Merge branch 'master' into fq2_neg_nonresidue

new add + mul by residue + 1
Add optimization for bls12_381 and bn254
2026-01-27 22:23:48 +01:00 · 2021-02-06 00:39:52 -06:00 · 2021-02-05 20:13:02 -06:00 · 2021-02-05 12:48:57 -06:00 · 2021-02-05 11:53:30 -06:00
89 changed files with 621 additions and 1552 deletions
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -29,8 +29,8 @@ jobs:
        command: fmt
        args: --all -- --check

-  check:
-    name: Check
+  test:
+    name: Test
    runs-on: ubuntu-latest
    env:
      RUSTFLAGS: -Dwarnings
@@ -78,60 +78,13 @@ jobs:
            args: --all-features --examples --workspace --benches
        if: matrix.rust == 'nightly'

-      
-
-  directories: # Job that list subdirectories
-    name: List directories for parallelizing tests
-    runs-on: ubuntu-latest
-    outputs:
-      dir: ${{ steps.set-dirs.outputs.dir }} # generate output name dir by using inner step output
-    steps:
-      - uses: actions/checkout@v2
-      - id: set-dirs # Give it an id to handle to get step outputs in the outputs key above
-        run: echo "::set-output name=dir::$(ls -d */ | jq -R -s -c 'split("\n")[:-1]')"
-        # Define step output named dir base on ls command transformed to JSON thanks to jq
-  test:
-    name: Test
-    runs-on: ubuntu-latest
-    needs: [directories] # Depends on previous job
-    strategy:
-      matrix:
-        dir: ${{fromJson(needs.directories.outputs.dir)}} # List matrix strategy from directories dynamically
-        # rust:
-        #   - stable
-        #   - nightly
-        exclude:
-          - dir: scripts/
-          - dir: curve-constraint-tests/
-          - dir: curve-benches/
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v2
-      - name: Run tests
-        run: |
-          cd ${{matrix.dir}}
-          cargo test --all-features
-
-  docs:
-    name: Check Documentation
-    runs-on: ubuntu-latest
-    steps:
-
-    - name: Checkout
-      uses: actions/checkout@v1
-    - name: Install Rust
-      uses: actions-rs/toolchain@v1
-      with:
-        profile: minimal
-        toolchain: stable
-        override: true
-        components: rustfmt
-
-    - name: cargo doc --all --no-deps --document-private-items --all-features
-      uses: actions-rs/cargo@v1
-      with:
-        command: doc
-        args: --all --no-deps --document-private-items --all-features
+      - name: Test
+        uses: actions-rs/cargo@v1
+        with:
+            command: test
+            args: "--workspace \
+                   --all-features \
+                   --exclude curve-benches"

  check_no_std:
    name: Check no_std
--- a/.github/workflows/linkify_changelog.yml
+++ b/.github/workflows/linkify_changelog.yml
@@ -1,20 +0,0 @@
-name: Linkify Changelog
-
-on:
-  workflow_dispatch
-
-jobs:
-  linkify:
-    runs-on: ubuntu-latest
-    steps:
-    - name: Checkout
-      uses: actions/checkout@v2
-    - name: Add links
-      run: python3 scripts/linkify_changelog.py CHANGELOG.md
-    - name: Commit
-      run: |
-          git config user.name github-actions
-          git config user.email github-actions@github.com
-          git add .
-          git commit -m "Linkify Changelog"
-          git push
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,39 +1,10 @@
-# CHANGELOG
-
 ## Pending

 ### Breaking changes
-
-### Features
-
-### Improvements
-
-### Bug fixes
-
-## v0.3.0 
-
-### Breaking changes
-
- [\#60](https://github.com/arkworks-rs/curves/pull/60) Change the scalar group generator of `Fr` of `bls12_377` Fr from `11` to `22`.
- [\#61](https://github.com/arkworks-rs/curves/pull/61) Remove `ATE_LOOP_COUNT_IS_NEGATIVE` from BN254 curve parameter.
-
-### Features
-
- [\#64](https://github.com/arkworks-rs/curves/pull/64) Implement the Bandersnatch curve, another twisted Edwards curve for BLS12-381.
-
-### Improvements
-
-### Bug fixes
-
-## v0.2.0
-
-### Breaking changes
-
 - Requires all crates from `arkworks-rs/algebra` to have version `v0.2.0` or greater.

 ### Features
-
- [\#3](https://github.com/arkworks-rs/curves/pull/3) Add constraints for
+- #3 Add constraints for 
        `ark-bls12-377`,
        `ark-ed-on-bls12-377`,
        `ark-ed-on-bls12-381`,
@@ -46,19 +17,15 @@
        `ark-mnt6-298`,
        `ark-mnt4-753`,
        `ark-mnt6-753`.
- [\#7](https://github.com/arkworks-rs/curves/pull/7) Add benchmarks for Edwards curves.
- [\#19](https://github.com/arkworks-rs/curves/pull/19) Change field constants to be provided as normal strings, instead of in Montgomery form.
- [\#53](https://github.com/arkworks-rs/curves/pull/53) Add benchmarks for Pallas and Vesta curves.
+- #7 Add benchmarks for Edwards curves.
+- #19 Change field constants to be provided as normal strings, instead of in montgomery form.

 ### Improvements
-
- [\#42](https://github.com/arkworks-rs/curves/pull/42) Remove the dependency of `rand_xorshift`.
+- #42 Remove the dependency of `rand_xorshift`.

 ### Bug fixes
-
- [\#28](https://github.com/arkworks-rs/curves/pