test::<Fq>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq2() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq2 = rng.gen();
-        let b: Fq2 = rng.gen();
-        field_test(a, b);
-        sqrt_field_test(a);
-    }
-    frobenius_test::<Fq2, _>(Fq::characteristic(), 13);
-    let byte_size = Fq2::zero().serialized_size();
-    field_serialization_test::<Fq2>(byte_size);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq6 = rng.gen();
-        let h: Fq6 = rng.gen();
-        field_test(g, h);
-    }
-
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-    let byte_size = Fq6::zero().serialized_size();
-    field_serialization_test::<Fq6>(byte_size);
-}
-
-#[test]
-fn test_fq12() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq12 = rng.gen();
-        let h: Fq12 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq12, _>(Fq::characteristic(), 13);
-    let byte_size = Fq12::zero().serialized_size();
-    field_serialization_test::<Fq12>(byte_size);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq2; Fq2);
+test_field!(fq6; Fq6);
+test_field!(fq12; Fq12);

 #[test]
 fn test_fq_repr_from() {
-    assert_eq!(
-        BigInteger384::from(100),
-        BigInteger384([100, 0, 0, 0, 0, 0])
-    );
+    assert_eq!(BigInt::from(100u64), BigInt::new([100, 0, 0, 0, 0, 0]));
 }

 #[test]
 fn test_fq_repr_is_odd() {
-    assert!(!BigInteger384::from(0).is_odd());
-    assert!(BigInteger384::from(0).is_even());
-    assert!(BigInteger384::from(1).is_odd());
-    assert!(!BigInteger384::from(1).is_even());
-    assert!(!BigInteger384::from(324834872).is_odd());
-    assert!(BigInteger384::from(324834872).is_even());
-    assert!(BigInteger384::from(324834873).is_odd());
-    assert!(!BigInteger384::from(324834873).is_even());
+    assert!(!BigInteger384::from(0u64).is_odd());
+    assert!(BigInteger384::from(0u64).is_even());
+    assert!(BigInteger384::from(1u64).is_odd());
+    assert!(!BigInteger384::from(1u64).is_even());
+    assert!(!BigInteger384::from(324834872u64).is_odd());
+    assert!(BigInteger384::from(324834872u64).is_even());
+    assert!(BigInteger384::from(324834873u64).is_odd());
+    assert!(!BigInteger384::from(324834873u64).is_even());
 }

 #[test]
 fn test_fq_repr_is_zero() {
-    assert!(BigInteger384::from(0).is_zero());
-    assert!(!BigInteger384::from(1).is_zero());
-    assert!(!BigInteger384([0, 0, 0, 0, 1, 0]).is_zero());
+    assert!(BigInteger384::from(0u64).is_zero());
+    assert!(!BigInteger384::from(1u64).is_zero());
+    assert!(!BigInt::new([0, 0, 0, 0, 1, 0]).is_zero());
 }

 #[test]
 fn test_fq_repr_num_bits() {
-    let mut a = BigInteger384::from(0);
+    let mut a = BigInteger384::from(0u64);
    assert_eq!(0, a.num_bits());
-    a = BigInteger384::from(1);
+    a = BigInteger384::from(1u64);
    for i in 1..385 {
        assert_eq!(i, a.num_bits());
        a.mul2();
@@ -129,229 +54,16 @@ fn test_fq_repr_num_bits() {
    assert_eq!(0, a.num_bits());
 }

-#[test]
-fn test_fq_add_assign() {
-    // Test associativity
-
-    let mut rng = test_rng();
-
-    for _ in 0..1000 {
-        // Generate a, b, c and ensure (a + b) + c == a + (b + c).
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.add_assign(&c);
-        tmp2.add_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_sub_assign() {
-    let mut rng = test_rng();
-
-    for _ in 0..1000 {
-        // Ensure that (a - b) + (b - a) = 0.
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.sub_assign(&b);
-
-        let mut tmp2 = b;
-        tmp2.sub_assign(&a);
-
-        tmp1.add_assign(&tmp2);
-        assert!(tmp1.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_mul_assign() {
-    let mut rng = test_rng();
-
-    for _ in 0..1000000 {
-        // Ensure that (a * b) * c = a * (b * c)
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.mul_assign(&b);
-        tmp1.mul_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.mul_assign(&c);
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-
-    for _ in 0..1000000 {
-        // Ensure that r * (a + b + c) = r*a + r*b + r*c
-
-        let r = Fq::rand(&mut rng);
-        let mut a = Fq::rand(&mut rng);
-        let mut b = Fq::rand(&mut rng);
-        let mut c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-        tmp1.mul_assign(&r);
-
-        a.mul_assign(&r);
-        b.mul_assign(&r);
-        c.mul_assign(&r);
-
-        a.add_assign(&b);
-        a.add_assign(&c);
-
-        assert_eq!(tmp1, a);
-    }
-}
-
-#[test]
-fn test_fq_squaring() {
-    let mut rng = test_rng();
-
-    for _ in 0..1000000 {
-        // Ensure that (a * a) = a^2
-        let a = Fq::rand(&mut rng);
-
-        let mut tmp = a;
-        tmp.square_in_place();
-
-        let mut tmp2 = a;
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_inverse() {
-    assert!(Fq::zero().inverse().is_none());
-
-    let mut rng = test_rng();
-
-    let one = Fq::one();
-
-    for _ in 0..1000 {
-        // Ensure that a * a^-1 = 1
-        let mut a = Fq::rand(&mut rng);
-        let ainv = a.inverse().unwrap();
-        a.mul_assign(&ainv);
-        assert_eq!(a, one);
-    }
-}
-
-#[test]
-fn test_fq_double_in_place() {
-    let mut rng = test_rng();
-
-    for _ in 0..1000 {
-        // Ensure doubling a is equivalent to adding a to itself.
-        let mut a = Fq::rand(&mut rng);
-        let mut b = a;
-        b.add_assign(&a);
-        a.double_in_place();
-        assert_eq!(a, b);
-    }
-}
-
-#[test]
-fn test_fq_negate() {
-    {
-        let a = -Fq::zero();
-
-        assert!(a.is_zero());
-    }
-
-    let mut rng = test_rng();
-
-    for _ in 0..1000 {
-        // Ensure (a - (-a)) = 0.
-        let mut a = Fq::rand(&mut rng);
-        let b = -a;
-        a.add_assign(&b);
-
-        assert!(a.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_pow() {
-    let mut rng = test_rng();
-
-    for i in 0..1000 {
-        // Exponentiate by various small numbers and ensure it consists with repeated
-        // multiplication.
-        let a = Fq::rand(&mut rng);
-        let target = a.pow(&[i]);
-        let mut c = Fq::one();
-        for _ in 0..i {
-            c.mul_assign(&a);
-        }
-        assert_eq!(c, target);
-    }
-
-    for _ in 0..1000 {
-        // Exponentiating by the modulus should have no effect in a prime field.
-        let a = Fq::rand(&mut rng);
-
-        assert_eq!(a, a.pow(Fq::characteristic()));
-    }
-}
-
-#[test]
-fn test_fq_sqrt() {
-    let mut rng = test_rng();
-
-    assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a^2) = a or -a
-        let a = Fq::rand(&mut rng);
-        let nega = -a;
-        let mut b = a;
-        b.square_in_place();
-
-        let b = b.sqrt().unwrap();
-
-        assert!(a == b || nega == b);
-    }
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a)^2 = a for random a
-        let a = Fq::rand(&mut rng);
-
-        if let Some(mut tmp) = a.sqrt() {
-            tmp.square_in_place();
-
-            assert_eq!(a, tmp);
-        }
-    }
-}
-
 #[test]
 fn test_fq_num_bits() {
-    assert_eq!(FqParameters::MODULUS_BITS, 377);
-    assert_eq!(FqParameters::CAPACITY, 376);
+    assert_eq!(Fq::MODULUS_BIT_SIZE, 377);
 }

 #[test]
 fn test_fq_root_of_unity() {
-    assert_eq!(FqParameters::TWO_ADICITY, 46);
+    assert_eq!(Fq::TWO_ADICITY, 46);
    assert_eq!(
-        Fq::multiplicative_generator().pow([
+        Fq::GENERATOR.pow([
            0x7510c00000021423,
            0x88bee82520005c2d,
            0x67cc03d44e3c7bcd,
@@ -359,21 +71,21 @@ fn test_fq_root_of_unity() {
            0xe9185f1443ab18ec,
            0x6b8
        ]),
-        Fq::two_adic_root_of_unity()
+        Fq::TWO_ADIC_ROOT_OF_UNITY
    );
    assert_eq!(
-        Fq::two_adic_root_of_unity().pow([1 << FqParameters::TWO_ADICITY]),
+        Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
        Fq::one()
    );
-    assert!(Fq::multiplicative_generator().sqrt().is_none());
+    assert!(Fq::GENERATOR.sqrt().is_none());
 }

 #[test]
 fn test_fq_ordering() {
    // BigInteger384's ordering is well-tested, but we still need to make sure the
    // Fq elements aren't being compared in Montgomery form.
-    for i in 0..100 {
-        assert!(Fq::from(BigInteger384::from(i + 1)) > Fq::from(BigInteger384::from(i)));
+    for i in 0..100u64 {
+        assert!(Fq::from(Fp384::from(i + 1)) > Fq::from(Fp384::from(i)));
    }
 }

@@ -383,14 +95,8 @@ fn test_fq_legendre() {

    assert_eq!(QuadraticResidue, Fq::one().legendre());
    assert_eq!(Zero, Fq::zero().legendre());
-    assert_eq!(
-        QuadraticResidue,
-        Fq::from(BigInteger384::from(4)).legendre()
-    );
-    assert_eq!(
-        QuadraticNonResidue,
-        Fq::from(BigInteger384::from(5)).legendre()
-    );
+    assert_eq!(QuadraticResidue, Fq::from(Fp384::from(4u64)).legendre());
+    assert_eq!(QuadraticNonResidue, Fq::from(Fp384::from(5u64)).legendre());
 }

 #[test]
@@ -430,30 +136,10 @@ fn test_fq2_legendre() {
    // i^2 = -1
    let mut m1 = -Fq2::one();
    assert_eq!(QuadraticResidue, m1.legendre());
-    m1 = Fq6Parameters::mul_fp2_by_nonresidue(&m1);
+    Fq6Config::mul_fp2_by_nonresidue_in_place(&mut m1);
    assert_eq!(QuadraticNonResidue, m1.legendre());
 }

-#[test]
-fn test_fq2_mul_nonresidue() {
-    let mut rng = test_rng();
-
-    let nqr = Fq2::new(Fq::zero(), Fq::one());
-
-    let quadratic_non_residue = Fq2::new(
-        Fq2Parameters::QUADRATIC_NONRESIDUE.0,
-        Fq2Parameters::QUADRATIC_NONRESIDUE.1,
-    );
-    for _ in 0..1000 {
-        let mut a = Fq2::rand(&mut rng);
-        let mut b = a;
-        a = quadratic_non_residue * &a;
-        b.mul_assign(&nqr);
-
-        assert_eq!(a, b);
-    }
-}
-
 #[test]
 fn test_fq6_mul_by_1() {
    let mut rng = test_rng();
--- a/bls12_377/src/lib.rs
+++ b/bls12_377/src/lib.rs
@@ -9,15 +9,17 @@
 #![forbid(unsafe_code)]

 //! This library implements the BLS12_377 curve generated in [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
-//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree 12,
-//! defined over a 377-bit (prime) field. The main feature of this curve is that
-//! both the scalar field and the base field are highly 2-adic.
-//! (This is in contrast to the BLS12_381 curve for which only the scalar field is highly 2-adic.)
+//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree
+//! 12, defined over a 377-bit (prime) field. The main feature of this curve is
+//! that both the scalar field and the base field are highly 2-adic.
+//! (This is in contrast to the BLS12_381 curve for which only the scalar field
+//! is highly 2-adic.)
 //!
 //!
 //! Curve information:
 //! * Base field: q = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
-//! * Scalar field: r = 8444461749428370424248824938781546531375899335154063827935233455917409239041
+//! * Scalar field: r =
+//!   8444461749428370424248824938781546531375899335154063827935233455917409239041
 //! * valuation(q - 1, 2) = 46
 //! * valuation(r - 1, 2) = 47
 //! * G1 curve equation: y^2 = x^3 + 1
--- a/bls12_381/Cargo.toml
+++ b/bls12_381/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "ark-bls12-381"
-version = "0.3.0"
+version = "0.4.0-alpha.1"
 authors = [ "arkworks contributors" ]
 description = "The BLS12-381 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
@@ -10,16 +10,18 @@ keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"

 [dependencies]
-ark-ff = { version="^0.3.0", default-features = false }
-ark-ec = { version="^0.3.0", default-features = false }
-ark-std = { version="^0.3.0", default-features = false }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }

 [dev-dependencies]
-ark-serialize = { version="^0.3.0", default-features = false }
-ark-algebra-test-templates = { version="^0.3.0", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }
+hex = "^0.4.0"

 [features]
 default = [ "curve" ]
@@ -27,3 +29,8 @@ std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]

 curve = [ "scalar_field" ]
 scalar_field = []
+
+[[bench]]
+name = "bls12_381"
+path = "benches/bls12_381.rs"
+harness = false
--- a/bls12_381/benches/bls12_381.rs
+++ b/bls12_381/benches/bls12_381.rs
@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bls12_381::{
+    fq::Fq, fq2::Fq2, fr::Fr, Bls12_381, Fq12, G1Projective as G1, G2Projective as G2,
+};
+
+bench!(
+    Name = "Bls12_381",
+    Pairing = Bls12_381,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq2,
+    TargetField = Fq12,
+);
--- a/bls12_381/scripts/base_field.sage
+++ b/bls12_381/scripts/base_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/bls12_381/scripts/scalar_field.sage
+++ b/bls12_381/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+
+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/bls12_381/src/curves/g1.rs
+++ b/bls12_381/src/curves/g1.rs
@@ -2,12 +2,17 @@ use crate::*;
 use ark_ec::{
    bls12,
    bls12::Bls12Parameters,
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::GroupAffine,
-    AffineCurve, ProjectiveCurve,
+    models::CurveConfig,
+    short_weierstrass::{Affine, SWCurveConfig},
+    AffineRepr, Group,
+};
+use ark_ff::{Field, MontFp, PrimeField, Zero};
+use ark_serialize::{Compress, SerializationError};
+use ark_std::{ops::Neg, One};
+
+use crate::util::{
+    read_g1_compressed, read_g1_uncompressed, serialize_fq, EncodingFlags, G1_SERIALIZED_SIZE,
 };
-use ark_ff::{biginteger::BigInteger256, field_new, Zero};
-use ark_std::ops::Neg;

 pub type G1Affine = bls12::G1Affine<crate::Parameters>;
 pub type G1Projective = bls12::G1Projective<crate::Parameters>;
@@ -15,73 +20,175 @@ pub type G1Projective = bls12::G1Projective<crate::Parameters>;
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    const COEFF_A: Fq = field_new!(Fq, "0");
-
-    /// COEFF_B = 4
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "4");

    /// COFACTOR = (x - 1)^2 / 3  = 76329603384216526031706109802092473003
    const COFACTOR: &'static [u64] = &[0x8c00aaab0000aaab, 0x396c8c005555e156];

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// = 52435875175126190458656871551744051925719901746859129887267498875565241663483
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "52435875175126190458656871551744051925719901746859129887267498875565241663483");
+    const COFACTOR_INV: Fr =
+        MontFp!("52435875175126190458656871551744051925719901746859129887267498875565241663483");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 4
+    const COEFF_B: Fq = MontFp!("4");

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);

    #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }

-    fn is_in_correct_subgroup_assuming_on_curve(p: &GroupAffine<Parameters>) -> bool {
+    #[inline]
+    fn is_in_correct_subgroup_assuming_on_curve(p: &G1Affine) -> bool {
        // Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
        //
        // Check that endomorphism_p(P) == -[X^2]P

-        let x = BigInteger256::new([crate::Parameters::X[0], 0, 0, 0]);
-
        // An early-out optimization described in Section 6.
-        // If uP == P but P != point of infinity, then the point is not in the right subgroup.
-        let x_times_p = p.mul(x);
+        // If uP == P but P != point of infinity, then the point is not in the right
+        // subgroup.
+        let x_times_p = p.mul_bigint(crate::Parameters::X);
        if x_times_p.eq(p) && !p.infinity {
            return false;
        }

-        let minus_x_squared_times_p = x_times_p.mul(x).neg();
+        let minus_x_squared_times_p = x_times_p.mul_bigint(crate::Parameters::X).neg();
        let endomorphism_p = endomorphism(p);
        minus_x_squared_times_p.eq(&endomorphism_p)
    }
+
+    #[inline]
+    fn clear_cofactor(p: &G1Affine) -> G1Affine {
+        // Using the effective cofactor, as explained in
+        // Section 5 of https://eprint.iacr.org/2019/403.pdf.
+        //
+        // It is enough to multiply by (1 - x), instead of (x - 1)^2 / 3
+        let h_eff = one_minus_x().into_bigint();
+        Parameters::mul_affine(&p, h_eff.as_ref()).into()
+    }
+
+    fn deserialize_with_mode<R: ark_serialize::Read>(
+        mut reader: R,
+        compress: ark_serialize::Compress,
+        validate: ark_serialize::Validate,
+    ) -> Result<Affine<Self>, ark_serialize::SerializationError> {
+        let p = if compress == ark_serialize::Compress::Yes {
+            read_g1_compressed(&mut reader)?
+        } else {
+            read_g1_uncompressed(&mut reader)?
+        };
+
+        if validate == ark_serialize::Validate::Yes && !p.is_in_correct_subgroup_assuming_on_curve()
+        {
+            return Err(SerializationError::InvalidData);
+        }
+        Ok(p)
+    }
+
+    fn serialize_with_mode<W: ark_serialize::Write>(
+        item: &Affine<Self>,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), SerializationError> {
+        let encoding = EncodingFlags {
+            is_compressed: compress == ark_serialize::Compress::Yes,
+            is_infinity: item.is_zero(),
+            is_lexographically_largest: item.y > -item.y,
+        };
+        let mut p = *item;
+        if encoding.is_infinity {
+            p = G1Affine::zero();
+        }
+        // need to access the field struct `x` directly, otherwise we get None from xy()
+        // method
+        let x_bytes = serialize_fq(p.x);
+        if encoding.is_compressed {
+            let mut bytes: [u8; G1_SERIALIZED_SIZE] = x_bytes;
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        } else {
+            let mut bytes = [0u8; 2 * G1_SERIALIZED_SIZE];
+            bytes[0..G1_SERIALIZED_SIZE].copy_from_slice(&x_bytes[..]);
+            bytes[G1_SERIALIZED_SIZE..].copy_from_slice(&serialize_fq(p.y)[..]);
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        };
+
+        Ok(())
+    }
+
+    fn serialized_size(compress: Compress) -> usize {
+        if compress == Compress::Yes {
+            G1_SERIALIZED_SIZE
+        } else {
+            G1_SERIALIZED_SIZE * 2
+        }
+    }
+}
+
+fn one_minus_x() -> Fr {
+    const X: Fr = Fr::from_sign_and_limbs(!crate::Parameters::X_IS_NEGATIVE, crate::Parameters::X);
+    Fr::one() - X
 }

 /// G1_GENERATOR_X =
 /// 3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, "3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");
+pub const G1_GENERATOR_X: Fq = MontFp!("3685416753713387016781088315183077757961620795782546409894578378688607592378376318836054947676345821548104185464507");

 /// G1_GENERATOR_Y =
 /// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");
+pub const G1_GENERATOR_Y: Fq = MontFp!("1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");

 /// BETA is a non-trivial cubic root of unity in Fq.
-pub const BETA: Fq = field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");
+pub const BETA: Fq = MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");

-pub fn endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
+pub fn endomorphism(p: &Affine<Parameters>) -> Affine<Parameters> {
    // 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.
+    // 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 *= BETA;
    res
 }
+
+#[cfg(test)]
+mod test {
+
+    use super::*;
+    use ark_std::{rand::Rng, UniformRand};
+
+    fn sample_unchecked() -> Affine<g1::Parameters> {
+        let mut rng = ark_std::test_rng();
+        loop {
+            let x = Fq::rand(&mut rng);
+            let greatest = rng.gen();
+
+            if let Some(p) = Affine::get_point_from_x_unchecked(x, greatest) {
+                return p;
+            }
+        }
+    }
+
+    #[test]
+    fn test_cofactor_clearing() {
+        const SAMPLES: usize = 100;
+        for _ in 0..SAMPLES {
+            let p: Affine<g1::Parameters> = sample_unchecked();
+            let p = p.clear_cofactor();
+            assert!(p.is_on_curve());
+            assert!(p.is_in_correct_subgroup_assuming_on_curve());
+        }
+    }
+}
--- a/bls12_381/src/curves/g2.rs
+++ b/bls12_381/src/curves/g2.rs
@@ -1,12 +1,20 @@
-use crate::*;
-use ark_ec::bls12::Bls12Parameters;
+use ark_std::ops::Neg;
+
 use ark_ec::{
    bls12,
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::GroupAffine,
-    AffineCurve,
+    bls12::Bls12Parameters,
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
+    AffineRepr, CurveGroup, Group,
+};
+use ark_ff::{Field, MontFp, Zero};
+use ark_serialize::{Compress, SerializationError};
+
+use super::util::{serialize_fq, EncodingFlags, G2_SERIALIZED_SIZE};
+use crate::{
+    util::{read_g2_compressed, read_g2_uncompressed},
+    *,
 };
-use ark_ff::{biginteger::BigInteger256, field_new, Field, Zero};

 pub type G2Affine = bls12::G2Affine<crate::Parameters>;
 pub type G2Projective = bls12::G2Projective<crate::Parameters>;
@@ -14,17 +22,9 @@ pub type G2Projective = bls12::G2Projective<crate::Parameters>;
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq2;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = [0, 0]
-    const COEFF_A: Fq2 = field_new!(Fq2, g1::Parameters::COEFF_A, g1::Parameters::COEFF_A,);
-
-    /// COEFF_B = [4, 4]
-    const COEFF_B: Fq2 = field_new!(Fq2, g1::Parameters::COEFF_B, g1::Parameters::COEFF_B,);

    /// COFACTOR = (x^8 - 4 x^7 + 5 x^6) - (4 x^4 + 6 x^3 - 4 x^2 - 4 x + 13) //
    /// 9
@@ -43,24 +43,31 @@ impl SWModelParameters for Parameters {

    /// COFACTOR_INV = COFACTOR^{-1} mod r
    /// 26652489039290660355457965112010883481355318854675681319708643586776743290055
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "26652489039290660355457965112010883481355318854675681319708643586776743290055");
+    const COFACTOR_INV: Fr =
+        MontFp!("26652489039290660355457965112010883481355318854675681319708643586776743290055");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = [0, 0]
+    const COEFF_A: Fq2 = Fq2::new(g1::Parameters::COEFF_A, g1::Parameters::COEFF_A);
+
+    /// COEFF_B = [4, 4]
+    const COEFF_B: Fq2 = Fq2::new(g1::Parameters::COEFF_B, g1::Parameters::COEFF_B);

    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);

    #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }

-    fn is_in_correct_subgroup_assuming_on_curve(point: &GroupAffine<Parameters>) -> bool {
+    fn is_in_correct_subgroup_assuming_on_curve(point: &G2Affine) -> bool {
        // Algorithm from Section 4 of https://eprint.iacr.org/2021/1130.
        //
        // Checks that [p]P = [X]P

-        let mut x_times_point = point.mul(BigInteger256([crate::Parameters::X[0], 0, 0, 0]));
+        let mut x_times_point = point.mul_bigint(crate::Parameters::X);
        if crate::Parameters::X_IS_NEGATIVE {
            x_times_point = -x_times_point;
        }
@@ -69,61 +76,162 @@ impl SWModelParameters for Parameters {

        x_times_point.eq(&p_times_point)
    }
+
+    #[inline]
+    fn clear_cofactor(p: &G2Affine) -> G2Affine {
+        // Based on Section 4.1 of https://eprint.iacr.org/2017/419.pdf
+        // [h(ψ)]P = [x^2 − x − 1]P + [x − 1]ψ(P) + (ψ^2)(2P)
+
+        // x = -15132376222941642752
+        // When multiplying, use -c1 instead, and then negate the result. That's much
+        // more efficient, since the scalar -c1 has less limbs and a much lower Hamming
+        // weight.
+        let x: &'static [u64] = crate::Parameters::X;
+        let p_projective = p.into_group();
+
+        // [x]P
+        let x_p = Parameters::mul_affine(p, &x).neg();
+        // ψ(P)
+        let psi_p = p_power_endomorphism(&p);
+        // (ψ^2)(2P)
+        let mut psi2_p2 = double_p_power_endomorphism(&p_projective.double());
+
+        // tmp = [x]P + ψ(P)
+        let mut tmp = x_p.clone();
+        tmp += &psi_p;
+
+        // tmp2 = [x^2]P + [x]ψ(P)
+        let mut tmp2: Projective<Parameters> = tmp;
+        tmp2 = tmp2.mul_bigint(x).neg();
+
+        // add up all the terms
+        psi2_p2 += tmp2;
+        psi2_p2 -= x_p;
+        psi2_p2 += &-psi_p;
+        (psi2_p2 - p_projective).into_affine()
    }

-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+    fn deserialize_with_mode<R: ark_serialize::Read>(
+        mut reader: R,
+        compress: ark_serialize::Compress,
+        validate: ark_serialize::Validate,
+    ) -> Result<Affine<Self>, ark_serialize::SerializationError> {
+        let p = if compress == ark_serialize::Compress::Yes {
+            read_g2_compressed(&mut reader)?
+        } else {
+            read_g2_uncompressed(&mut reader)?
+        };
+
+        if validate == ark_serialize::Validate::Yes && !p.is_in_correct_subgroup_assuming_on_curve()
+        {
+            return Err(SerializationError::InvalidData);
+        }
+        Ok(p)
+    }
+
+    fn serialize_with_mode<W: ark_serialize::Write>(
+        item: &Affine<Self>,
+        mut writer: W,
+        compress: ark_serialize::Compress,
+    ) -> Result<(), SerializationError> {
+        let encoding = EncodingFlags {
+            is_compressed: compress == ark_serialize::Compress::Yes,
+            is_infinity: item.is_zero(),
+            is_lexographically_largest: item.y > -item.y,
+        };
+        let mut p = *item;
+        if encoding.is_infinity {
+            p = G2Affine::zero();
+        }
+
+        let mut x_bytes = [0u8; G2_SERIALIZED_SIZE];
+        let c1_bytes = serialize_fq(p.x.c1);
+        let c0_bytes = serialize_fq(p.x.c0);
+        x_bytes[0..48].copy_from_slice(&c1_bytes[..]);
+        x_bytes[48..96].copy_from_slice(&c0_bytes[..]);
+        if encoding.is_compressed {
+            let mut bytes: [u8; G2_SERIALIZED_SIZE] = x_bytes;
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        } else {
+            let mut bytes = [0u8; 2 * G2_SERIALIZED_SIZE];
+
+            let mut y_bytes = [0u8; G2_SERIALIZED_SIZE];
+            let c1_bytes = serialize_fq(p.y.c1);
+            let c0_bytes = serialize_fq(p.y.c0);
+            y_bytes[0..48].copy_from_slice(&c1_bytes[..]);
+            y_bytes[48..96].copy_from_slice(&c0_bytes[..]);
+            bytes[0..G2_SERIALIZED_SIZE].copy_from_slice(&x_bytes);
+            bytes[G2_SERIALIZED_SIZE..].copy_from_slice(&y_bytes);
+
+            encoding.encode_flags(&mut bytes);
+            writer.write_all(&bytes)?;
+        };
+
+        Ok(())
+    }
+
+    fn serialized_size(compress: ark_serialize::Compress) -> usize {
+        if compress == Compress::Yes {
+            G2_SERIALIZED_SIZE
+        } else {
+            2 * G2_SERIALIZED_SIZE
+        }
+    }
+}
+
+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);

 /// G2_GENERATOR_X_C0 =
 /// 352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160");

 /// G2_GENERATOR_X_C1 =
 /// 3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758");

 /// G2_GENERATOR_Y_C0 =
 /// 1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905");

 /// G2_GENERATOR_Y_C1 =
 /// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");

 // psi(x,y) = (x**p * PSI_X, y**p * PSI_Y) is the Frobenius composed
 // with the quadratic twist and its inverse

 // PSI_X = 1/(u+1)^((p-1)/3)
-pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = field_new!(
-    Fq2,
-    FQ_ZERO,
-    field_new!(
-       Fq,
+pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = Fq2::new(
+    Fq::ZERO,
+    MontFp!(
                "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"
    )
 );

 // PSI_Y = 1/(u+1)^((p-1)/2)
-pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = field_new!(
-    Fq2,
-    field_new!(
-       Fq,
+pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = Fq2::new(
+    MontFp!(
                "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
-    field_new!(
-       Fq,
+    MontFp!(
                "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
 );

-pub fn p_power_endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
+pub const DOUBLE_P_POWER_ENDOMORPHISM: Fq2 = Fq2::new(
+    MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+    Fq::ZERO
+);
+
+pub fn p_power_endomorphism(p: &Affine<Parameters>) -> Affine<Parameters> {
    // The p-power endomorphism for G2 is defined as follows:
-    // 1. Note that G2 is defined on curve E': y^2 = x^3 + 4(u+1). To map a point (x, y) in E' to (s, t) in E,
-    //    one set s = x / ((u+1) ^ (1/3)), t = y / ((u+1) ^ (1/2)), because E: y^2 = x^3 + 4.
-    // 2. Apply the Frobenius endomorphism (s, t) => (s', t'), another point on curve E,
-    //    where s' = s^p, t' = t^p.
+    // 1. Note that G2 is defined on curve E': y^2 = x^3 + 4(u+1).
+    //    To map a point (x, y) in E' to (s, t) in E,
+    //    one set s = x / ((u+1) ^ (1/3)), t = y / ((u+1) ^ (1/2)),
+    //    because E: y^2 = x^3 + 4.
+    // 2. Apply the Frobenius endomorphism (s, t) => (s', t'),
+    //    another point on curve E, where s' = s^p, t' = t^p.
    // 3. Map the point from E back to E'; that is,
    //    one set x' = s' * ((u+1) ^ (1/3)), y' = t' * ((u+1) ^ (1/2)).
    //
@@ -142,3 +250,47 @@ pub fn p_power_endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Paramete

    res
 }
+
+/// For a p-power endomorphism psi(P), compute psi(psi(P))
+pub fn double_p_power_endomorphism(p: &Projective<Parameters>) -> Projective<Parameters> {
+    let mut res = *p;
+
+    res.x *= DOUBLE_P_POWER_ENDOMORPHISM;
+    res.y = res.y.neg();
+
+    res
+}
+
+#[cfg(test)]
+mod test {
+
+    use super::*;
+    use ark_std::UniformRand;
+
+    #[test]
+    fn test_cofactor_clearing() {
+        // multiplying by h_eff and clearing the cofactor by the efficient
+        // endomorphism-based method should yield the same result.
+        let h_eff: &'static [u64] = &[
+            0xe8020005aaa95551,
+            0x59894c0adebbf6b4,
+            0xe954cbc06689f6a3,
+            0x2ec0ec69d7477c1a,
+            0x6d82bf015d1212b0,
+            0x329c2f178731db95,
+            0x9986ff031508ffe1,
+            0x88e2a8e9145ad768,
+            0x584c6a0ea91b3528,
+            0xbc69f08f2ee75b3,
+        ];
+
+        let mut rng = ark_std::test_rng();
+        const SAMPLES: usize = 10;
+        for _ in 0..SAMPLES {
+            let p = Affine::<g2::Parameters>::rand(&mut rng);
+            let optimised = p.clear_cofactor().into_group();
+            let naive = g2::Parameters::mul_affine(&p, h_eff);
+            assert_eq!(optimised, naive);
+        }
+    }
+}
--- a/bls12_381/src/curves/mod.rs
+++ b/bls12_381/src/curves/mod.rs
@@ -1,9 +1,10 @@
 use ark_ec::bls12::{Bls12, Bls12Parameters, TwistType};

-use crate::{Fq, Fq12Parameters, Fq2Parameters, Fq6Parameters};
+use crate::{Fq, Fq12Config, Fq2Config, Fq6Config};

 pub mod g1;
 pub mod g2;
+pub(crate) mod util;

 #[cfg(test)]
 mod tests;
@@ -22,9 +23,9 @@ impl Bls12Parameters for Parameters {
    const X_IS_NEGATIVE: bool = true;
    const TWIST_TYPE: TwistType = TwistType::M;
    type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
    type G1Parameters = self::g1::Parameters;
    type G2Parameters = self::g2::Parameters;
 }
--- a/bls12_381/src/curves/tests.rs
+++ b/bls12_381/src/curves/tests.rs
@@ -1,173 +0,0 @@
-#![allow(unused_imports)]
-use ark_ec::{
-    models::SWModelParameters,
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
-    AffineCurve, PairingEngine, ProjectiveCurve,
-};
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    BitIteratorBE, One, UniformRand, Zero,
-};
-use ark_serialize::CanonicalSerialize;
-use ark_std::rand::Rng;
-use ark_std::test_rng;
-use core::ops::{AddAssign, MulAssign};
-
-use crate::{g1, g2, Bls12_381, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
-use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::group::Group;
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let mut sa = a;
-    sa.mul_assign(s);
-    let mut sb = b;
-    sb.mul_assign(s);
-
-    let ans1 = Bls12_381::pairing(sa, b);
-    let ans2 = Bls12_381::pairing(a, sb);
-    let ans3 = Bls12_381::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq12::one());
-    assert_ne!(ans2, Fq12::one());
-    assert_ne!(ans3, Fq12::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq12::one());
-}
-
-#[test]
-fn test_g1_generator_raw() {
-    let mut x = Fq::zero();
-    let mut i = 0;
-    loop {
-        // y^2 = x^3 + b
-        let mut rhs = x;
-        rhs.square_in_place();
-        rhs.mul_assign(&x);
-        rhs.add_assign(&g1::Parameters::COEFF_B);
-
-        if let Some(y) = rhs.sqrt() {
-            let p = G1Affine::new(x, if y < -y { y } else { -y }, false);
-            assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-
-            let g1 = p.scale_by_cofactor();
-            if !g1.is_zero() {
-                assert_eq!(i, 4);
-                let g1 = G1Affine::from(g1);
-
-                assert!(g1.is_in_correct_subgroup_assuming_on_curve());
-
-                assert_eq!(g1, G1Affine::prime_subgroup_generator());
-                break;
-            }
-        }
-
-        i += 1;
-        x.add_assign(&Fq::one());
-    }
-}
-
-#[test]
-fn test_g1_endomorphism_beta() {
-    assert!(g1::BETA.pow(&[3u64]).is_one());
-}
-
-#[test]
-fn test_g1_subgroup_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    let generator = G1Projective::rand(&mut rng).into_affine();
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g1_subgroup_non_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    loop {
-        let x = Fq::rand(&mut rng);
-        let greatest = rng.gen();
-
-        if let Some(p) = G1Affine::get_point_from_x(x, greatest) {
-            if !p.into_projective().mul(Fr::characteristic()).is_zero() {
-                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-                return;
-            }
-        }
-    }
-}
-
-#[test]
-fn test_g2_subgroup_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    let generator = G2Projective::rand(&mut rng).into_affine();
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_subgroup_non_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    loop {
-        let x = Fq2::rand(&mut rng);
-        let greatest = rng.gen();
-
-        if let Some(p) = G2Affine::get_point_from_x(x, greatest) {
-            if !p.into_projective().mul(Fr::characteristic()).is_zero() {
-                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-                return;
-            }
-        }
-    }
-}
--- a/bls12_381/src/curves/tests/g1_compressed_valid_test_vectors.dat
+++ b/bls12_381/src/curves/tests/g1_compressed_valid_test_vectors.dat
--- a/bls12_381/src/curves/tests/g1_uncompressed_valid_test_vectors.dat
+++ b/bls12_381/src/curves/tests/g1_uncompressed_valid_test_vectors.dat
--- a/bls12_381/src/curves/tests/g2_compressed_valid_test_vectors.dat
+++ b/bls12_381/src/curves/tests/g2_compressed_valid_test_vectors.dat
--- a/bls12_381/src/curves/tests/g2_uncompressed_valid_test_vectors.dat
+++ b/bls12_381/src/curves/tests/g2_uncompressed_valid_test_vectors.dat
--- a/bls12_381/src/curves/tests/mod.rs
+++ b/bls12_381/src/curves/tests/mod.rs
@@ -0,0 +1,119 @@
+use ark_algebra_test_templates::*;
+use ark_ec::{AffineRepr, CurveGroup, Group};
+use ark_ff::{fields::Field, One, UniformRand, Zero};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize, Compress, Validate};
+use ark_std::{rand::Rng, test_rng, vec};
+
+use crate::{Bls12_381, Fq, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
+
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<Bls12_381>; msm);
+test_pairing!(pairing; crate::Bls12_381);
+
+#[test]
+fn test_g1_endomorphism_beta() {
+    assert!(crate::g1::BETA.pow(&[3u64]).is_one());
+}
+
+#[test]
+fn test_g1_subgroup_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    let generator = G1Projective::rand(&mut rng).into_affine();
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_g1_subgroup_non_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    loop {
+        let x = Fq::rand(&mut rng);
+        let greatest = rng.gen();
+
+        if let Some(p) = G1Affine::get_point_from_x_unchecked(x, greatest) {
+            if !p.mul_bigint(Fr::characteristic()).is_zero() {
+                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
+                return;
+            }
+        }
+    }
+}
+
+#[test]
+fn test_g2_subgroup_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    let generator = G2Projective::rand(&mut rng).into_affine();
+    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
+}
+
+#[test]
+fn test_g2_subgroup_non_membership_via_endomorphism() {
+    let mut rng = test_rng();
+    loop {
+        let x = Fq2::rand(&mut rng);
+        let greatest = rng.gen();
+
+        if let Some(p) = G2Affine::get_point_from_x_unchecked(x, greatest) {
+            if !p.mul_bigint(Fr::characteristic()).is_zero() {
+                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
+                return;
+            }
+        }
+    }
+}
+
+// Test vectors and macro adapted from https://github.com/zkcrypto/bls12_381/blob/e224ad4ea1babfc582ccd751c2bf128611d10936/src/tests/mod.rs
+macro_rules! test_vectors {
+    ($projective:ident, $affine:ident, $compress:expr, $expected:ident) => {
+        let mut e = $projective::zero();
+
+        let mut v = vec![];
+        {
+            let mut expected = $expected;
+            for _ in 0..1000 {
+                let e_affine = $affine::from(e);
+                let mut serialized = vec![0u8; e.serialized_size($compress)];
+                e_affine
+                    .serialize_with_mode(serialized.as_mut_slice(), $compress)
+                    .unwrap();
+                v.extend_from_slice(&serialized[..]);
+
+                let mut decoded = serialized;
+                let len_of_encoding = decoded.len();
+                (&mut decoded[..]).copy_from_slice(&expected[0..len_of_encoding]);
+                expected = &expected[len_of_encoding..];
+                let decoded =
+                    $affine::deserialize_with_mode(&decoded[..], $compress, Validate::Yes).unwrap();
+                assert_eq!(e_affine, decoded);
+
+                e += &$projective::generator();
+            }
+        }
+
+        assert_eq!(&v[..], $expected);
+    };
+}
+
+#[test]
+fn g1_compressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g1_compressed_valid_test_vectors.dat");
+    test_vectors!(G1Projective, G1Affine, Compress::Yes, bytes);
+}
+
+#[test]
+fn g1_uncompressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g1_uncompressed_valid_test_vectors.dat");
+    test_vectors!(G1Projective, G1Affine, Compress::No, bytes);
+}
+
+#[test]
+fn g2_compressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g2_compressed_valid_test_vectors.dat");
+    test_vectors!(G2Projective, G2Affine, Compress::Yes, bytes);
+}
+
+#[test]
+fn g2_uncompressed_valid_test_vectors() {
+    let bytes: &'static [u8] = include_bytes!("g2_uncompressed_valid_test_vectors.dat");
+    test_vectors!(G2Projective, G2Affine, Compress::No, bytes);
+}
--- a/bls12_381/src/curves/util.rs
+++ b/bls12_381/src/curves/util.rs
@@ -0,0 +1,217 @@
+use ark_ec::{short_weierstrass::Affine, AffineRepr};
+use ark_ff::{BigInteger384, PrimeField};
+use ark_serialize::SerializationError;
+
+use crate::{
+    g1::Parameters as G1Parameters, g2::Parameters as G2Parameters, Fq, Fq2, G1Affine, G2Affine,
+};
+
+pub const G1_SERIALIZED_SIZE: usize = 48;
+pub const G2_SERIALIZED_SIZE: usize = 96;
+
+pub struct EncodingFlags {
+    pub is_compressed: bool,
+    pub is_infinity: bool,
+    pub is_lexographically_largest: bool,
+}
+
+impl EncodingFlags {
+    pub fn get_flags(bytes: &[u8]) -> Self {
+        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,
+        }
+    }
+    pub fn encode_flags(&self, bytes: &mut [u8]) {
+        if self.is_compressed {
+            bytes[0] |= 1 << 7;
+        }
+
+        if self.is_infinity {
+            bytes[0] |= 1 << 6;
+        }
+
+        if self.is_compressed && !self.is_infinity && self.is_lexographically_largest {
+            bytes[0] |= 1 << 5;
+        }
+    }
+}
+
+pub(crate) fn deserialize_fq(bytes: [u8; 48]) -> Option<Fq> {
+    let mut tmp = BigInteger384::new([0, 0, 0, 0, 0, 0]);
+
+    // Note: The following unwraps are if the compiler cannot convert
+    // the byte slice into [u8;8], we know this is infallible since we
+    // are providing the indices at compile time and bytes has a fixed size
+    tmp.0[5] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[0..8]).unwrap());
+    tmp.0[4] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[8..16]).unwrap());
+    tmp.0[3] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[16..24]).unwrap());
+    tmp.0[2] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[24..32]).unwrap());
+    tmp.0[1] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[32..40]).unwrap());
+    tmp.0[0] = u64::from_be_bytes(<[u8; 8]>::try_from(&bytes[40..48]).unwrap());
+
+    Fq::from_bigint(tmp)
+}
+
+pub(crate) fn serialize_fq(field: Fq) -> [u8; 48] {
+    let mut result = [0u8; 48];
+
+    let rep = field.into_bigint();
+
+    result[0..8].copy_from_slice(&rep.0[5].to_be_bytes());
+    result[8..16].copy_from_slice(&rep.0[4].to_be_bytes());
+    result[16..24].copy_from_slice(&rep.0[3].to_be_bytes());
+    result[24..32].copy_from_slice(&rep.0[2].to_be_bytes());
+    result[32..40].copy_from_slice(&rep.0[1].to_be_bytes());
+    result[40..48].copy_from_slice(&rep.0[0].to_be_bytes());
+
+    result
+}
+
+pub(crate) fn read_fq_with_offset(
+    bytes: &[u8],
+    offset: usize,
+    mask: bool,
+) -> Result<Fq, ark_serialize::SerializationError> {
+    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;
+    }
+    deserialize_fq(tmp).ok_or(SerializationError::InvalidData)
+}
+
+pub(crate) fn read_g1_compressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G1Parameters>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; G1_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .ok()
+        .ok_or(SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes[..]);
+
+    // we expect to be deserializing a compressed point
+    if !flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        return Ok(G1Affine::zero());
+    }
+
+    // Attempt to obtain the x-coordinate
+    let x = read_fq_with_offset(&bytes, 0, true)?;
+
+    let p = G1Affine::get_point_from_x_unchecked(x, flags.is_lexographically_largest)
+        .ok_or(SerializationError::InvalidData)?;
+
+    Ok(p)
+}
+
+pub(crate) fn read_g1_uncompressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G1Parameters>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; 2 * G1_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .map_err(|_| SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes[..]);
+
+    // we expect to be deserializing an uncompressed point
+    if flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        return Ok(G1Affine::zero());
+    }
+
+    // Attempt to obtain the x-coordinate
+    let x = read_fq_with_offset(&bytes, 0, true)?;
+    // Attempt to obtain the y-coordinate
+    let y = read_fq_with_offset(&bytes, 1, false)?;
+
+    let p = G1Affine::new_unchecked(x, y);
+
+    Ok(p)
+}
+
+pub(crate) fn read_g2_compressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G2Parameters>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; G2_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .map_err(|_| SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes);
+
+    // we expect to be deserializing a compressed point
+    if !flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        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 x = Fq2::new(xc0, xc1);
+
+    let p = G2Affine::get_point_from_x_unchecked(x, flags.is_lexographically_largest)
+        .ok_or(SerializationError::InvalidData)?;
+
+    Ok(p)
+}
+
+pub(crate) fn read_g2_uncompressed<R: ark_serialize::Read>(
+    mut reader: R,
+) -> Result<Affine<G2Parameters>, ark_serialize::SerializationError> {
+    let mut bytes = [0u8; 2 * G2_SERIALIZED_SIZE];
+    reader
+        .read_exact(&mut bytes)
+        .map_err(|_| SerializationError::InvalidData)?;
+
+    // Obtain the three flags from the start of the byte sequence
+    let flags = EncodingFlags::get_flags(&bytes);
+
+    // we expect to be deserializing an uncompressed point
+    if flags.is_compressed {
+        return Err(SerializationError::UnexpectedFlags);
+    }
+
+    if flags.is_infinity {
+        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 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);
+
+    Ok(p)
+}
--- a/bls12_381/src/fields/fq.rs
+++ b/bls12_381/src/fields/fq.rs
@@ -1,115 +1,7 @@
-use ark_ff::{
-    biginteger::BigInteger384 as BigInteger,
-    field_new,
-    fields::{FftParameters, Fp384, Fp384Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp384, MontBackend, MontConfig};

-pub type Fq = Fp384<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp384Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 1;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0x43f5fffffffcaaae,
-        0x32b7fff2ed47fffd,
-        0x7e83a49a2e99d69,
-        0xeca8f3318332bb7a,
-        0xef148d1ea0f4c069,
-        0x40ab3263eff0206,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0xb9feffffffffaaab,
-        0x1eabfffeb153ffff,
-        0x6730d2a0f6b0f624,
-        0x64774b84f38512bf,
-        0x4b1ba7b6434bacd7,
-        0x1a0111ea397fe69a,
-    ]);
-
-    const MODULUS_BITS: u32 = 381;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 3;
-
-    /// R = 3380320199399472671518931668520476396067793891014375699959770179129436917079669831430077592723774664465579537268733
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0x760900000002fffd,
-        0xebf4000bc40c0002,
-        0x5f48985753c758ba,
-        0x77ce585370525745,
-        0x5c071a97a256ec6d,
-        0x15f65ec3fa80e493,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xf4df1f341c341746,
-        0xa76e6a609d104f1,
-        0x8de5476c4c95b6d5,
-        0x67eb88a9939d83c0,
-        0x9a793e85b519952d,
-        0x11988fe592cae3aa,
-    ]);
-
-    const INV: u64 = 0x89f3fffcfffcfffd;
-
-    /// GENERATOR = 2
-    /// Encoded in Montgomery form, so the value is
-    /// 2 * R % q = 2758230843577277949620073511305048635578704962089743514587482222134842183668501798417467556318533664893264801977679
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0x321300000006554f,
-        0xb93c0018d6c40005,
-        0x57605e0db0ddbb51,
-        0x8b256521ed1f9bcb,
-        0x6cf28d7901622c03,
-        0x11ebab9dbb81e28c,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xdcff7fffffffd555,
-        0xf55ffff58a9ffff,
-        0xb39869507b587b12,
-        0xb23ba5c279c2895f,
-        0x258dd3db21a5d66b,
-        0xd0088f51cbff34d,
-    ]);
-
-    /// T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-    /// For T coprime to 2
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0xdcff7fffffffd555,
-        0xf55ffff58a9ffff,
-        0xb39869507b587b12,
-        0xb23ba5c279c2895f,
-        0x258dd3db21a5d66b,
-        0xd0088f51cbff34d,
-    ]);
-
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xee7fbfffffffeaaa,
-        0x7aaffffac54ffff,
-        0xd9cc34a83dac3d89,
-        0xd91dd2e13ce144af,
-        0x92c6e9ed90d2eb35,
-        0x680447a8e5ff9a6,
-    ]);
-}
-
-pub const FQ_ONE: Fq = field_new!(Fq, "1");
-pub const FQ_ZERO: Fq = field_new!(Fq, "0");
+#[derive(MontConfig)]
+#[modulus = "4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp384<MontBackend<FqConfig, 6>>;
--- a/bls12_381/src/fields/fq12.rs
+++ b/bls12_381/src/fields/fq12.rs
@@ -1,76 +1,77 @@
-use crate::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;

 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;

-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;

-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);

    const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
-            field_new!(Fq, "151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
+        Fq2::new(
+            MontFp!("3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
+            MontFp!("151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
-            field_new!(Fq, "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
+        Fq2::new(
+            MontFp!("2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+            MontFp!("1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
-            field_new!(Fq, "877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
+        Fq2::new(
+            MontFp!("3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
+            MontFp!("877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
        ),
        // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "-1"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
-            field_new!(Fq, "3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
+        Fq2::new(
+            MontFp!("151655185184498381465642749684540099398075398968325446656007613510403227271200139370504932015952886146304766135027"),
+            MontFp!("3850754370037169011952147076051364057158807420970682438676050522613628423219637725072182697113062777891589506424760"),
        ),
        // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
-            field_new!(Fq, "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
+        Fq2::new(
+            MontFp!("1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257"),
+            MontFp!("2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
        ),
        // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
-            field_new!(Fq, "3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
+        Fq2::new(
+            MontFp!("877076961050607968509681729531255177986764537961432449499635504522207616027455086505066378536590128544573588734230"),
+            MontFp!("3125332594171059424908108096204648978570118281977575435832422631601824034463382777937621250592425535493320683825557"),
        ),
    ];
 }
--- a/bls12_381/src/fields/fq2.rs
+++ b/bls12_381/src/fields/fq2.rs
@@ -1,35 +1,42 @@
+use ark_ff::{fields::*, MontFp};
+
 use crate::*;
-use ark_ff::{field_new, fields::*};

-pub type Fq2 = Fp2<Fq2Parameters>;
+pub type Fq2 = Fp2<Fq2Config>;

-pub struct Fq2Parameters;
+pub struct Fq2Config;

-impl Fp2Parameters for Fq2Parameters {
+impl Fp2Config for Fq2Config {
    type Fp = Fq;

    /// NONRESIDUE = -1
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, "-1");
-
-    /// QUADRATIC_NONRESIDUE = (U + 1)
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (FQ_ONE, FQ_ONE);
+    const NONRESIDUE: Fq = MontFp!("-1");

    /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
        // Fq(-1)**(((q^0) - 1) / 2)
-        field_new!(Fq, "1"),
+        Fq::ONE,
        // Fq(-1)**(((q^1) - 1) / 2)
-        field_new!(Fq, "-1"),
+        MontFp!("-1"),
    ];

    #[inline(always)]
-    fn mul_fp_by_nonresidue(fp: &Self::Fp) -> Self::Fp {
-        -(*fp)
-    }
+    fn mul_fp_by_nonresidue_in_place(fp: &mut Self::Fp) -> &mut Self::Fp {
+        fp.neg_in_place()
    }

-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(y: &mut Self::Fp, x: &Self::Fp) {
+        *y += x;
+    }
+
+    #[inline(always)]
+    fn mul_fp_by_nonresidue_plus_one_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        *y = *x;
+    }
+
+    fn mul_fp_by_nonresidue_and_add(y: &mut Self::Fp, x: &Self::Fp) {
+        y.neg_in_place();
+        *y += x;
+    }
+}
--- a/bls12_381/src/fields/fq6.rs
+++ b/bls12_381/src/fields/fq6.rs
@@ -1,96 +1,91 @@
-use crate::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;

 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;

-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;

    /// NONRESIDUE = (U + 1)
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2,
-        field_new!(Fq, "1"),
-        field_new!(Fq, "1"),
-    );
+    const NONRESIDUE: Fq2 = Fq2::new(Fq::ONE, Fq::ONE);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "0"),
-            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+        Fq2::new(
+            Fq::ZERO,
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "0"),
-            field_new!(Fq, "1"),
+        Fq2::new(
+            Fq::ZERO,
+            Fq::ONE,
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "0"),
-            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+        Fq2::new(
+            Fq::ZERO,
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
        ),
 ];

    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
        // Fq2(u + 1)**(((2q^0) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            Fq::ONE,
+            Fq::ZERO,
        ),
        // Fq2(u + 1)**(((2q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"),
+            Fq::ZERO,
        ),
        // Fq2(u + 1)**(((2q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939436"),
+            Fq::ZERO,
        ),
        // Fq2(u + 1)**(((2q^3) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "-1"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("-1"),
+            Fq::ZERO,
        ),
        // Fq2(u + 1)**(((2q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350"),
+            Fq::ZERO,
        ),
        // Fq2(u + 1)**(((2q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620351"),
+            Fq::ZERO,
        ),
    ];

    /// Multiply this element by the quadratic nonresidue 1 + u.
    /// Make this generic.
-    fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
-        let mut copy = *fe;
-        let t0 = copy.c0;
-        copy.c0 -= &fe.c1;
-        copy.c1 += &t0;
-        copy
+    fn mul_fp2_by_nonresidue_in_place(fe: &mut Fq2) -> &mut Fq2 {
+        let t0 = fe.c0;
+        fe.c0 -= &fe.c1;
+        fe.c1 += &t0;
+        fe
    }
 }
--- a/bls12_381/src/fields/fr.rs
+++ b/bls12_381/src/fields/fr.rs
@@ -1,100 +1,7 @@
-use ark_ff::{
-    biginteger::BigInteger256 as BigInteger,
-    fields::{FftParameters, Fp256, Fp256Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};

-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 32;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0xb9b58d8c5f0e466a,
-        0x5b1b4c801819d7ec,
-        0xaf53ae352a31e64,
-        0x5bf3adda19e9b27b,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 52435875175126190479447740508185965837690552500527637822603658699938581184513
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0xffffffff00000001,
-        0x53bda402fffe5bfe,
-        0x3339d80809a1d805,
-        0x73eda753299d7d48,
-    ]);
-
-    const MODULUS_BITS: u32 = 255;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 1;
-
-    /// R = 10920338887063814464675503992315976177888879664585288394250266608035967270910
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0x1fffffffe,
-        0x5884b7fa00034802,
-        0x998c4fefecbc4ff5,
-        0x1824b159acc5056f,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xc999e990f3f29c6d,
-        0x2b6cedcb87925c23,
-        0x5d314967254398f,
-        0x748d9d99f59ff11,
-    ]);
-
-    const INV: u64 = 0xfffffffeffffffff;
-
-    /// GENERATOR = 7
-    /// Encoded in Montgomery form, so the value here is
-    /// 7 * R % q = 24006497034320510773280787438025867407531605151569380937148207556313189711857
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0xefffffff1,
-        0x17e363d300189c0f,
-        0xff9c57876f8457b0,
-        0x351332208fc5a8c4,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x7fffffff80000000,
-        0xa9ded2017fff2dff,
-        0x199cec0404d0ec02,
-        0x39f6d3a994cebea4,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-    // For T coprime to 2
-
-    // T = (MODULUS - 1) / 2^S =
-    // 12208678567578594777604504606729831043093128246378069236549469339647
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0xfffe5bfeffffffff,
-        0x9a1d80553bda402,
-        0x299d7d483339d808,
-        0x73eda753,
-    ]);
-
-    // (T - 1) / 2 =
-    // 6104339283789297388802252303364915521546564123189034618274734669823
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x7fff2dff7fffffff,
-        0x4d0ec02a9ded201,
-        0x94cebea4199cec04,
-        0x39f6d3a9,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "52435875175126190479447740508185965837690552500527637822603658699938581184513"]
+#[generator = "7"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
--- a/bls12_381/src/fields/mod.rs
+++ b/bls12_381/src/fields/mod.rs
@@ -23,5 +23,5 @@ pub mod fq12;
 #[cfg(feature = "curve")]
 pub use self::fq12::*;

-#[cfg(all(feature = "curve", feature = "std", test))]
+#[cfg(all(feature = "curve", test))]
 mod tests;
--- a/bls12_381/src/fields/tests.rs
+++ b/bls12_381/src/fields/tests.rs
--- a/bls12_381/src/lib.rs
+++ b/bls12_381/src/lib.rs
@@ -9,15 +9,16 @@
 #![forbid(unsafe_code)]

 //! This library implements the BLS12_381 curve generated by [Sean Bowe](https://electriccoin.co/blog/new-snark-curve/).
-//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree 12,
-//! defined over a 381-bit (prime) field.
-//! This curve was intended to replace the BN254 curve to provide a higher security
-//! level without incurring a large performance overhead.
+//! The name denotes that it is a Barreto--Lynn--Scott curve of embedding degree
+//! 12, defined over a 381-bit (prime) field.
+//! This curve was intended to replace the BN254 curve to provide a higher
+//! security level without incurring a large performance overhead.
 //!
 //!
 //! Curve information:
 //! * Base field: q = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
-//! * Scalar field: r = 52435875175126190479447740508185965837690552500527637822603658699938581184513
+//! * Scalar field: r =
+//!   52435875175126190479447740508185965837690552500527637822603658699938581184513
 //! * valuation(q - 1, 2) = 1
 //! * valuation(r - 1, 2) = 32
 //! * G1 curve equation: y^2 = x^3 + 4
--- a/bn254/Cargo.toml
+++ b/bn254/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "ark-bn254"
-version = "0.3.0"
+version = "0.4.0-alpha.1"
 authors = [ "arkworks contributors" ]
 description = "The BN254 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
@@ -10,16 +10,17 @@ keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"

 [dependencies]
-ark-ff = { version="^0.3.0", default-features = false }
-ark-ec = { version="^0.3.0", default-features = false }
-ark-std = { version="^0.3.0", default-features = false }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }

 [dev-dependencies]
-ark-serialize = { version="^0.3.0", default-features = false }
-ark-algebra-test-templates = { version="^0.3.0", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }

 [features]
 default = [ "curve" ]
@@ -27,3 +28,8 @@ std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]

 curve = [ "scalar_field" ]
 scalar_field = []
+
+[[bench]]
+name = "bn254"
+path = "benches/bn254.rs"
+harness = false
--- a/bn254/benches/bn254.rs
+++ b/bn254/benches/bn254.rs
@@ -0,0 +1,13 @@
+use ark_algebra_bench_templates::*;
+use ark_bn254::{fq::Fq, fq2::Fq2, fr::Fr, Bn254, Fq12, G1Projective as G1, G2Projective as G2};
+
+bench!(
+    Name = "BN254",
+    Pairing = Bn254,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq2,
+    TargetField = Fq12,
+);
--- a/bn254/scripts/base_field.sage
+++ b/bn254/scripts/base_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/bn254/scripts/scalar_field.sage
+++ b/bn254/scripts/scalar_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/bn254/src/curves/g1.rs
+++ b/bn254/src/curves/g1.rs
@@ -1,41 +1,45 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{field_new, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};

 use crate::{Fq, Fr};

 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+pub type G1Affine = Affine<Parameters>;
+
+impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    const COEFF_A: Fq = field_new!(Fq, "0");
-
-    /// COEFF_B = 3
-    const COEFF_B: Fq = field_new!(Fq, "3");

    /// COFACTOR = 1
    const COFACTOR: &'static [u64] = &[0x1];

    /// COFACTOR_INV = COFACTOR^{-1} mod r = 1
-    const COFACTOR_INV: Fr = field_new!(Fr, "1");
+    const COFACTOR_INV: Fr = Fr::ONE;
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 3
+    const COEFF_B: Fq = MontFp!("3");

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);

    #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }
 }

 /// G1_GENERATOR_X = 1
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, "1");
+pub const G1_GENERATOR_X: Fq = Fq::ONE;

 /// G1_GENERATOR_Y = 2
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "2");
+pub const G1_GENERATOR_Y: Fq = MontFp!("2");
--- a/bn254/src/curves/g2.rs
+++ b/bn254/src/curves/g2.rs
@@ -1,31 +1,22 @@
-use ark_ec::models::{ModelParameters, SWModelParameters};
-use ark_ff::{field_new, Zero};
+use ark_ec::{
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::Affine,
+};
+use ark_ff::{Field, MontFp, Zero};

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

+pub type G2Affine = Affine<Parameters>;
+
 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq2;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = [0, 0]
-    #[rustfmt::skip]
-    const COEFF_A: Fq2 = field_new!(Fq2, field_new!(Fq, "0"), field_new!(Fq, "0"));
-
-    /// COEFF_B = 3/(u+9)
-    ///         = (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
-    #[rustfmt::skip]
-    const COEFF_B: Fq2 = field_new!(Fq2,
-        field_new!(Fq, "19485874751759354771024239261021720505790618469301721065564631296452457478373"),
-        field_new!(Fq, "266929791119991161246907387137283842545076965332900288569378510910307636690"),
-    );

    /// COFACTOR = (36 * X^4) + (36 * X^3) + (30 * X^2) + 6*X + 1
-    ///          = 21888242871839275222246405745257275088844257914179612981679871602714643921549
+    /// 21888242871839275222246405745257275088844257914179612981679871602714643921549
    #[rustfmt::skip]
    const COFACTOR: &'static [u64] = &[
        0x345f2299c0f9fa8d,
@@ -35,40 +26,49 @@ impl SWModelParameters for Parameters {
    ];

    /// COFACTOR_INV = COFACTOR^{-1} mod r
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "10944121435919637613327163357776759465618812564592884533313067514031822496649");
+    const COFACTOR_INV: Fr =
+        MontFp!("10944121435919637613327163357776759465618812564592884533313067514031822496649");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = [0, 0]
+    const COEFF_A: Fq2 = Fq2::ZERO;
+
+    /// COEFF_B = 3/(u+9)
+    /// (19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
+    const COEFF_B: Fq2 = Fq2::new(
+        MontFp!("19485874751759354771024239261021720505790618469301721065564631296452457478373"),
+        MontFp!("266929791119991161246907387137283842545076965332900288569378510910307636690"),
+    );

    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);

    #[inline(always)]
-    fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
+    fn mul_by_a(_: Self::BaseField) -> Self::BaseField {
        Self::BaseField::zero()
    }
 }

-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq2 = field_new!(Fq2, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1);
+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);

 /// G2_GENERATOR_X_C0 =
 /// 10857046999023057135944570762232829481370756359578518086990519993285655852781
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "10857046999023057135944570762232829481370756359578518086990519993285655852781");
+pub const G2_GENERATOR_X_C0: Fq =
+    MontFp!("10857046999023057135944570762232829481370756359578518086990519993285655852781");

 /// G2_GENERATOR_X_C1 =
 /// 11559732032986387107991004021392285783925812861821192530917403151452391805634
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "11559732032986387107991004021392285783925812861821192530917403151452391805634");
+pub const G2_GENERATOR_X_C1: Fq =
+    MontFp!("11559732032986387107991004021392285783925812861821192530917403151452391805634");

 /// G2_GENERATOR_Y_C0 =
 /// 8495653923123431417604973247489272438418190587263600148770280649306958101930
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "8495653923123431417604973247489272438418190587263600148770280649306958101930");
+pub const G2_GENERATOR_Y_C0: Fq =
+    MontFp!("8495653923123431417604973247489272438418190587263600148770280649306958101930");

 /// G2_GENERATOR_Y_C1 =
 /// 4082367875863433681332203403145435568316851327593401208105741076214120093531
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "4082367875863433681332203403145435568316851327593401208105741076214120093531");
+pub const G2_GENERATOR_Y_C1: Fq =
+    MontFp!("4082367875863433681332203403145435568316851327593401208105741076214120093531");
--- a/bn254/src/curves/mod.rs
+++ b/bn254/src/curves/mod.rs
@@ -1,9 +1,11 @@
-use crate::*;
 use ark_ec::{
    bn,
    bn::{Bn, BnParameters, TwistType},
 };
-use ark_ff::field_new;
+use ark_ff::MontFp;
+
+use crate::*;
+
 pub mod g1;
 pub mod g2;

@@ -22,33 +24,19 @@ impl BnParameters for Parameters {
        -1, 0, 0, 1, 0, 1, 1,
    ];

-    const TWIST_MUL_BY_Q_X: Fq2 = field_new!(
-        Fq2,
-        field_new!(
-            Fq,
-            "21575463638280843010398324269430826099269044274347216827212613867836435027261"
-        ),
-        field_new!(
-            Fq,
-            "10307601595873709700152284273816112264069230130616436755625194854815875713954"
-        ),
+    const TWIST_MUL_BY_Q_X: Fq2 = Fq2::new(
+        MontFp!("21575463638280843010398324269430826099269044274347216827212613867836435027261"),
+        MontFp!("10307601595873709700152284273816112264069230130616436755625194854815875713954"),
    );
-    const TWIST_MUL_BY_Q_Y: Fq2 = field_new!(
-        Fq2,
-        field_new!(
-            Fq,
-            "2821565182194536844548159561693502659359617185244120367078079554186484126554"
-        ),
-        field_new!(
-            Fq,
-            "3505843767911556378687030309984248845540243509899259641013678093033130930403"
-        ),
+    const TWIST_MUL_BY_Q_Y: Fq2 = Fq2::new(
+        MontFp!("2821565182194536844548159561693502659359617185244120367078079554186484126554"),
+        MontFp!("3505843767911556378687030309984248845540243509899259641013678093033130930403"),
    );
    const TWIST_TYPE: TwistType = TwistType::D;
    type Fp = Fq;
-    type Fp2Params = Fq2Parameters;
-    type Fp6Params = Fq6Parameters;
-    type Fp12Params = Fq12Parameters;
+    type Fp2Config = Fq2Config;
+    type Fp6Config = Fq6Config;
+    type Fp12Config = Fq12Config;
    type G1Parameters = g1::Parameters;
    type G2Parameters = g2::Parameters;
 }
--- a/bn254/src/curves/tests.rs
+++ b/bn254/src/curves/tests.rs
@@ -1,86 +1,9 @@
-#![allow(unused_imports)]
-use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    fields::{Field, FpParameters, PrimeField, SquareRootField},
-    One, Zero,
-};
-use ark_serialize::CanonicalSerialize;
-use ark_std::rand::Rng;
-use ark_std::test_rng;
-use core::ops::{AddAssign, MulAssign};
+use ark_algebra_test_templates::*;
+use ark_ff::fields::Field;

-use crate::{g1, g2, Bn254, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
+use crate::{Bn254, G1Projective, G2Projective};

-use ark_algebra_test_templates::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let mut sa = a;
-    sa.mul_assign(s);
-    let mut sb = b;
-    sb.mul_assign(s);
-
-    let ans1 = Bn254::pairing(sa, b);
-    let ans2 = Bn254::pairing(a, sb);
-    let ans3 = Bn254::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq12::one());
-    assert_ne!(ans2, Fq12::one());
-    assert_ne!(ans3, Fq12::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq12::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq12::one());
-}
+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);
--- a/bn254/src/fields/fq.rs
+++ b/bn254/src/fields/fq.rs
@@ -1,96 +1,7 @@
-use ark_ff::{biginteger::BigInteger256 as BigInteger, field_new, fields::*};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};

-pub type Fq = Fp256<FqParameters>;
-
-pub struct FqParameters;
-
-impl Fp256Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 1;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0x68c3488912edefaa,
-        0x8d087f6872aabf4f,
-        0x51e1a24709081231,
-        0x2259d6b14729c0fa,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 21888242871839275222246405745257275088696311157297823662689037894645226208583
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0x3c208c16d87cfd47,
-        0x97816a916871ca8d,
-        0xb85045b68181585d,
-        0x30644e72e131a029,
-    ]);
-
-    const MODULUS_BITS: u32 = 254;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 2;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0xd35d438dc58f0d9d,
-        0x0a78eb28f5c70b3d,
-        0x666ea36f7879462c,
-        0xe0a77c19a07df2f,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xf32cfc5b538afa89,
-        0xb5e71911d44501fb,
-        0x47ab1eff0a417ff6,
-        0x6d89f71cab8351f,
-    ]);
-
-    const INV: u64 = 9786893198990664585u64;
-
-    // GENERATOR = 3
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0x7a17caa950ad28d7,
-        0x1f6ac17ae15521b9,
-        0x334bea4e696bd284,
-        0x2a1f6744ce179d8e,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x9e10460b6c3e7ea3,
-        0xcbc0b548b438e546,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where MODULUS - 1 = 2^S * T
-
-    // T = (MODULUS - 1) // 2^S =
-    // 10944121435919637611123202872628637544348155578648911831344518947322613104291
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x9e10460b6c3e7ea3,
-        0xcbc0b548b438e546,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // (T - 1) // 2 =
-    // 5472060717959818805561601436314318772174077789324455915672259473661306552145
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x4f082305b61f3f51,
-        0x65e05aa45a1c72a3,
-        0x6e14116da0605617,
-        0xc19139cb84c680a,
-    ]);
-}
-
-pub const FQ_ONE: Fq = field_new!(Fq, "1");
-pub const FQ_ZERO: Fq = field_new!(Fq, "0");
+#[derive(MontConfig)]
+#[modulus = "21888242871839275222246405745257275088696311157297823662689037894645226208583"]
+#[generator = "3"]
+pub struct FqConfig;
+pub type Fq = Fp256<MontBackend<FqConfig, 4>>;
--- a/bn254/src/fields/fq12.rs
+++ b/bn254/src/fields/fq12.rs
@@ -1,77 +1,89 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq12 = Fp12<Fq12Parameters>;
+use crate::*;
+
+pub type Fq12 = Fp12<Fq12Config>;

 #[derive(Clone, Copy)]
-pub struct Fq12Parameters;
+pub struct Fq12Config;

-impl Fp12Parameters for Fq12Parameters {
-    type Fp6Params = Fq6Parameters;
+impl Fp12Config for Fq12Config {
+    type Fp6Config = Fq6Config;

-    const NONRESIDUE: Fq6 = field_new!(Fq6, FQ2_ZERO, FQ2_ONE, FQ2_ZERO);
+    const NONRESIDUE: Fq6 = Fq6::new(Fq2::ZERO, Fq2::ONE, Fq2::ZERO);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP12_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "8376118865763821496583973867626364092589906065868298776909617916018768340080"),
-            field_new!(Fq, "16469823323077808223889137241176536799009286646108169935659301613961712198316"),
+        Fq2::new(
+            MontFp!("8376118865763821496583973867626364092589906065868298776909617916018768340080"),
+            MontFp!(
+                "16469823323077808223889137241176536799009286646108169935659301613961712198316"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556617"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556617"
+            ),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "11697423496358154304825782922584725312912383441159505038794027105778954184319"),
-            field_new!(Fq, "303847389135065887422783454877609941456349188919719272345083954437860409601"),
+        Fq2::new(
+            MontFp!(
+                "11697423496358154304825782922584725312912383441159505038794027105778954184319"
+            ),
+            MontFp!("303847389135065887422783454877609941456349188919719272345083954437860409601"),
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "3321304630594332808241809054958361220322477375291206261884409189760185844239"),
-            field_new!(Fq, "5722266937896532885780051958958348231143373700109372999374820235121374419868"),
+        Fq2::new(
+            MontFp!("3321304630594332808241809054958361220322477375291206261884409189760185844239"),
+            MontFp!("5722266937896532885780051958958348231143373700109372999374820235121374419868"),
        ),
        // Fp2::NONRESIDUE^(((q^6) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "-1"),
-            field_new!(Fq, "0"),
-        ),
+        Fq2::new(MontFp!("-1"), Fq::ZERO),
        // Fp2::NONRESIDUE^(((q^7) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "13512124006075453725662431877630910996106405091429524885779419978626457868503"),
-            field_new!(Fq, "5418419548761466998357268504080738289687024511189653727029736280683514010267"),
+        Fq2::new(
+            MontFp!(
+                "13512124006075453725662431877630910996106405091429524885779419978626457868503"
+            ),
+            MontFp!("5418419548761466998357268504080738289687024511189653727029736280683514010267"),
        ),
        // Fp2::NONRESIDUE^(((q^8) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^9) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "10190819375481120917420622822672549775783927716138318623895010788866272024264"),
-            field_new!(Fq, "21584395482704209334823622290379665147239961968378104390343953940207365798982"),
+        Fq2::new(
+            MontFp!(
+                "10190819375481120917420622822672549775783927716138318623895010788866272024264"
+            ),
+            MontFp!(
+                "21584395482704209334823622290379665147239961968378104390343953940207365798982"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^10) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651967"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651967"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^11) - 1) / 6)
-        field_new!(Fq2,
-            field_new!(Fq, "18566938241244942414004596690298913868373833782006617400804628704885040364344"),
-            field_new!(Fq, "16165975933942742336466353786298926857552937457188450663314217659523851788715"),
+        Fq2::new(
+            MontFp!(
+                "18566938241244942414004596690298913868373833782006617400804628704885040364344"
+            ),
+            MontFp!(
+                "16165975933942742336466353786298926857552937457188450663314217659523851788715"
+            ),
        ),
    ];
 }
--- a/bn254/src/fields/fq2.rs
+++ b/bn254/src/fields/fq2.rs
@@ -1,38 +1,27 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq2 = Fp2<Fq2Parameters>;
+use crate::*;

-pub struct Fq2Parameters;
+pub type Fq2 = Fp2<Fq2Config>;

-impl Fp2Parameters for Fq2Parameters {
+pub struct Fq2Config;
+
+impl Fp2Config for Fq2Config {
    type Fp = Fq;

    /// NONRESIDUE = -1
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, "-1");
-
-    /// QUADRATIC_NONRESIDUE = U+2
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE: (Fq, Fq) = (
-        field_new!(Fq, "2"),
-        field_new!(Fq, "1"),
-    );
+    const NONRESIDUE: Fq = MontFp!("-1");

    /// Coefficients for the Frobenius automorphism.
-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
        // NONRESIDUE**(((q^0) - 1) / 2)
-        field_new!(Fq, "1"),
+        Fq::ONE,
        // NONRESIDUE**(((q^1) - 1) / 2)
-        field_new!(Fq, "-1"),
+        MontFp!("-1"),
    ];

    #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
-        -(*fe)
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
+        fe.neg_in_place()
    }
 }
-
-pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
-pub const FQ2_ONE: Fq2 = field_new!(Fq2, FQ_ONE, FQ_ZERO);
--- a/bn254/src/fields/fq6.rs
+++ b/bn254/src/fields/fq6.rs
@@ -1,92 +1,105 @@
-use super::*;
-use ark_ff::{field_new, fields::*};
+use ark_ff::{fields::*, MontFp};

-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::*;
+
+pub type Fq6 = Fp6<Fq6Config>;

 #[derive(Clone, Copy)]
-pub struct Fq6Parameters;
+pub struct Fq6Config;

-impl Fp6Parameters for Fq6Parameters {
-    type Fp2Params = Fq2Parameters;
+impl Fp6Config for Fq6Config {
+    type Fp2Config = Fq2Config;

    /// NONRESIDUE = U+9
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq2 = field_new!(Fq2, field_new!(Fq, "9"), field_new!(Fq, "1"));
+    const NONRESIDUE: Fq2 = Fq2::new(MontFp!("9"), Fq::ONE);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^(((q^0) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^(((q^1) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "21575463638280843010398324269430826099269044274347216827212613867836435027261"),
-            field_new!(Fq, "10307601595873709700152284273816112264069230130616436755625194854815875713954"),
+        Fq2::new(
+            MontFp!(
+                "21575463638280843010398324269430826099269044274347216827212613867836435027261"
+            ),
+            MontFp!(
+                "10307601595873709700152284273816112264069230130616436755625194854815875713954"
+            ),
        ),
        // Fp2::NONRESIDUE^(((q^2) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^3) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "3772000881919853776433695186713858239009073593817195771773381919316419345261"),
-            field_new!(Fq, "2236595495967245188281701248203181795121068902605861227855261137820944008926"),
+        Fq2::new(
+            MontFp!("3772000881919853776433695186713858239009073593817195771773381919316419345261"),
+            MontFp!("2236595495967245188281701248203181795121068902605861227855261137820944008926"),
        ),
        // Fp2::NONRESIDUE^(((q^4) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^(((q^5) - 1) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "18429021223477853657660792034369865839114504446431234726392080002137598044644"),
-            field_new!(Fq, "9344045779998320333812420223237981029506012124075525679208581902008406485703"),
+        Fq2::new(
+            MontFp!(
+                "18429021223477853657660792034369865839114504446431234726392080002137598044644"
+            ),
+            MontFp!("9344045779998320333812420223237981029506012124075525679208581902008406485703"),
        ),
    ];
-    #[rustfmt::skip]
+
    const FROBENIUS_COEFF_FP6_C2: &'static [Fq2] = &[
        // Fp2::NONRESIDUE^((2*(q^0) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "1"),
-            field_new!(Fq, "0"),
-        ),
+        Fq2::new(Fq::ONE, Fq::ZERO),
        // Fp2::NONRESIDUE^((2*(q^1) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "2581911344467009335267311115468803099551665605076196740867805258568234346338"),
-            field_new!(Fq, "19937756971775647987995932169929341994314640652964949448313374472400716661030"),
+        Fq2::new(
+            MontFp!("2581911344467009335267311115468803099551665605076196740867805258568234346338"),
+            MontFp!(
+                "19937756971775647987995932169929341994314640652964949448313374472400716661030"
+            ),
        ),
        // Fp2::NONRESIDUE^((2*(q^2) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "2203960485148121921418603742825762020974279258880205651966"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!("2203960485148121921418603742825762020974279258880205651966"),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^((2*(q^3) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "5324479202449903542726783395506214481928257762400643279780343368557297135718"),
-            field_new!(Fq, "16208900380737693084919495127334387981393726419856888799917914180988844123039"),
+        Fq2::new(
+            MontFp!("5324479202449903542726783395506214481928257762400643279780343368557297135718"),
+            MontFp!(
+                "16208900380737693084919495127334387981393726419856888799917914180988844123039"
+            ),
        ),
        // Fp2::NONRESIDUE^((2*(q^4) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "21888242871839275220042445260109153167277707414472061641714758635765020556616"),
-            field_new!(Fq, "0"),
+        Fq2::new(
+            MontFp!(
+                "21888242871839275220042445260109153167277707414472061641714758635765020556616"
+            ),
+            Fq::ZERO,
        ),
        // Fp2::NONRESIDUE^((2*(q^5) - 2) / 3)
-        field_new!(Fq2,
-            field_new!(Fq, "13981852324922362344252311234282257507216387789820983642040889267519694726527"),
-            field_new!(Fq, "7629828391165209371577384193250820201684255241773809077146787135900891633097"),
+        Fq2::new(
+            MontFp!(
+                "13981852324922362344252311234282257507216387789820983642040889267519694726527"
+            ),
+            MontFp!("7629828391165209371577384193250820201684255241773809077146787135900891633097"),
        ),
    ];

    #[inline(always)]
-    fn mul_fp2_by_nonresidue(fe: &Fq2) -> Fq2 {
+    fn mul_fp2_by_nonresidue_in_place(fe: &mut Fq2) -> &mut Fq2 {
        // (c0+u*c1)*(9+u) = (9*c0-c1)+u*(9*c1+c0)
        let mut f = *fe;
        f.double_in_place().double_in_place().double_in_place();
-        let c0 = f.c0 + fe.c0 + Fq2Parameters::mul_fp_by_nonresidue(&fe.c1);
+        let mut c0 = fe.c1;
+        Fq2Config::mul_fp_by_nonresidue_in_place(&mut c0);
+        c0 += &f.c0;
+        c0 += &fe.c0;
        let c1 = f.c1 + fe.c1 + fe.c0;
-        field_new!(Fq2, c0, c1)
+        *fe = Fq2::new(c0, c1);
+        fe
    }
 }
--- a/bn254/src/fields/fr.rs
+++ b/bn254/src/fields/fr.rs
@@ -1,100 +1,7 @@
-use ark_ff::{biginteger::BigInteger256 as BigInteger, fields::*};
+use ark_ff::fields::{Fp256, MontBackend, MontConfig};

-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 28;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        7164790868263648668u64,
-        11685701338293206998u64,
-        6216421865291908056u64,
-        1756667274303109607u64,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// MODULUS = 21888242871839275222246405745257275088548364400416034343698204186575808495617
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        4891460686036598785u64,
-        2896914383306846353u64,
-        13281191951274694749u64,
-        3486998266802970665u64,
-    ]);
-
-    const MODULUS_BITS: u32 = 254;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 2;
-
-    /// R = pow(2, 320) % MODULUS
-    ///   = 6350874878119819312338956282401532410528162663560392320966563075034087161851
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        12436184717236109307u64,
-        3962172157175319849u64,
-        7381016538464732718u64,
-        1011752739694698287u64,
-    ]);
-
-    /// R2 = R * R % MODULUS
-    ///    = 944936681149208446651664254269745548490766851729442924617792859073125903783
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        1997599621687373223u64,
-        6052339484930628067u64,
-        10108755138030829701u64,
-        150537098327114917u64,
-    ]);
-
-    /// INV = (-MODULUS) ^ {-1} % pow(2, 64) = 14042775128853446655
-    const INV: u64 = 14042775128853446655u64;
-
-    /// GENERATOR = 5
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        1949230679015292902u64,
-        16913946402569752895u64,
-        5177146667339417225u64,
-        1571765431670520771u64,
-    ]);
-
-    /// (MODULUS - 1)/2 =
-    /// 10944121435919637611123202872628637544274182200208017171849102093287904247808
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xa1f0fac9f8000000,
-        0x9419f4243cdcb848,
-        0xdc2822db40c0ac2e,
-        0x183227397098d014,
-    ]);
-
-    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t
-
-    /// T = (MODULUS - 1) / 2^s =
-    /// 81540058820840996586704275553141814055101440848469862132140264610111
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x9b9709143e1f593f,
-        0x181585d2833e8487,
-        0x131a029b85045b68,
-        0x30644e72e,
-    ]);
-
-    /// (T - 1) / 2 =
-    /// 40770029410420498293352137776570907027550720424234931066070132305055
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xcdcb848a1f0fac9f,
-        0x0c0ac2e9419f4243,
-        0x098d014dc2822db4,
-        0x183227397,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "21888242871839275222246405745257275088548364400416034343698204186575808495617"]
+#[generator = "5"]
+pub struct FrConfig;
+pub type Fr = Fp256<MontBackend<FrConfig, 4>>;
--- a/bn254/src/fields/tests.rs
+++ b/bn254/src/fields/tests.rs
@@ -1,123 +1,51 @@
+use ark_algebra_test_templates::*;
 use ark_ff::{
-    biginteger::{BigInteger, BigInteger256},
-    fields::{
-        fp6_3over2::Fp6Parameters, FftField, FftParameters, Field, FpParameters, PrimeField,
-        SquareRootField,
-    },
+    biginteger::{BigInt, BigInteger, BigInteger256},
+    fields::{FftField, Field, Fp6Config, PrimeField},
    One, UniformRand, Zero,
 };
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use ark_std::rand::Rng;
-use ark_std::test_rng;
-use core::{
+use ark_std::{
    cmp::Ordering,
-    ops::{AddAssign, MulAssign, SubAssign},
+    ops::{AddAssign, MulAssign},
 };

-use crate::{Fq, Fq12, Fq2, Fq6, Fq6Parameters, FqParameters, Fr};
-use ark_algebra_test_templates::fields::*;
+use crate::{Fq, Fq12, Fq2, Fq6, Fq6Config, Fr};

-pub(crate) const ITERATIONS: usize = 5;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fr = rng.gen();
-        let b: Fr = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fr>();
-        sqrt_field_test(b);
-        let byte_size = a.serialized_size();
-        field_serialization_test::<Fr>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq = rng.gen();
-        let b: Fq = rng.gen();
-        field_test(a, b);
-        primefield_test::<Fq>();
-        sqrt_field_test(a);
-        let byte_size = a.serialized_size();
-        let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-        assert_eq!(byte_size, buffer_size);
-        field_serialization_test::<Fq>(byte_size);
-    }
-}
-
-#[test]
-fn test_fq2() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let a: Fq2 = rng.gen();
-        let b: Fq2 = rng.gen();
-        field_test(a, b);
-        sqrt_field_test(a);
-    }
-    frobenius_test::<Fq2, _>(Fq::characteristic(), 13);
-    let byte_size = Fq2::zero().serialized_size();
-    field_serialization_test::<Fq2>(byte_size);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq6 = rng.gen();
-        let h: Fq6 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-    let byte_size = Fq6::zero().serialized_size();
-    field_serialization_test::<Fq6>(byte_size);
-}
-
-#[test]
-fn test_fq12() {
-    let mut rng = test_rng();
-    for _ in 0..ITERATIONS {
-        let g: Fq12 = rng.gen();
-        let h: Fq12 = rng.gen();
-        field_test(g, h);
-    }
-    frobenius_test::<Fq12, _>(Fq::characteristic(), 13);
-    let byte_size = Fq12::zero().serialized_size();
-    field_serialization_test::<Fq12>(byte_size);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq2; Fq2);
+test_field!(fq6; Fq6);
+test_field!(fq12; Fq12);

 #[test]
 fn test_fq_repr_from() {
-    assert_eq!(BigInteger256::from(100), BigInteger256([100, 0, 0, 0]));
+    assert_eq!(BigInteger256::from(100u64), BigInt::new([100, 0, 0, 0]));
 }

 #[test]
 fn test_fq_repr_is_odd() {
-    assert!(!BigInteger256::from(0).is_odd());
-    assert!(BigInteger256::from(0).is_even());
-    assert!(BigInteger256::from(1).is_odd());
-    assert!(!BigInteger256::from(1).is_even());
-    assert!(!BigInteger256::from(324834872).is_odd());
-    assert!(BigInteger256::from(324834872).is_even());
-    assert!(BigInteger256::from(324834873).is_odd());
-    assert!(!BigInteger256::from(324834873).is_even());
+    assert!(!BigInteger256::from(0u64).is_odd());
+    assert!(BigInteger256::from(0u64).is_even());
+    assert!(BigInteger256::from(1u64).is_odd());
+    assert!(!BigInteger256::from(1u64).is_even());
+    assert!(!BigInteger256::from(324834872u64).is_odd());
+    assert!(BigInteger256::from(324834872u64).is_even());
+    assert!(BigInteger256::from(324834873u64).is_odd());
+    assert!(!BigInteger256::from(324834873u64).is_even());
 }

 #[test]
 fn test_fq_repr_is_zero() {
-    assert!(BigInteger256::from(0).is_zero());
-    assert!(!BigInteger256::from(1).is_zero());
-    assert!(!BigInteger256([0, 0, 1, 0]).is_zero());
+    assert!(BigInteger256::from(0u64).is_zero());
+    assert!(!BigInteger256::from(1u64).is_zero());
+    assert!(!BigInt::new([0, 0, 1, 0]).is_zero());
 }

 #[test]
 fn test_fq_repr_num_bits() {
-    let mut a = BigInteger256::from(0);
+    let mut a = BigInteger256::from(0u64);
    assert_eq!(0, a.num_bits());
-    a = BigInteger256::from(1);
+    a = BigInteger256::from(1u64);
    for i in 1..257 {
        assert_eq!(i, a.num_bits());
        a.mul2();
@@ -125,248 +53,35 @@ fn test_fq_repr_num_bits() {
    assert_eq!(0, a.num_bits());
 }

-#[test]
-fn test_fq_add_assign() {
-    // Test associativity
-
-    let mut rng = ark_std::test_rng();
-
-    for _ in 0..1000 {
-        // Generate a, b, c and ensure (a + b) + c == a + (b + c).
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.add_assign(&c);
-        tmp2.add_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_sub_assign() {
-    let mut rng = ark_std::test_rng();
-
-    for _ in 0..1000 {
-        // Ensure that (a - b) + (b - a) = 0.
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.sub_assign(&b);
-
-        let mut tmp2 = b;
-        tmp2.sub_assign(&a);
-
-        tmp1.add_assign(&tmp2);
-        assert!(tmp1.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_mul_assign() {
-    let mut rng = ark_std::test_rng();
-
-    for _ in 0..1000000 {
-        // Ensure that (a * b) * c = a * (b * c)
-        let a = Fq::rand(&mut rng);
-        let b = Fq::rand(&mut rng);
-        let c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.mul_assign(&b);
-        tmp1.mul_assign(&c);
-
-        let mut tmp2 = b;
-        tmp2.mul_assign(&c);
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp1, tmp2);
-    }
-
-    for _ in 0..1000000 {
-        // Ensure that r * (a + b + c) = r*a + r*b + r*c
-
-        let r = Fq::rand(&mut rng);
-        let mut a = Fq::rand(&mut rng);
-        let mut b = Fq::rand(&mut rng);
-        let mut c = Fq::rand(&mut rng);
-
-        let mut tmp1 = a;
-        tmp1.add_assign(&b);
-        tmp1.add_assign(&c);
-        tmp1.mul_assign(&r);
-
-        a.mul_assign(&r);
-        b.mul_assign(&r);
-        c.mul_assign(&r);
-
-        a.add_assign(&b);
-        a.add_assign(&c);
-
-        assert_eq!(tmp1, a);
-    }
-}
-
-#[test]
-fn test_fq_squaring() {
-    let mut rng = ark_std::test_rng();
-
-    for _ in 0..1000000 {
-        // Ensure that (a * a) = a^2
-        let a = Fq::rand(&mut rng);
-
-        let mut tmp = a;
-        tmp.square_in_place();
-
-        let mut tmp2 = a;
-        tmp2.mul_assign(&a);
-
-        assert_eq!(tmp, tmp2);
-    }
-}
-
-#[test]
-fn test_fq_inverse() {
-    assert!(Fq::zero().inverse().is_none());
-
-    let mut rng = ark_std::test_rng();
-
-    let one = Fq::one();
-
-    for _ in 0..1000 {
-        // Ensure that a * a^-1 = 1
-        let mut a = Fq::rand(&mut rng);
-        let ainv = a.inverse().unwrap();
-        a.mul_assign(&ainv);
-        assert_eq!(a, one);
-    }
-}
-
-#[test]
-fn test_fq_double_in_place() {
-    let mut rng = ark_std::test_rng();
-
-    for _ in 0..1000 {
-        // Ensure doubling a is equivalent to adding a to itself.
-        let mut a = Fq::rand(&mut rng);
-        let mut b = a;
-        b.add_assign(&a);
-        a.double_in_place();
-        assert_eq!(a, b);
-    }
-}
-
-#[test]
-fn test_fq_negate() {
-    {
-        let a = -Fq::zero();
-
-        assert!(a.is_zero());
-    }
-
-    let mut rng = ark_std::test_rng();
-
-    for _ in 0..1000 {
-        // Ensure (a - (-a)) = 0.
-        let mut a = Fq::rand(&mut rng);
-        let b = -a;
-        a.add_assign(&b);
-
-        assert!(a.is_zero());
-    }
-}
-
-#[test]
-fn test_fq_pow() {
-    let mut rng = ark_std::test_rng();
-
-    for i in 0..1000 {
-        // Exponentiate by various small numbers and ensure it consists with repeated
-        // multiplication.
-        let a = Fq::rand(&mut rng);
-        let target = a.pow(&[i]);
-        let mut c = Fq::one();
-        for _ in 0..i {
-            c.mul_assign(&a);
-        }
-        assert_eq!(c, target);
-    }
-
-    for _ in 0..1000 {
-        // Exponentiating by the modulus should have no effect in a prime field.
-        let a = Fq::rand(&mut rng);
-
-        assert_eq!(a, a.pow(Fq::characteristic()));
-    }
-}
-
-#[test]
-fn test_fq_sqrt() {
-    let mut rng = ark_std::test_rng();
-
-    assert_eq!(Fq::zero().sqrt().unwrap(), Fq::zero());
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a^2) = a or -a
-        let a = Fq::rand(&mut rng);
-        let nega = -a;
-        let mut b = a;
-        b.square_in_place();
-
-        let b = b.sqrt().unwrap();
-
-        assert!(a == b || nega == b);
-    }
-
-    for _ in 0..1000 {
-        // Ensure sqrt(a)^2 = a for random a
-        let a = Fq::rand(&mut rng);
-
-        if let Some(mut tmp) = a.sqrt() {
-            tmp.square_in_place();
-
-            assert_eq!(a, tmp);
-        }
-    }
-}
-
 #[test]
 fn test_fq_num_bits() {
-    assert_eq!(FqParameters::MODULUS_BITS, 254);
-    assert_eq!(FqParameters::CAPACITY, 253);
+    assert_eq!(Fq::MODULUS_BIT_SIZE, 254);
 }

 #[test]
 fn test_fq_root_of_unity() {
-    assert_eq!(FqParameters::TWO_ADICITY, 1);
+    assert_eq!(Fq::TWO_ADICITY, 1);
    assert_eq!(
-        Fq::multiplicative_generator().pow([
+        Fq::GENERATOR.pow([
            0x9e10460b6c3e7ea3,
            0xcbc0b548b438e546,
            0xdc2822db40c0ac2e,
            0x183227397098d014,
        ]),
-        Fq::two_adic_root_of_unity()
+        Fq::TWO_ADIC_ROOT_OF_UNITY
    );
    assert_eq!(
-        Fq::two_adic_root_of_unity().pow([1 << FqParameters::TWO_ADICITY]),
+        Fq::TWO_ADIC_ROOT_OF_UNITY.pow([1 << Fq::TWO_ADICITY]),
        Fq::one()
    );
-    assert!(Fq::multiplicative_generator().sqrt().is_none());
+    assert!(Fq::GENERATOR.sqrt().is_none());
 }

 #[test]
 fn test_fq_ordering() {
    // BigInteger256's ordering is well-tested, but we still need to make sure the
    // Fq elements aren't being compared in Montgomery form.
-    for i in 0..100 {
+    for i in 0..100u64 {
        assert!(Fq::from(BigInteger256::from(i + 1)) > Fq::from(BigInteger256::from(i)));
    }
 }
@@ -379,11 +94,11 @@ fn test_fq_legendre() {
    assert_eq!(Zero, Fq::zero().legendre());
    assert_eq!(
        QuadraticResidue,
-        Fq::from(BigInteger256::from(4)).legendre()
+        Fq::from(BigInteger256::from(4u64)).legendre()
    );
    assert_eq!(
        QuadraticNonResidue,
-        Fq::from(BigInteger256::from(5)).legendre()
+        Fq::from(BigInteger256::from(5u64)).legendre()
    );
 }

@@ -424,7 +139,7 @@ fn test_fq2_legendre() {
    // i^2 = -1
    let mut m1 = -Fq2::one();
    assert_eq!(QuadraticResidue, m1.legendre());
-    m1 = Fq6Parameters::mul_fp2_by_nonresidue(&m1);
+    Fq6Config::mul_fp2_by_nonresidue_in_place(&mut m1);
    assert_eq!(QuadraticNonResidue, m1.legendre());
 }

--- a/bn254/src/lib.rs
+++ b/bn254/src/lib.rs
@@ -20,14 +20,17 @@
 //!
 //!
 //! Curve information:
-//! * Base field: q = 21888242871839275222246405745257275088696311157297823662689037894645226208583
-//! * Scalar field: r = 21888242871839275222246405745257275088548364400416034343698204186575808495617
+//! * Base field: q =
+//!   21888242871839275222246405745257275088696311157297823662689037894645226208583
+//! * Scalar field: r =
+//!   21888242871839275222246405745257275088548364400416034343698204186575808495617
 //! * valuation(q - 1, 2) = 1
 //! * valuation(r - 1, 2) = 28
 //! * G1 curve equation: y^2 = x^3 + 3
 //! * G2 curve equation: y^2 = x^3 + B, where
-//!    * B = 3/(u+9) where Fq2 is represented as Fq\[u\]/(u^2+1)
-//!        = Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)
+//!    * B = 3/(u+9) where Fq2 is represented as Fq\[u\]/(u^2+1) =
+//!      Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373,
+//!      266929791119991161246907387137283842545076965332900288569378510910307636690)

 #[cfg(feature = "curve")]
 mod curves;
--- a/bw6_761/Cargo.toml
+++ b/bw6_761/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "ark-bw6-761"
-version = "0.3.0"
+version = "0.4.0-alpha.1"
 authors = [ "arkworks contributors" ]
 description = "The BW6-761 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
@@ -10,18 +10,24 @@ keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"

 [dependencies]
-ark-ff = { version="^0.3.0", default-features = false }
-ark-ec = { version="^0.3.0", default-features = false }
-ark-std = { version="^0.3.0", default-features = false }
-ark-bls12-377 = { version="^0.3.0", path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+ark-ff = { version="0.4.0-alpha", default-features = false }
+ark-ec = { version="0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-bls12-377 = { version = "0.4.0-alpha", path = "../bls12_377", default-features = false, features = [ "base_field" ] }

 [dev-dependencies]
-ark-serialize = { version="^0.3.0", default-features = false }
-ark-algebra-test-templates = { version="^0.3.0", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }

 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bls12-377/std" ]
+
+[[bench]]
+name = "bw6_761"
+path = "benches/bw6_761.rs"
+harness = false
--- a/curve-benches/LICENSE-APACHE
+++ b/curve-benches/LICENSE-APACHE
--- a/curve-benches/LICENSE-MIT
+++ b/curve-benches/LICENSE-MIT
--- a/bw6_761/benches/bw6_761.rs
+++ b/bw6_761/benches/bw6_761.rs
@@ -0,0 +1,16 @@
+use ark_algebra_bench_templates::*;
+
+use ark_bw6_761::{
+    fq::Fq, fq3::Fq3, fq6::Fq6, fr::Fr, g1::G1Projective as G1, g2::G2Projective as G2, BW6_761,
+};
+
+bench!(
+    Name = "BW6_761",
+    Pairing = BW6_761,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq3,
+    TargetField = Fq6,
+);
--- a/bw6_761/scripts/base_field.sage
+++ b/bw6_761/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
+
+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_761/scripts/scalar_field.sage
+++ b/bw6_761/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+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_761/src/curves/g1.rs
+++ b/bw6_761/src/curves/g1.rs
@@ -1,30 +1,20 @@
-use crate::{Fq, Fr};
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
-use ark_ff::field_new;
+use ark_ff::{Field, MontFp};

-pub type G1Affine = GroupAffine<Parameters>;
-pub type G1Projective = GroupProjective<Parameters>;
+use crate::{Fq, Fr};
+
+pub type G1Affine = Affine<Parameters>;
+pub type G1Projective = Projective<Parameters>;

 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    #[rustfmt::skip]
-
-    const COEFF_A: Fq = field_new!(Fq, "0");
-
-    /// COEFF_B = -1
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "-1");

    /// COFACTOR =
    /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194876
@@ -40,14 +30,20 @@ impl SWModelParameters for Parameters {

    /// COFACTOR^(-1) mod r =
    /// 91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804");
+    const COFACTOR_INV: Fr = MontFp!("91141326767669940707819291241958318717982251277713150053234367522357946997763584490607453720072232540829942217804");
+}
+
+impl SWCurveConfig for Parameters {
+    /// 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 AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (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 {
+    fn mul_by_a(_elem: Self::BaseField) -> Self::BaseField {
        use ark_ff::Zero;
        Self::BaseField::zero()
    }
@@ -55,10 +51,8 @@ impl SWModelParameters for Parameters {

 /// G1_GENERATOR_X =
 /// 6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, "6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");
+pub const G1_GENERATOR_X: Fq = MontFp!("6238772257594679368032145693622812838779005809760824733138787810501188623461307351759238099287535516224314149266511977132140828635950940021790489507611754366317801811090811367945064510304504157188661901055903167026722666149426237");

 /// G1_GENERATOR_Y =
 /// 2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099");
+pub const G1_GENERATOR_Y: Fq = MontFp!("2101735126520897423911504562215834951148127555913367997162789335052900271653517958562461315794228241561913734371411178226936527683203879553093934185950470971848972085321797958124416462268292467002957525517188485984766314758624099");
--- a/bw6_761/src/curves/g2.rs
+++ b/bw6_761/src/curves/g2.rs
@@ -1,30 +1,20 @@
-use crate::{Fq, Fr};
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
 };
-use ark_ff::field_new;
+use ark_ff::{Field, MontFp};

-pub type G2Affine = GroupAffine<Parameters>;
-pub type G2Projective = GroupProjective<Parameters>;
+use crate::{Fq, Fr};
+
+pub type G2Affine = Affine<Parameters>;
+pub type G2Projective = Projective<Parameters>;

 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 0
-    #[rustfmt::skip]
-
-    const COEFF_A: Fq = field_new!(Fq, "0");
-
-    /// COEFF_B = 4
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "4");

    /// COFACTOR =
    /// 26642435879335816683987677701488073867751118270052650655942102502312977592501693353047140953112195348280268661194869
@@ -40,14 +30,21 @@ impl SWModelParameters for Parameters {

    /// COFACTOR^(-1) mod r =
    /// 214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124");
+    const COFACTOR_INV: Fr = MontFp!("214911522365886453591244899095480747723790054550866810551297776298664428889000553861210287833206024638187939842124");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 0
+    const COEFF_A: Fq = Fq::ZERO;
+
+    /// COEFF_B = 4
+    const COEFF_B: Fq = MontFp!("4");

    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (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 {
+    fn mul_by_a(_elem: Self::BaseField) -> Self::BaseField {
        use ark_ff::Zero;
        Self::BaseField::zero()
    }
@@ -55,10 +52,8 @@ impl SWModelParameters for Parameters {

 /// G2_GENERATOR_X =
 ///  6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428
-#[rustfmt::skip]
-pub const G2_GENERATOR_X: Fq = field_new!(Fq, "6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");
+pub const G2_GENERATOR_X: Fq = MontFp!("6445332910596979336035888152774071626898886139774101364933948236926875073754470830732273879639675437155036544153105017729592600560631678554299562762294743927912429096636156401171909259073181112518725201388196280039960074422214428");

 /// G2_GENERATOR_Y =
 /// 562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y: Fq = field_new!(Fq, "562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041");
+pub const G2_GENERATOR_Y: Fq = MontFp!("562923658089539719386922163444547387757586534741080263946953401595155211934630598999300396317104182598044793758153214972605680357108252243146746187917218885078195819486220416605630144001533548163105316661692978285266378674355041");
--- a/bw6_761/src/curves/mod.rs
+++ b/bw6_761/src/curves/mod.rs
@@ -1,9 +1,10 @@
-use crate::*;
 use ark_ec::{
    bw6,
    bw6::{BW6Parameters, TwistType, BW6},
 };
-use ark_ff::biginteger::BigInteger768 as BigInteger;
+use ark_ff::{biginteger::BigInteger768 as BigInteger, BigInt};
+
+use crate::*;

 pub mod g1;
 pub mod g2;
@@ -15,7 +16,7 @@ mod tests;
 pub struct Parameters;

 impl BW6Parameters for Parameters {
-    const X: BigInteger = BigInteger([
+    const X: BigInteger = BigInt::new([
        0x8508c00000000001,
        0x0,
        0x0,
@@ -47,8 +48,8 @@ impl BW6Parameters for Parameters {
    const ATE_LOOP_COUNT_2_IS_NEGATIVE: bool = false;
    const TWIST_TYPE: TwistType = TwistType::M;
    type Fp = Fq;
-    type Fp3Params = Fq3Parameters;
-    type Fp6Params = Fq6Parameters;
+    type Fp3Config = Fq3Config;
+    type Fp6Config = Fq6Config;
    type G1Parameters = g1::Parameters;
    type G2Parameters = g2::Parameters;
 }
--- a/bw6_761/src/curves/tests.rs
+++ b/bw6_761/src/curves/tests.rs
@@ -1,78 +1,8 @@
-use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{Field, One, PrimeField};
-use ark_std::rand::Rng;
-use ark_std::test_rng;
-
 use crate::*;
+use ark_algebra_test_templates::*;
+use ark_ff::Field;

-use ark_algebra_test_templates::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let sa = a.mul(s.into_repr());
-    let sb = b.mul(s.into_repr());
-
-    let ans1 = BW6_761::pairing(sa, b);
-    let ans2 = BW6_761::pairing(a, sb);
-    let ans3 = BW6_761::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq6::one());
-    assert_ne!(ans2, Fq6::one());
-    assert_ne!(ans3, Fq6::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq6::one());
-}
+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);
--- a/bw6_761/src/fields/fq.rs
+++ b/bw6_761/src/fields/fq.rs
@@ -1,175 +1,7 @@
-use ark_ff::{
-    biginteger::BigInteger768 as BigInteger,
-    field_new,
-    fields::{FftParameters, Fp768, Fp768Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp768, MontBackend, MontConfig};

-pub type Fq = Fp768<FqParameters>;
-
-pub struct FqParameters;
-
-pub const FQ_ONE: Fq = field_new!(Fq, "1");
-pub const FQ_ZERO: Fq = field_new!(Fq, "0");
-
-impl Fp768Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    // The internal representation of this type is six 64-bit unsigned
-    // integers in little-endian order. Values are always in
-    // Montgomery form; i.e., Scalar(a) = aR mod p, with R=2^768.
-
-    // (MODULUS - 1) % 2^TWO_ADICITY == 0
-    const TWO_ADICITY: u32 = 1;
-
-    // least_quadratic_nonresidue(MODULUS) in Sage.
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        17481284903592032950u64,
-        10104133845767975835u64,
-        8607375506753517913u64,
-        13706168424391191299u64,
-        9580010308493592354u64,
-        14241333420363995524u64,
-        6665632285037357566u64,
-        5559902898979457045u64,
-        15504799981718861253u64,
-        8332096944629367896u64,
-        18005297320867222879u64,
-        58811391084848524u64,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-       0xf49d00000000008b,
-       0xe6913e6870000082,
-       0x160cf8aeeaf0a437,
-       0x98a116c25667a8f8,
-       0x71dcd3dc73ebff2e,
-       0x8689c8ed12f9fd90,
-       0x03cebaff25b42304,
-       0x707ba638e584e919,
-       0x528275ef8087be41,
-       0xb926186a81d14688,
-       0xd187c94004faff3e,
-       0x122e824fb83ce0a
-    ]);
-
-    const MODULUS_BITS: u32 = 761;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    // gap to 64-bit machine word
-    const REPR_SHAVE_BITS: u32 = 7;
-
-    // 2^768 % MODULUS
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        144959613005956565u64,
-        6509995272855063783u64,
-        11428286765660613342u64,
-        15738672438262922740u64,
-        17071399330169272331u64,
-        13899911246788437003u64,
-        12055474021000362245u64,
-        2545351818702954755u64,
-        8887388221587179644u64,
-        5009280847225881135u64,
-        15539704305423854047u64,
-        23071597697427581u64,
-    ]);
-
-    // R^2
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        14305184132582319705u64,
-        8868935336694416555u64,
-        9196887162930508889u64,
-        15486798265448570248u64,
-        5402985275949444416u64,
-        10893197322525159598u64,
-        3204916688966998390u64,
-        12417238192559061753u64,
-        12426306557607898622u64,
-        1305582522441154384u64,
-        10311846026977660324u64,
-        48736111365249031u64,
-    ]);
-
-    // (-1/MODULUS) % 2^64
-    const INV: u64 = 744663313386281181u64;
-
-    /// GENERATOR = 2
-    // primitive_root(MODULUS)
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        289919226011913130u64,
-        13019990545710127566u64,
-        4409829457611675068u64,
-        13030600802816293865u64,
-        15696054586628993047u64,
-        9353078419867322391u64,
-        5664203968291172875u64,
-        5090703637405909511u64,
-        17774776443174359288u64,
-        10018561694451762270u64,
-        12632664537138156478u64,
-        46143195394855163u64,
-    ]);
-
-    // (MODULUS - 1) / 2
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x7a4e800000000045,
-        0xf3489f3438000041,
-        0x0b067c577578521b,
-        0x4c508b612b33d47c,
-        0x38ee69ee39f5ff97,
-        0x4344e476897cfec8,
-        0x81e75d7f92da1182,
-        0xb83dd31c72c2748c,
-        0x29413af7c043df20,
-        0x5c930c3540e8a344,
-        0x68c3e4a0027d7f9f,
-        0x9174127dc1e705,
-    ]);
-
-    // T =
-    // 3445725192157866269698394841137828771239834456268075054756895080104811711121745868043841591644705843820432283876893306725580879560277123879674755849562650799475802549689254425186271815711798397975949850214984556421382456559534149
-    // (MODULUS - 1) / 2 ^ TWO_ADICITY
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x7a4e800000000045,
-        0xf3489f3438000041,
-        0x0b067c577578521b,
-        0x4c508b612b33d47c,
-        0x38ee69ee39f5ff97,
-        0x4344e476897cfec8,
-        0x81e75d7f92da1182,
-        0xb83dd31c72c2748c,
-        0x29413af7c043df20,
-        0x5c930c3540e8a344,
-        0x68c3e4a0027d7f9f,
-        0x9174127dc1e705,
-    ]);
-
-    // (T - 1)/2 =
-    // 1722862596078933134849197420568914385619917228134037527378447540052405855560872934021920795822352921910216141938446653362790439780138561939837377924781325399737901274844627212593135907855899198987974925107492278210691228279767074
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xbd27400000000022,
-        0xf9a44f9a1c000020,
-        0x05833e2bbabc290d,
-        0xa62845b09599ea3e,
-        0x1c7734f71cfaffcb,
-        0x21a2723b44be7f64,
-        0x40f3aebfc96d08c1,
-        0x5c1ee98e39613a46,
-        0x14a09d7be021ef90,
-        0xae49861aa07451a2,
-        0xb461f250013ebfcf,
-        0x48ba093ee0f382,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299"]
+#[generator = "2"]
+pub struct FqConfig;
+pub type Fq = Fp768<MontBackend<FqConfig, 12>>;
--- a/bw6_761/src/fields/fq3.rs
+++ b/bw6_761/src/fields/fq3.rs
@@ -1,31 +1,27 @@
 use ark_ff::{
-    field_new,
-    fields::fp3::{Fp3, Fp3Parameters},
+    fields::fp3::{Fp3, Fp3Config},
+    Field, MontFp,
 };

-use crate::{
-    fields::{FQ_ONE, FQ_ZERO},
-    Fq,
-};
+use crate::Fq;

-pub type Fq3 = Fp3<Fq3Parameters>;
+pub type Fq3 = Fp3<Fq3Config>;

-pub struct Fq3Parameters;
+pub struct Fq3Config;

-impl Fp3Parameters for Fq3Parameters {
+impl Fp3Config for Fq3Config {
    type Fp = Fq;

    /// NONRESIDUE = -4
    // Fq3 = Fq\[u\]/u^3+4
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, "-4");
+    const NONRESIDUE: Fq = MontFp!("-4");

    // (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 T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+    const TRACE_MINUS_ONE_DIV_TWO: &'static [u64] = &[
        0xb5e7c000000a3eac,
        0xf79b99dbf41cf4ab,
        0xe9372b1919e55ee5,
@@ -65,33 +61,28 @@ impl Fp3Parameters for Fq3Parameters {
    ];

    // NONRESIDUE^T % q
-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
-        field_new!(Fq, "6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068298"),
+        Fq::ZERO,
+        Fq::ZERO,
    );

    // NQR ^ (MODULUS^i - 1)/3, i=0,1,2 with NQR = u = (0,1,0)
-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        FQ_ONE,
-        field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
-        field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        Fq::ONE,
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
    ];

    // NQR ^ (2*MODULUS^i - 2)/3, i=0,1,2 with NQR = u = (0,1,0)
-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        FQ_ONE,
-        field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
-        field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        Fq::ONE,
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
    ];

    #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
-        let original = -(*fe);
-        let double = original + &original;
-        double + &double
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
+        fe.double_in_place().double_in_place().neg_in_place()
    }
 }
--- a/bw6_761/src/fields/fq6.rs
+++ b/bw6_761/src/fields/fq6.rs
@@ -1,27 +1,26 @@
-use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO};
 use ark_ff::{
-    field_new,
-    fields::fp6_2over3::{Fp6, Fp6Parameters},
+    fields::fp6_2over3::{Fp6, Fp6Config},
+    Field, MontFp,
 };

-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::{Fq, Fq3, Fq3Config};

-pub struct Fq6Parameters;
+pub type Fq6 = Fp6<Fq6Config>;

-impl Fp6Parameters for Fq6Parameters {
-    type Fp3Params = Fq3Parameters;
+pub struct Fq6Config;
+
+impl Fp6Config for Fq6Config {
+    type Fp3Config = Fq3Config;

    /// NONRESIDUE = (0, 1, 0)
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        field_new!(Fq, "1"),
-        field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775649"),
-        field_new!(Fq, "4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
-        field_new!(Fq, "-1"),
-        field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
-        field_new!(Fq, "1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292651"),
+        Fq::ONE,
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775649"),
+        MontFp!("4922464560225523242118178942575080391082002530232324381063048548642823052024664478336818169867474395270858391911405337707247735739826664939444490469542109391530482826728203582549674992333383150446779312029624171857054392282775648"),
+        MontFp!("-1"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292650"),
+        MontFp!("1968985824090209297278610739700577151397666382303825728450741611566800370218827257750865013421937292370006175842381275743914023380727582819905021229583192207421122272650305267822868639090213645505120388400344940985710520836292651"),
    ];
 }
--- a/bw6_761/src/fields/fr.rs
+++ b/bw6_761/src/fields/fr.rs
@@ -1 +1 @@
-pub use ark_bls12_377::{Fq as Fr, FqParameters as FrParameters};
+pub use ark_bls12_377::{Fq as Fr, FqConfig as FrConfig};
--- a/bw6_761/src/fields/tests.rs
+++ b/bw6_761/src/fields/tests.rs
@@ -1,52 +1,7 @@
-use ark_ff::{Field, PrimeField};
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use ark_std::rand::Rng;
-use ark_std::test_rng;
-
 use crate::*;
+use ark_algebra_test_templates::*;

-use ark_algebra_test_templates::fields::*;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    let a: Fr = rng.gen();
-    let b: Fr = rng.gen();
-    field_test(a, b);
-    sqrt_field_test(a);
-    primefield_test::<Fr>();
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    let a: Fq = rng.gen();
-    let b: Fq = rng.gen();
-    field_test(a, b);
-    primefield_test::<Fq>();
-    sqrt_field_test(a);
-
-    let byte_size = a.serialized_size();
-    let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-    assert_eq!(byte_size, buffer_size);
-    field_serialization_test::<Fq>(byte_size);
-}
-
-#[test]
-fn test_fq3() {
-    let mut rng = test_rng();
-    let a: Fq3 = rng.gen();
-    let b: Fq3 = rng.gen();
-    field_test(a, b);
-    sqrt_field_test(a);
-    frobenius_test::<Fq3, _>(Fq::characteristic(), 13);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    let a: Fq6 = rng.gen();
-    let b: Fq6 = rng.gen();
-    field_test(a, b);
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq3; Fq3);
+test_field!(fq6; Fq6);
--- a/bw6_761/src/lib.rs
+++ b/bw6_761/src/lib.rs
@@ -9,9 +9,10 @@
 #![forbid(unsafe_code)]

 //! This library implements the BW6_761 curve generated in [\[EG20\]](https://eprint.iacr.org/2020/351).
-//! 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_377 curve.
+//! 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_377 curve.
 //!
 //! Curve information:
 //! * Base field: q = 6891450384315732539396789682275657542479668912536150109513790160209623422243491736087683183289411687640864567753786613451161759120554247759349511699125301598951605099378508850372543631423596795951899700429969112842764913119068299
--- a/cp6_782/Cargo.toml
+++ b/cp6_782/Cargo.toml
@@ -1,6 +1,6 @@
 [package]
 name = "ark-cp6-782"
-version = "0.3.0"
+version = "0.4.0-alpha.1"
 authors = [ "arkworks contributors" ]
 description = "The CP6-782 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
@@ -10,18 +10,25 @@ keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
-edition = "2018"
+edition = "2021"

 [dependencies]
-ark-ff = { version = "^0.3.0", default-features = false }
-ark-ec = { version = "^0.3.0", default-features = false }
-ark-std = { version = "^0.3.0", default-features = false }
-ark-bls12-377 = { version = "^0.3.0", path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+ark-ff = { version = "0.4.0-alpha", default-features = false }
+ark-ec = { version = "0.4.0-alpha", default-features = false }
+ark-std = { version = "0.4.0-alpha", default-features = false }
+ark-bls12-377 = { version = "0.4.0-alpha", path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+itertools = { version = "0.10", default-features = false }
+ark-serialize = { version = "0.4.0-alpha", default-features = false }

 [dev-dependencies]
-ark-serialize = { version = "^0.3.0", default-features = false }
-ark-algebra-test-templates = { version = "^0.3.0", default-features = false }
+ark-algebra-test-templates = { version = "0.4.0-alpha", default-features = false }
+ark-algebra-bench-templates = { version = "0.4.0-alpha", default-features = false }

 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bls12-377/std" ]
+
+[[bench]]
+name = "cp6_782"
+path = "benches/cp6_782.rs"
+harness = false
--- a/cp6_782/LICENSE-APACHE
+++ b/cp6_782/LICENSE-APACHE
@@ -0,0 +1 @@
+../LICENSE-APACHE
--- a/cp6_782/LICENSE-MIT
+++ b/cp6_782/LICENSE-MIT
@@ -0,0 +1 @@
+../LICENSE-MIT
--- a/cp6_782/benches/cp6_782.rs
+++ b/cp6_782/benches/cp6_782.rs
@@ -0,0 +1,15 @@
+use ark_algebra_bench_templates::*;
+use ark_cp6_782::{
+    fq::Fq, fq3::Fq3, fq6::Fq6, fr::Fr, g1::G1Projective as G1, g2::G2Projective as G2, CP6_782,
+};
+
+bench!(
+    Name = "CP6_782",
+    Pairing = CP6_782,
+    G1 = G1,
+    G2 = G2,
+    ScalarField = Fr,
+    G1BaseField = Fq,
+    G2BaseField = Fq3,
+    TargetField = Fq6,
+);
--- a/cp6_782/scripts/base_field.sage
+++ b/cp6_782/scripts/base_field.sage
@@ -0,0 +1,28 @@
+modulus = 22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577
+
+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/cp6_782/scripts/scalar_field.sage
+++ b/cp6_782/scripts/scalar_field.sage
@@ -0,0 +1,28 @@
+modulus = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
+
+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/cp6_782/src/curves/g1.rs
+++ b/cp6_782/src/curves/g1.rs
@@ -1,30 +1,62 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::{short_weierstrass::SWCurveConfig, CurveConfig},
+    short_weierstrass::{Affine, Projective},
+    AffineRepr, CurveGroup,
 };
-use ark_ff::field_new;
+use ark_ff::MontFp;
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
+use ark_std::vec::Vec;

 use crate::{Fq, Fr};

-pub type G1Affine = GroupAffine<Parameters>;
-pub type G1Projective = GroupProjective<Parameters>;
+pub type G1Affine = Affine<Parameters>;
+pub type G1Projective = Projective<Parameters>;
+
+#[derive(Clone, Debug, PartialEq, Eq, CanonicalSerialize, CanonicalDeserialize)]
+pub struct G1Prepared(pub G1Affine);
+
+impl From<G1Affine> for G1Prepared {
+    fn from(other: G1Affine) -> Self {
+        G1Prepared(other)
+    }
+}
+
+impl From<G1Projective> for G1Prepared {
+    fn from(q: G1Projective) -> Self {
+        q.into_affine().into()
+    }
+}
+
+impl<'a> From<&'a G1Affine> for G1Prepared {
+    fn from(other: &'a G1Affine) -> Self {
+        G1Prepared(*other)
+    }
+}
+
+impl<'a> From<&'a G1Projective> for G1Prepared {
+    fn from(q: &'a G1Projective) -> Self {
+        q.into_affine().into()
+    }
+}
+
+impl G1Prepared {
+    pub fn is_zero(&self) -> bool {
+        self.0.is_zero()
+    }
+}
+
+impl Default for G1Prepared {
+    fn default() -> Self {
+        G1Prepared(G1Affine::generator())
+    }
+}

 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = 5
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "5");
-
-    /// COEFF_B = 17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414");

    /// COFACTOR =
    /// 86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951561028
@@ -41,20 +73,24 @@ impl SWModelParameters for Parameters {

    /// COFACTOR^(-1) mod r =
    /// 163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788");
+    const COFACTOR_INV: Fr = MontFp!("163276846538158998893990986356139314746223949404500031940624325017036397274793417940375498603127780919653358641788");
+}
+
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = 5
+    const COEFF_A: Fq = MontFp!("5");
+
+    /// COEFF_B = 17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414
+    const COEFF_B: Fq = MontFp!("17764315118651679038286329069295091506801468118146712649886336045535808055361274148466772191243305528312843236347777260247138934336850548243151534538734724191505953341403463040067571652261229308333392040104884438208594329793895206056414");

    /// AFFINE_GENERATOR_COEFFS = (G1_GENERATOR_X, G1_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G1_GENERATOR_X, G1_GENERATOR_Y);
+    const GENERATOR: G1Affine = G1Affine::new_unchecked(G1_GENERATOR_X, G1_GENERATOR_Y);
 }

 /// G1_GENERATOR_X =
 /// 5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646
-#[rustfmt::skip]
-pub const G1_GENERATOR_X: Fq = field_new!(Fq, "5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646");
+pub const G1_GENERATOR_X: Fq = MontFp!("5511163824921585887915590525772884263960974614921003940645351443740084257508990841338974915037175497689287870585840954231884082785026301437744745393958283053278991955159266640440849940136976927372133743626748847559939620888818486853646");

 /// G1_GENERATOR_Y =
 /// 7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443
-#[rustfmt::skip]
-pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443");
+pub const G1_GENERATOR_Y: Fq = MontFp!("7913123550914612057135582061699117755797758113868200992327595317370485234417808273674357776714522052694559358668442301647906991623400754234679697332299689255516547752391831738454121261248793568285885897998257357202903170202349380518443");
--- a/cp6_782/src/curves/g2.rs
+++ b/cp6_782/src/curves/g2.rs
@@ -1,40 +1,62 @@
 use ark_ec::{
-    models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
+    models::CurveConfig,
+    short_weierstrass::{Affine, Projective, SWCurveConfig},
+    AffineRepr, CurveGroup,
 };
-use ark_ff::field_new;
+use ark_ff::{Field, MontFp};
+use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
+use ark_std::vec::Vec;

-use crate::{Fq, Fq3, Fr, FQ_ZERO};
+use crate::{Fq, Fq3, Fr};

-pub type G2Affine = GroupAffine<Parameters>;
-pub type G2Projective = GroupProjective<Parameters>;
+pub type G2Affine = Affine<Parameters>;
+pub type G2Projective = Projective<Parameters>;
+
+#[derive(Clone, Debug, PartialEq, Eq, CanonicalSerialize, CanonicalDeserialize)]
+pub struct G2Prepared(pub G2Affine);
+
+impl From<G2Affine> for G2Prepared {
+    fn from(other: G2Affine) -> Self {
+        G2Prepared(other)
+    }
+}
+
+impl From<G2Projective> for G2Prepared {
+    fn from(q: G2Projective) -> Self {
+        q.into_affine().into()
+    }
+}
+
+impl<'a> From<&'a G2Affine> for G2Prepared {
+    fn from(other: &'a G2Affine) -> Self {
+        G2Prepared(*other)
+    }
+}
+
+impl<'a> From<&'a G2Projective> for G2Prepared {
+    fn from(q: &'a G2Projective) -> Self {
+        q.into_affine().into()
+    }
+}
+
+impl G2Prepared {
+    pub fn is_zero(&self) -> bool {
+        self.0.is_zero()
+    }
+}
+
+impl Default for G2Prepared {
+    fn default() -> Self {
+        G2Prepared(G2Affine::generator())
+    }
+}

 #[derive(Clone, Default, PartialEq, Eq)]
 pub struct Parameters;

-impl ModelParameters for Parameters {
+impl CurveConfig for Parameters {
    type BaseField = Fq3;
    type ScalarField = Fr;
-}
-
-impl SWModelParameters for Parameters {
-    /// COEFF_A = (0, 0, COEFF_A * TWIST^2) = (0, 0, 5)
-    #[rustfmt::skip]
-    const COEFF_A: Fq3 = field_new!(Fq3,
-        FQ_ZERO,
-        FQ_ZERO,
-        field_new!(Fq, "5"),
-    );
-
-    /// COEFF_B = (G1::COEFF_B * TWIST^3, 0, 0) =
-    /// (7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612,
-    /// 0, 0)
-    #[rustfmt::skip]
-    const COEFF_B: Fq3 = field_new!(Fq3,
-        field_new!(Fq, "7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612"),
-        FQ_ZERO,
-        FQ_ZERO,
-    );

    /// COFACTOR =
    /// 43276679045916726782882096851503554444292580777869919574700824986947162516693702667493938255647666346010819253090121562084993205202476199057555142869892665220155573207800985012241638987472334344174208389303164492698303448192856551557283997344470334833850065978668184377503856699635686872344035470027430053642178229054516302338812152178131995800255516474185251732445975837621097393375441662426280154371264547168198834382681059556891327702516519955053315674076980350109237328216856859758931256208439575383786363605925879337208599843910819433766160937121108797819223653884174994325142959644019600
@@ -75,45 +97,49 @@ impl SWModelParameters for Parameters {

    /// COFACTOR^(-1) mod r =
    /// 45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598");
-
-    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (G2_GENERATOR_X, G2_GENERATOR_Y);
+    const COFACTOR_INV: Fr = MontFp!("45586359457219724873147353901735745013467692594291916855200979604570630929674383405372210802279573887880950375598");
 }

-const G2_GENERATOR_X: Fq3 =
-    field_new!(Fq3, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
-const G2_GENERATOR_Y: Fq3 =
-    field_new!(Fq3, G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);
+impl SWCurveConfig for Parameters {
+    /// COEFF_A = (0, 0, COEFF_A * TWIST^2) = (0, 0, 5)
+    const COEFF_A: Fq3 = Fq3::new(Fq::ZERO, Fq::ZERO, MontFp!("5"));
+
+    /// COEFF_B = (G1::COEFF_B * TWIST^3, 0, 0) =
+    /// (7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612,
+    /// 0, 0)
+    const COEFF_B: Fq3 = Fq3::new(
+        MontFp!("7237353553714858194254855835825640240663090882935418626687402315497764195116318527743248304684159666286416318482685337633828994152723793439622384740540789612754127688659139509552568164770448654259255628317166934203899992395064470477612"),
+        Fq::ZERO,
+        Fq::ZERO,
+    );
+
+    /// AFFINE_GENERATOR_COEFFS = (G2_GENERATOR_X, G2_GENERATOR_Y)
+    const GENERATOR: G2Affine = G2Affine::new_unchecked(G2_GENERATOR_X, G2_GENERATOR_Y);
+}
+
+const G2_GENERATOR_X: Fq3 = Fq3::new(G2_GENERATOR_X_C0, G2_GENERATOR_X_C1, G2_GENERATOR_X_C2);
+const G2_GENERATOR_Y: Fq3 = Fq3::new(G2_GENERATOR_Y_C0, G2_GENERATOR_Y_C1, G2_GENERATOR_Y_C2);

 /// G2_GENERATOR_X_C0 =
 /// 13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C0: Fq = field_new!(Fq, "13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338");
+pub const G2_GENERATOR_X_C0: Fq = MontFp!("13426761183630949215425595811885033211332897733228446437546263564078445562454176776915160094418980045665397361295624472103734543457352048745726512354895954850428989867542989474136256025045975283415690491751906307188562464175510373683338");

 /// G2_GENERATOR_X_C1 =
 /// 20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C1: Fq = field_new!(Fq, "20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610");
+pub const G2_GENERATOR_X_C1: Fq = MontFp!("20471601555918880743198170952645906008198510944268658573129351735028343217532386920456705632337352161031960990613816401042894531220068552819818037605513359562118363589199569321421558696125646867661360498323171027455638052943806292028610");

 /// G2_GENERATOR_X_C2 =
 /// 3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980
-#[rustfmt::skip]
-pub const G2_GENERATOR_X_C2: Fq = field_new!(Fq, "3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980");
+pub const G2_GENERATOR_X_C2: Fq = MontFp!("3905053196875761830053608605277158152930144841844497593936739534395003062685449846381431331169369910535935138116320442345524758217411779027270883193856999691582831339845600938304719916501940381093815781408183227875600753651697934495980");

 /// G2_GENERATOR_Y_C0 =
 /// 8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243");
+pub const G2_GENERATOR_Y_C0: Fq = MontFp!("8567517639523571619872938228644013584947463594196306323477160496987712111576624702939472765993995586889532559039169098780892505598589581147768095093536988446010255611523736706017580686335404469207486594272103717837888228343074699140243");

 /// G2_GENERATOR_Y_C1 =
 /// 3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752");
+pub const G2_GENERATOR_Y_C1: Fq = MontFp!("3890537069205870914984502594450293167889863914413852788876350245583932846980126025043974070704295857226211547108005650399870458089721518559480870503159804530091559886149680718531004778697982910253701559194337987238111062202037698927752");

 /// G2_GENERATOR_Y_C2 =
 /// 10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721
-#[rustfmt::skip]
-pub const G2_GENERATOR_Y_C2: Fq = field_new!(Fq, "10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721");
+pub const G2_GENERATOR_Y_C2: Fq = MontFp!("10936269922612615564271188303104593362724754284143779051599749016735041389483971486958818324356025479751246744831831158558101688599198721653921723013062333636402617118847009085485166284126970598561393411916461254016145116183331671450721");
--- a/cp6_782/src/curves/mod.rs
+++ b/cp6_782/src/curves/mod.rs
@@ -1,18 +1,19 @@
-use ark_ec::{models::SWModelParameters, PairingEngine};
-use ark_ff::{
-    biginteger::BigInteger832,
-    field_new,
-    fields::{BitIteratorBE, Field},
-    One,
+use ark_ec::{
+    models::short_weierstrass::SWCurveConfig,
+    pairing::{MillerLoopOutput, Pairing, PairingOutput},
 };
+use ark_ff::{
+    biginteger::BigInteger832, BigInt, BitIteratorBE, CyclotomicMultSubgroup, Field, One,
+};
+use itertools::Itertools;

-use crate::{Fq, Fq3, Fq6, Fr, FQ_ONE, FQ_ZERO};
+use crate::{Fq, Fq3, Fq6, Fr};

 pub mod g1;
-pub use self::g1::{G1Affine, G1Projective};
+pub use self::g1::{G1Affine, G1Prepared, G1Projective};

 pub mod g2;
-pub use self::g2::{G2Affine, G2Projective};
+pub use self::g2::{G2Affine, G2Prepared, G2Projective};

 #[cfg(test)]
 mod tests;
@@ -22,40 +23,40 @@ pub type GT = Fq6;
 #[derive(Copy, Clone, Debug, PartialEq, Eq)]
 pub struct CP6_782;

-impl PairingEngine for CP6_782 {
-    type Fr = Fr;
-    type G1Projective = G1Projective;
+impl Pairing for CP6_782 {
+    type ScalarField = Fr;
+    type BaseField = Fq;
+    type G1 = G1Projective;
    type G1Affine = G1Affine;
-    type G1Prepared = G1Affine;
-    type G2Projective = G2Projective;
+    type G1Prepared = G1Prepared;
+    type G2 = G2Projective;
    type G2Affine = G2Affine;
-    type G2Prepared = G2Affine;
-    type Fq = Fq;
-    type Fqe = Fq3;
-    type Fqk = Fq6;
+    type G2Prepared = G2Prepared;
+    type TargetField = Fq6;

-    fn miller_loop<'a, I>(i: I) -> Self::Fqk
-    where
-        I: IntoIterator<Item = &'a (Self::G1Prepared, Self::G2Prepared)>,
-    {
-        let mut result = Self::Fqk::one();
-        for &(ref p, ref q) in i {
-            result *= &CP6_782::ate_miller_loop(p, q);
-        }
-        result
+    fn multi_miller_loop(
+        a: impl IntoIterator<Item = impl Into<Self::G1Prepared>>,
+        b: impl IntoIterator<Item = impl Into<Self::G2Prepared>>,
+    ) -> MillerLoopOutput<Self> {
+        let mut result = Self::TargetField::one();
+        a.into_iter().zip_eq(b).for_each(|(p, q)| {
+            let (p, q) = (p.into(), q.into());
+            result *= &CP6_782::ate_miller_loop(&p, &q);
+        });
+
+        MillerLoopOutput(result)
    }

-    fn final_exponentiation(r: &Self::Fqk) -> Option<Self::Fqk> {
-        Some(CP6_782::final_exponentiation(r))
+    fn final_exponentiation(r: MillerLoopOutput<Self>) -> Option<PairingOutput<Self>> {
+        Some(PairingOutput(CP6_782::final_exponentiation(&r.0)))
    }
 }

 impl CP6_782 {
-    pub fn ate_pairing(p: &G1Affine, q: &G2Affine) -> GT {
-        CP6_782::final_exponentiation(&CP6_782::ate_miller_loop(p, q))
-    }
+    fn ate_miller_loop(p: &G1Prepared, q: &G2Prepared) -> Fq6 {
+        let p = p.0;
+        let q = q.0;

-    fn ate_miller_loop(p: &G1Affine, q: &G2Affine) -> Fq6 {
        let px = p.x;
        let py = p.y;
        let qx = q.x;
@@ -88,7 +89,7 @@ impl CP6_782 {

            let x = py_twist_squared;
            let y = gamma_old_rx - &old_ry - &gamma_twist_px;
-            let ell_rr_at_p = Fq6::new(x, y);
+            let ell_rr_at_p: Fq6 = Fq6::new(x, y);

            rx = gamma.square() - &old_rx.double();
            ry = gamma * &(old_rx - &rx) - &old_ry;
@@ -106,7 +107,7 @@ impl CP6_782 {

                let x = py_twist_squared;
                let y = gamma_qx - &qy - &gamma_twist_px;
-                let ell_rq_at_p = Fq6::new(x, y);
+                let ell_rq_at_p: Fq6 = Fq6::new(x, y);

                rx = gamma.square() - &old_rx - &qx;
                ry = gamma * &(old_rx - &rx) - &old_ry;
@@ -154,7 +155,7 @@ impl CP6_782 {
 }

 /// TWIST = (0, 1, 0)
-pub const TWIST: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+pub const TWIST: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);

 /// ATE_IS_LOOP_COUNT_NEG = false
 pub const ATE_IS_LOOP_COUNT_NEG: bool = false;
@@ -182,7 +183,7 @@ 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 = BigInteger832([
+pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInt::new([
    0xb62ef36af72855d1,
    0x676b5cef49d290fa,
    0xd17fcf3c60947427,
@@ -200,7 +201,7 @@ pub const FINAL_EXPONENT_LAST_CHUNK_ABS_OF_W0: BigInteger832 = BigInteger832([

 /// FINAL_EXPONENT_LAST_CHUNK_W1 =
 /// 86482221941698704497288378992285180119495364068003923046442785886272123124361700722982503222189455144364945735564951562986
-pub const FINAL_EXPONENT_LAST_CHUNK_W1: BigInteger832 = BigInteger832([
+pub const FINAL_EXPONENT_LAST_CHUNK_W1: BigInteger832 = BigInt::new([
    0x5657b9b57b942aea,
    0x84f9a65f3bd54eaf,
    0x5ea4214e35cd127,
--- a/cp6_782/src/curves/tests.rs
+++ b/cp6_782/src/curves/tests.rs
@@ -1,78 +1,9 @@
-use ark_ec::{AffineCurve, PairingEngine, ProjectiveCurve};
-use ark_ff::{Field, One, PrimeField};
-use ark_std::rand::Rng;
-use ark_std::test_rng;
+use ark_algebra_test_templates::*;
+use ark_ff::Field;

 use crate::*;

-use ark_algebra_test_templates::{curves::*, groups::*};
-
-#[test]
-fn test_g1_projective_curve() {
-    curve_tests::<G1Projective>();
-
-    sw_tests::<g1::Parameters>();
-}
-
-#[test]
-fn test_g1_projective_group() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G1Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g1_generator() {
-    let generator = G1Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_projective_curve() {
-    curve_tests::<G2Projective>();
-
-    sw_tests::<g2::Parameters>();
-}
-
-#[test]
-fn test_g2_projective_group() {
-    let mut rng = test_rng();
-    let a: G2Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    group_test(a, b);
-}
-
-#[test]
-fn test_g2_generator() {
-    let generator = G2Affine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_bilinearity() {
-    let mut rng = test_rng();
-    let a: G1Projective = rng.gen();
-    let b: G2Projective = rng.gen();
-    let s: Fr = rng.gen();
-
-    let sa = a.mul(s.into_repr());
-    let sb = b.mul(s.into_repr());
-
-    let ans1 = CP6_782::pairing(sa, b);
-    let ans2 = CP6_782::pairing(a, sb);
-    let ans3 = CP6_782::pairing(a, b).pow(s.into_repr());
-
-    assert_eq!(ans1, ans2);
-    assert_eq!(ans2, ans3);
-
-    assert_ne!(ans1, Fq6::one());
-    assert_ne!(ans2, Fq6::one());
-    assert_ne!(ans3, Fq6::one());
-
-    assert_eq!(ans1.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans2.pow(Fr::characteristic()), Fq6::one());
-    assert_eq!(ans3.pow(Fr::characteristic()), Fq6::one());
-}
+test_group!(g1; G1Projective; sw);
+test_group!(g2; G2Projective; sw);
+test_group!(pairing_output; ark_ec::pairing::PairingOutput<CP6_782>; msm);
+test_pairing!(pairing; crate::CP6_782);
--- a/cp6_782/src/fields/fq.rs
+++ b/cp6_782/src/fields/fq.rs
@@ -1,169 +1,7 @@
-use ark_ff::{
-    biginteger::BigInteger832 as BigInteger,
-    fields::{FftParameters, Fp832, Fp832Parameters, FpParameters},
-};
+use ark_ff::fields::{Fp832, MontBackend, MontConfig};

-pub type Fq = Fp832<FqParameters>;
-
-pub struct FqParameters;
-
-pub const FQ_ONE: Fq = ark_ff::field_new!(Fq, "1");
-pub const FQ_ZERO: Fq = ark_ff::field_new!(Fq, "0");
-
-impl Fp832Parameters for FqParameters {}
-impl FftParameters for FqParameters {
-    type BigInt = BigInteger;
-
-    const TWO_ADICITY: u32 = 3;
-
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        18044746167194862600u64,
-        63590321303744709u64,
-        5009346151370959890u64,
-        2859114157767503991u64,
-        8301813204852325413u64,
-        5629414263664332594u64,
-        2637340888701394641u64,
-        17433538052687852753u64,
-        2230763098934759248u64,
-        3785382115983092023u64,
-        8895511354022222370u64,
-        15792083141709071785u64,
-        1328u64,
-    ]);
-}
-impl FpParameters for FqParameters {
-    /// MODULUS = 22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0xdace79b57b942ae9,
-        0x545d85c16dfd424a,
-        0xee135c065f4d26b7,
-        0x9c2f764a12c4024b,
-        0x1ad533049cfe6a39,
-        0x52a3fb77c79c1320,
-        0xab3596c8617c5792,
-        0x830c728d80f9d78b,
-        0x6a7223ee72023d07,
-        0xbc5d176b746af026,
-        0xe959283d8f526663,
-        0xc4d2263babf8941f,
-        0x3848,
-    ]);
-
-    const MODULUS_BITS: u32 = 782;
-
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    const REPR_SHAVE_BITS: u32 = 50;
-
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        11190988450819017841u64,
-        16170411717126802030u64,
-        2265463223430229059u64,
-        16946880912571045974u64,
-        11155248462028513229u64,
-        12855672356664541314u64,
-        8489376931127408159u64,
-        2655797810825538098u64,
-        9648483887143916718u64,
-        17514963461276738952u64,
-        16777089214204267338u64,
-        15649035958020076168u64,
-        8659u64,
-    ]);
-
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        13983406830510863714u64,
-        17863856572171232656u64,
-        1698388424046564526u64,
-        1773634430448388392u64,
-        8684647957094413275u64,
-        3992637317298078843u64,
-        18420879196616862245u64,
-        3238482510270583127u64,
-        7928200707794018216u64,
-        10024831010452223910u64,
-        9613847725664942650u64,
-        15361265984156787358u64,
-        7833u64,
-    ]);
-
-    const INV: u64 = 14469047335842394791u64;
-
-    /// GENERATOR = 13
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        16669393626057438558u64,
-        1640520694378723217u64,
-        1598646156981121135u64,
-        12401834967100173388u64,
-        2356467520877704673u64,
-        14759118825104212161u64,
-        5556628239575210651u64,
-        5317520392768798654u64,
-        16398429955031064995u64,
-        3556102264904210145u64,
-        8166834915717907988u64,
-        11926665585800594452u64,
-        11716u64,
-    ]);
-
-    #[rustfmt::skip]
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0x6d673cdabdca1574,
-        0xaa2ec2e0b6fea125,
-        0xf709ae032fa6935b,
-        0xce17bb2509620125,
-        0xd6a99824e7f351c,
-        0x2951fdbbe3ce0990,
-        0xd59acb6430be2bc9,
-        0xc1863946c07cebc5,
-        0x353911f739011e83,
-        0xde2e8bb5ba357813,
-        0xf4ac941ec7a93331,
-        0x6269131dd5fc4a0f,
-        0x1c24,
-    ]);
-
-    // (T - 1)/2 =
-    // 1398117143679731058146671387906315933423474966581074036386468539227923378278626533764529938634242576261128410962740119034868607201414583335758422276643816405480145410934911750070786645716409577212967755581539567265673914343284832551598
-    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xadace79b57b942ae,
-        0x7545d85c16dfd424,
-        0xbee135c065f4d26b,
-        0x99c2f764a12c4024,
-        0x1ad533049cfe6a3,
-        0x252a3fb77c79c132,
-        0xbab3596c8617c579,
-        0x7830c728d80f9d78,
-        0x66a7223ee72023d0,
-        0x3bc5d176b746af02,
-        0xfe959283d8f52666,
-        0x8c4d2263babf8941,
-        0x384,
-    ]);
-
-    // T =
-    // 2796234287359462116293342775812631866846949933162148072772937078455846756557253067529059877268485152522256821925480238069737214402829166671516844553287632810960290821869823500141573291432819154425935511163079134531347828686569665103197
-    #[rustfmt::skip]
-    const T: BigInteger = BigInteger([
-        0x5b59cf36af72855d,
-        0xea8bb0b82dbfa849,
-        0x7dc26b80cbe9a4d6,
-        0x3385eec942588049,
-        0x35aa660939fcd47,
-        0x4a547f6ef8f38264,
-        0x7566b2d90c2f8af2,
-        0xf0618e51b01f3af1,
-        0xcd4e447dce4047a0,
-        0x778ba2ed6e8d5e04,
-        0xfd2b2507b1ea4ccc,
-        0x189a44c7757f1283,
-        0x709,
-    ]);
-}
+#[derive(MontConfig)]
+#[modulus = "22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577"]
+#[generator = "13"]
+pub struct FqConfig;
+pub type Fq = Fp832<MontBackend<FqConfig, 13>>;
--- a/cp6_782/src/fields/fq3.rs
+++ b/cp6_782/src/fields/fq3.rs
@@ -1,25 +1,24 @@
-use crate::{fields::FQ_ZERO, Fq};
 use ark_ff::{
-    field_new,
-    fields::fp3::{Fp3, Fp3Parameters},
-    Field,
+    fields::fp3::{Fp3, Fp3Config},
+    Field, MontFp,
 };

-pub type Fq3 = Fp3<Fq3Parameters>;
+use crate::Fq;

-pub struct Fq3Parameters;
+pub type Fq3 = Fp3<Fq3Config>;

-impl Fp3Parameters for Fq3Parameters {
+pub struct Fq3Config;
+
+impl Fp3Config for Fq3Config {
    type Fp = Fq;

    /// NONRESIDUE = 13
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq = field_new!(Fq, "13");
+    const NONRESIDUE: Fq = MontFp!("13");

    const TWO_ADICITY: u32 = 3;

    #[rustfmt::skip]
-    const T_MINUS_ONE_DIV_TWO: &'static [u64] = &[
+    const TRACE_MINUS_ONE_DIV_TWO: &'static [u64] = &[
        0x62730e2cd2029617,
        0x660647f735cb88cf,
        0x274359d60784f69d,
@@ -59,33 +58,31 @@ impl Fp3Parameters for Fq3Parameters {
        0x2b87fda171,
    ];

-    #[rustfmt::skip]
-    const QUADRATIC_NONRESIDUE_TO_T: (Fq, Fq, Fq) = (
-        field_new!(Fq, "5759691735434357221228070840130186543101559976323700017469395641639510585333061695996665166662748527158637897523704071820491869715512532675375604262649010727161924084052120196921150869218319839231115277876207074651754402338718419191428"),
-        FQ_ZERO,
-        FQ_ZERO,
+    const QUADRATIC_NONRESIDUE_TO_T: Fq3 = Fq3::new(
+        MontFp!("5759691735434357221228070840130186543101559976323700017469395641639510585333061695996665166662748527158637897523704071820491869715512532675375604262649010727161924084052120196921150869218319839231115277876207074651754402338718419191428"),
+        Fq::ZERO,
+        Fq::ZERO,
    );

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP3_C1: &'static [Fq] = &[
-        field_new!(Fq, "1"),
-        field_new!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
-        field_new!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        Fq::ONE,
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
    ];

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP3_C2: &'static [Fq] = &[
-        field_new!(Fq, "1"),
-        field_new!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
-        field_new!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        Fq::ONE,
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
    ];

    #[inline(always)]
-    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
+    fn mul_fp_by_nonresidue_in_place(fe: &mut Self::Fp) -> &mut Self::Fp {
        let original = *fe;
-        let mut four_fe = fe.double();
-        four_fe.double_in_place();
-        let eight_fe = four_fe.double();
-        eight_fe + &four_fe + &original
+        fe.double_in_place();
+        *fe += original;
+        fe.double_in_place().double_in_place();
+        *fe += original;
+        fe
    }
 }
--- a/cp6_782/src/fields/fq6.rs
+++ b/cp6_782/src/fields/fq6.rs
@@ -1,27 +1,26 @@
-use crate::{Fq, Fq3, Fq3Parameters, FQ_ONE, FQ_ZERO};
 use ark_ff::{
-    field_new,
-    fields::fp6_2over3::{Fp6, Fp6Parameters},
+    fields::fp6_2over3::{Fp6, Fp6Config},
+    Field, MontFp,
 };

-pub type Fq6 = Fp6<Fq6Parameters>;
+use crate::{Fq, Fq3, Fq3Config};

-pub struct Fq6Parameters;
+pub type Fq6 = Fp6<Fq6Config>;

-impl Fp6Parameters for Fq6Parameters {
-    type Fp3Params = Fq3Parameters;
+pub struct Fq6Config;
+
+impl Fp6Config for Fq6Config {
+    type Fp3Config = Fq3Config;

    /// NONRESIDUE = (0, 1, 0).
-    #[rustfmt::skip]
-    const NONRESIDUE: Fq3 = field_new!(Fq3, FQ_ZERO, FQ_ONE, FQ_ZERO);
+    const NONRESIDUE: Fq3 = Fq3::new(Fq::ZERO, Fq::ONE, Fq::ZERO);

-    #[rustfmt::skip]
    const FROBENIUS_COEFF_FP6_C1: &'static [Fq] = &[
-        field_new!(Fq, "1"),
-        field_new!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756862"),
-        field_new!(Fq, "2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
-        field_new!(Fq, "22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825576"),
-        field_new!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
-        field_new!(Fq, "19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068716"),
+        Fq::ONE,
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756862"),
+        MontFp!("2416169158604010336818399199316106389588878314690767988978701685873498866746813334102117883272276610365242925950967572554030909749205624998805208910209389668659757274773858916683688639755413288353778854399286396639505385648830027756861"),
+        MontFp!("22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825576"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068715"),
+        MontFp!("19953705140271686593528343007184948545186721150606416593204794941773275185711211206130361134875604609812811649452874332003866805473427708373329547516091672819022569300184729084448897691707139947053705234905346679611277243843727293068716"),
    ];
 }
--- a/cp6_782/src/fields/fr.rs
+++ b/cp6_782/src/fields/fr.rs
@@ -1 +1 @@
-pub use ark_bls12_377::{Fq as Fr, FqParameters as FrParameters};
+pub use ark_bls12_377::{Fq as Fr, FqConfig as FrConfig};
--- a/cp6_782/src/fields/mod.rs
+++ b/cp6_782/src/fields/mod.rs
@@ -10,5 +10,5 @@ pub use self::fq3::*;
 pub mod fq6;
 pub use self::fq6::*;

-#[cfg(all(feature = "cp6_782", test))]
+#[cfg(test)]
 mod tests;
--- a/cp6_782/src/fields/tests.rs
+++ b/cp6_782/src/fields/tests.rs
@@ -1,52 +1,7 @@
-use ark_ff::{Field, PrimeField};
-use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use ark_std::rand::Rng;
-use ark_std::test_rng;
-
 use crate::*;
+use ark_algebra_test_templates::*;

-use ark_algebra_test_templates::fields::*;
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    let a: Fr = rng.gen();
-    let b: Fr = rng.gen();
-    field_test(a, b);
-    sqrt_field_test(a);
-    primefield_test::<Fr>();
-}
-
-#[test]
-fn test_fq() {
-    let mut rng = test_rng();
-    let a: Fq = rng.gen();
-    let b: Fq = rng.gen();
-    field_test(a, b);
-    primefield_test::<Fq>();
-    sqrt_field_test(a);
-
-    let byte_size = a.serialized_size();
-    let (_, buffer_size) = buffer_bit_byte_size(Fq::size_in_bits());
-    assert_eq!(byte_size, buffer_size);
-    field_serialization_test::<Fq>(byte_size);
-}
-
-#[test]
-fn test_fq3() {
-    let mut rng = test_rng();
-    let a: Fq3 = rng.gen();
-    let b: Fq3 = rng.gen();
-    field_test(a, b);
-    sqrt_field_test(a);
-    frobenius_test::<Fq3, _>(Fq::characteristic(), 13);
-}
-
-#[test]
-fn test_fq6() {
-    let mut rng = test_rng();
-    let a: Fq6 = rng.gen();
-    let b: Fq6 = rng.gen();
-    field_test(a, b);
-    frobenius_test::<Fq6, _>(Fq::characteristic(), 13);
-}
+test_field!(fr; Fr; mont_prime_field);
+test_field!(fq; Fq; mont_prime_field);
+test_field!(fq3; Fq3);
+test_field!(fq6; Fq6);
--- a/cp6_782/src/lib.rs
+++ b/cp6_782/src/lib.rs
@@ -9,8 +9,9 @@
 #![forbid(unsafe_code)]

 //! This library implements the CP6_782 curve generated in [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
-//! The name denotes that it was generated using the Cocks--Pinch method for the embedding degree 6.
-//! The main feature of this curve is that the scalar field equals the base field of the BLS12_377 curve.
+//! The name denotes that it was generated using the Cocks--Pinch method for the
+//! embedding degree 6. The main feature of this curve is that the scalar field
+//! equals the base field of the BLS12_377 curve.
 //!
 //! Curve information:
 //! * Base field: q = 22369874298875696930346742206501054934775599465297184582183496627646774052458024540232479018147881220178054575403841904557897715222633333372134756426301062487682326574958588001132586331462553235407484089304633076250782629492557320825577
--- a/curve-benches/Cargo.toml
+++ b/curve-benches/Cargo.toml
@@ -1,115 +0,0 @@
-[package]
-name = "ark-curve-benches"
-version = "0.3.0"
-authors = [
-    "Sean Bowe",
-    "Alessandro Chiesa",
-    "Matthew Green",
-    "Ian Miers",
-    "Pratyush Mishra",
-    "Howard Wu",
-    "Daira Hopwood"
-]
-description = "A benchmark library for finite fields and elliptic curves"
-homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
-documentation = "https://docs.rs/algebra/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves", "pairing"]
-categories = ["cryptography"]
-include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
-license = "MIT/Apache-2.0"
-edition = "2018"
-publish = false
-build = "build.rs"
-
-################################# Dependencies ################################
-
-[dependencies]
-bencher = { version = "0.1.5" }
-
-[dev-dependencies]
-ark-std = { version = "^0.3.0", default-features = false }
-ark-ec = { version = "^0.3.0", default-features = false }
-ark-ff = { version = "^0.3.0", default-features = false }
-ark-serialize = { version = "^0.3.0", default-features = false }
-
-ark-mnt4-298 = { path = "../mnt4_298" }
-ark-mnt6-298 = { path = "../mnt6_298" }
-ark-mnt4-753 = { path = "../mnt4_753" }
-ark-mnt6-753 = { path = "../mnt6_753" }
-ark-bn254 = { path = "../bn254" }
-ark-bls12-377 = { path = "../bls12_377" }
-ark-bls12-381 = { path = "../bls12_381" }
-ark-ed-on-bls12-381 = { path = "../ed_on_bls12_381" }
-ark-bw6-761 = { path = "../bw6_761" }
-ark-cp6-782 = { path = "../cp6_782" }
-ark-pallas = { path = "../pallas" }
-ark-vesta = { path = "../vesta" }
-
-[features]
-asm = [ "ark-ff/asm"]
-parallel = [ "ark-ff/parallel",  "ark-ec/parallel", ]
-n_fold = []
-
-[build-dependencies]
-rustc_version = "0.2"
-
-[[bench]]
-name = "bls12_377"
-path = "benches/bls12_377.rs"
-harness = false
-
-[[bench]]
-name = "bls12_381"
-path = "benches/bls12_381.rs"
-harness = false
-
-[[bench]]
-name = "bn254"
-path = "benches/bn254.rs"
-harness = false
-
-[[bench]]
-name = "bw6_761"
-path = "benches/bw6_761.rs"
-harness = false
-
-[[bench]]
-name = "cp6_782"
-path = "benches/cp6_782.rs"
-harness = false
-
-[[bench]]
-name = "ed_on_bls12_381"
-path = "benches/ed_on_bls12_381.rs"
-harness = false
-
-[[bench]]
-name = "mnt4_298"
-path = "benches/mnt4_298.rs"
-harness = false
-
-[[bench]]
-name = "mnt6_298"
-path = "benches/mnt6_298.rs"
-harness = false
-
-[[bench]]
-name = "mnt4_753"
-path = "benches/mnt4_753.rs"
-harness = false
-
-[[bench]]
-name = "mnt6_753"
-path = "benches/mnt6_753.rs"
-harness = false
-
-[[bench]]
-name = "pallas"
-path = "benches/pallas.rs"
-harness = false
-
-[[bench]]
-name = "vesta"
-path = "benches/vesta.rs"
-harness = false
--- a/curve-benches/benches/bls12_377.rs
+++ b/curve-benches/benches/bls12_377.rs
@@ -1,30 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_bls12_377::{
-    fq::Fq, fq2::Fq2, fr::Fr, Bls12_377, Fq12, G1Affine, G1Projective as G1, G2Affine,
-    G2Projective as G2,
-};
-use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::{BigInteger256 as FrRepr, BigInteger384 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-
-mod g1 {
-    use super::*;
-    ec_bench!(G1, G1Affine);
-}
-mod g2 {
-    use super::*;
-    ec_bench!(G2, G2Affine);
-}
-
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FrRepr, FrRepr, fr);
-f_bench!(extension, Fq2, Fq2, fq2);
-f_bench!(target, Fq12, Fq12, fq12);
-
-pairing_bench!(Bls12_377, Fq12);
-
-bencher::benchmark_main!(fq, fr, fq2, fq12, g1::group_ops, g2::group_ops, pairing);
--- a/curve-benches/benches/bls12_381.rs
+++ b/curve-benches/benches/bls12_381.rs
@@ -1,30 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_bls12_381::{
-    fq::Fq, fq2::Fq2, fr::Fr, Bls12_381, Fq12, G1Affine, G1Projective as G1, G2Affine,
-    G2Projective as G2,
-};
-use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::{BigInteger256 as FrRepr, BigInteger384 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-
-mod g1 {
-    use super::*;
-    ec_bench!(G1, G1Affine);
-}
-mod g2 {
-    use super::*;
-    ec_bench!(G2, G2Affine);
-}
-
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FrRepr, FrRepr, fr);
-f_bench!(extension, Fq2, Fq2, fq2);
-f_bench!(target, Fq12, Fq12, fq12);
-
-pairing_bench!(Bls12_381, Fq12);
-
-bencher::benchmark_main!(fq, fr, fq2, fq12, g1::group_ops, g2::group_ops, pairing);
--- a/curve-benches/benches/bn254.rs
+++ b/curve-benches/benches/bn254.rs
@@ -1,30 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_bn254::{
-    fq::Fq, fq2::Fq2, fr::Fr, Bn254, Fq12, G1Affine, G1Projective as G1, G2Affine,
-    G2Projective as G2,
-};
-use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::{BigInteger256 as FrRepr, BigInteger256 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-
-mod g1 {
-    use super::*;
-    ec_bench!(G1, G1Affine);
-}
-mod g2 {
-    use super::*;
-    ec_bench!(G2, G2Affine);
-}
-
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FrRepr, FrRepr, fr);
-f_bench!(extension, Fq2, Fq2, fq2);
-f_bench!(target, Fq12, Fq12, fq12);
-
-pairing_bench!(Bn254, Fq12);
-
-bencher::benchmark_main!(fq, fr, fq2, fq12, g1::group_ops, g2::group_ops, pairing);
--- a/curve-benches/benches/bw6_761.rs
+++ b/curve-benches/benches/bw6_761.rs
@@ -1,29 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_bw6_761::{
-    fq::Fq, fq3::Fq3, fr::Fr, Fq6, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
-    BW6_761,
-};
-use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::{BigInteger384 as FrRepr, BigInteger768 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-
-mod g1 {
-    use super::*;
-    ec_bench!(G1, G1Affine);
-}
-mod g2 {
-    use super::*;
-    ec_bench!(G2, G2Affine);
-}
-
-f_bench!(extension, Fq3, Fq3, fq3);
-f_bench!(target, Fq6, Fq6, fq6);
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FrRepr, FrRepr, fr);
-pairing_bench!(BW6_761, Fq6);
-
-bencher::benchmark_main!(fq, fr, fq3, fq6, g1::group_ops, g2::group_ops, pairing);
--- a/curve-benches/benches/cp6_782.rs
+++ b/curve-benches/benches/cp6_782.rs
@@ -1,29 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_cp6_782::{
-    fq::Fq, fq3::Fq3, fr::Fr, Fq6, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
-    CP6_782,
-};
-use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::{BigInteger384 as FrRepr, BigInteger832 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-
-mod g1 {
-    use super::*;
-    ec_bench!(G1, G1Affine);
-}
-mod g2 {
-    use super::*;
-    ec_bench!(G2, G2Affine);
-}
-
-f_bench!(extension, Fq3, Fq3, fq3);
-f_bench!(target, Fq6, Fq6, fq6);
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FrRepr, FrRepr, fr);
-pairing_bench!(CP6_782, Fq6);
-
-bencher::benchmark_main!(fq, fr, fq3, fq6, g1::group_ops, g2::group_ops, pairing);
--- a/curve-benches/benches/ed_on_bls12_381.rs
+++ b/curve-benches/benches/ed_on_bls12_381.rs
@@ -1,19 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_ec::ProjectiveCurve;
-use ark_ed_on_bls12_381::{fq::Fq, fr::Fr, EdwardsAffine as GAffine, EdwardsProjective as G};
-use ark_ff::{
-    biginteger::{BigInteger256 as FrRepr, BigInteger256 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-
-mod g {
-    use super::*;
-    ec_bench!(G, GAffine);
-}
-
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FrRepr, FrRepr, fr);
-
-bencher::benchmark_main!(fq, fr, g::group_ops);
--- a/curve-benches/benches/mnt4_298.rs
+++ b/curve-benches/benches/mnt4_298.rs
@@ -1,29 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_ec::{PairingEngine, ProjectiveCurve};
-use ark_ff::{
-    biginteger::BigInteger320 as FqRepr, BigInteger, Field, PrimeField, SquareRootField,
-    UniformRand,
-};
-use ark_mnt4_298::{
-    fq::Fq, fq2::Fq2, fr::Fr, Fq4, G1Affine, G1Projective as G1, G2Affine, G2Projective as G2,
-    MNT4_298,
-};
-
-mod g1 {
-    use super::*;
-    ec_bench!(G1, G1Affine);
-}
-mod g2 {
-    use super::*;
-    ec_bench!(G2, G2Affine);
-}
-
-f_bench!(extension, Fq2, Fq2, fq2);
-f_bench!(target, Fq4, Fq4, fq4);
-f_bench!(Fq, Fq, FqRepr, FqRepr, fq);
-f_bench!(Fr, Fr, FqRepr, FqRepr, fr);
-pairing_bench!(MNT4_298, Fq4);
-
-bencher::benchmark_main!(fq, fr, fq2, fq4, g1::group_ops, g2::group_ops, pairing);
--- a/Show More
+++ b/Show More
Author	SHA1	Message	Date
Marcin	1e951b3fc4	missed two dependencies	2022-11-19 13:36:02 +01:00
Marcin	9bbf909175	bump relations & r1cs-std dependency after their alpha version is out	2022-11-19 13:28:57 +01:00
Marcin	15c0777ae2	Version 0.4.0-alpha	2022-11-12 20:14:24 +01:00
Weikeng Chen	99831650f8	Prepared G2 consistency test (#70 ) * add the g2 check * fmt * fix * fix * fix * fix * changelog * test macos for curve tests * use macos only for mnt6-753 * fix * fix name consistency * adjust the order * mnt4 753 * fix Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu> Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-10-31 17:12:52 -07:00
Weikeng Chen	db03d405b5	Add the curve25519 curve (#124 ) * add ed25519 curve * changelog * curve info * fix * edit * update * add more explanation * Update curve25519/src/curves/mod.rs * Update curve25519/src/curves/mod.rs * fixed the comment * Update curve25519/src/curves/mod.rs Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-10-29 19:55:35 -07:00
Weikeng Chen	a7d266f73d	Add the ed25519 curve (#121 ) * add ed25519 curve * changelog * curve info * fix * cleanup the script * Update ed25519/src/curves/mod.rs * Update ed25519/src/curves/mod.rs Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-10-29 19:33:55 -07:00
Weikeng Chen	5d6d31d213	Fix the location of BitIteratorBE (#132 ) * fix * fix Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-10-29 11:29:45 -07:00
mmagician	df39c78a5b	Update changelog (#131 )	2022-10-19 10:06:42 -07:00
mmagician	138b23f2fa	Zcash-style serialization for BLS12-381 (#129 ) Co-authored-by: kevaundray <37423678+kevaundray@users.noreply.github.com> Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2022-10-18 22:44:43 -07:00
mmagician	4bcf87de22	Faster cofactor clearing for G1 & G2 of bls12-381 + benchmarking (#103 )	2022-10-16 10:13:57 -07:00
Pratyush Mishra	efefa209d6	Fix mul-by-non-residue for bw6::fq3	2022-10-02 09:15:25 -07:00
Pratyush Mishra	1833cbfb29	Tweaks	2022-10-02 09:15:25 -07:00
Pratyush Mishra	f43d59c958	Rename	2022-10-02 09:15:25 -07:00
Pratyush Mishra	68f500da01	Optimizations to field and curve arithmetic	2022-10-02 09:15:25 -07:00
Pratyush Mishra	363426c1d4	Update to new benchmarking framework (#126 )	2022-09-09 19:24:33 -07:00
Pratyush Mishra	55a092a6c7	`is_identity` -> `is_zero` (#125 )	2022-09-09 11:07:42 -07:00
Weikeng Chen	f74378c017	Add serialization for CP6-782 (#120 ) Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-09-03 22:55:16 -07:00
Weikeng Chen	3af6ec17d6	Fix Bandersnatch parameters and the constraint tests (#119 ) Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-09-03 12:32:28 -07:00
Weikeng Chen	dc555882cd	Fix the remaining curve and field tests (#118 ) * push * push * cargo ready Co-authored-by: onewayfunc <onewayfunc@gmail.com>	2022-09-03 00:34:13 -07:00
Weikeng Chen	3c4c67f114	Sync with the recent changes in ark-algebra on pairing and testing (#116 ) * Fix another typo in the Jubjub curve comment * fix * progress * get_point_from_x_unchecked * fix * soft link * Fix Bandersnatch * Fix Edwards form of Bandersnatch * Actually fix ed_on_bls12_381_bandersnatch/src/curves/mod.rs * fix * fix * curve-benches * fix the last mul_by_a; fmt Co-authored-by: onewayfunc <onewayfunc@gmail.com> Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2022-09-02 16:31:58 -07:00
mmagician	42289245a6	Replace `ATE_LOOP_COUNT` with its 2-NAF for MNT curves (#107 ) * Replace ATE_LOOP_COUNT by its 2-NAF * Add constant references * Apply suggestions from code review Co-authored-by: Weikeng Chen <w.k@berkeley.edu>	2022-09-02 08:19:51 -07:00
Weikeng Chen	b433045f4d	Fix a typo in the Jubjub curve comment (#114 )	2022-08-27 14:17:37 -07:00
Weikeng Chen	52577f93ba	Last PR to get the curve tests to work (#113 )	2022-08-21 21:08:38 -07:00
Weikeng Chen	6d94362894	Let `ark-curve-constraint-tests` work with latest arkworks-rs algebra (#112 )	2022-08-21 19:58:41 -07:00
Weikeng Chen	435de9fc36	Let `cargo build` work again for the new arkworks-rs algebra (#111 )	2022-08-21 18:22:43 -07:00
Pratyush Mishra	e75546313a	Fix benchmarks and fix accidental renaming of Pallas/Vesta (#108 )	2022-08-01 13:46:52 -07:00
kevaundray	67d5a8582e	Document Bandersnatch as an incomplete twisted Edwards curve (#85 )	2022-08-01 10:32:08 -07:00
Marcin	93e64df895	Catch up with algebra (#106 ) Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2022-07-29 12:16:16 -07:00
Marcin	76579d0fbb	`QUADRATIC_NONRESIDUE` is never used, remove (#104 ) * `QUADRATIC_NONRESIDUE` is never used, remove * Update CHANGELOG.md * Remove unused imports	2022-06-30 11:00:01 -07:00
Marcin	9a89ea8adc	Pull ark-std from latest master (#100 )	2022-04-11 15:17:18 -07:00
Pratyush Mishra	5a1e16e2b7	Fix benchmark imports (#99 )	2022-03-07 21:01:29 -08:00
Pratyush Mishra	1551d6d76c	Upgrade to work with latest `ark-ff` (#95 ) Co-authored-by: Sun <huachuang20@gmail.com>	2022-03-07 13:12:03 -08:00
Marcin	d0dc200f22	Sqrt fq2 bls12 381 regression (#89 ) Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2022-01-11 09:28:17 -08:00
Marcin	6a5cf1d84a	`BigInt` fixes corresponding to algebra#372 Co-authored-by: Pratyush Mishra <pratyushmishra@berkeley.edu>	2022-01-10 11:03:40 -08:00
Pratyush Mishra	d1ced15cc2	Upgrade for algebra/365 (#92 ) * Upgrade for algebra/365 * Merge fix * Fix	2021-12-29 17:07:52 +01:00
Yuncong Hu	677b4ae751	Simplify the field and curve tests using macros (#90 ) * Simplify the field and curve tests using macros * minor * remove redundant code Co-authored-by: weikeng <w.k@berkeley.edu>	2021-12-06 00:03:29 -08:00
Michael Rosenberg	c5547905d0	Fixed curve-bench compile error (#83 ) * Fixed benchmarking compile error * Updated CHANGELOG * patch `algebra-test-templates` due to breaking changes since the last release Co-authored-by: Marcin Górny <marcin.gorny.94@protonmail.com>	2021-12-05 17:48:33 +01:00
Popog	f1e36c5bed	Documentation provides incorrect calculation (#81 )	2021-11-15 10:55:32 -08:00
Weikeng Chen	3a0f858adb	Revise the version number of Bandersnatch (#80 )	2021-11-10 22:20:01 -08:00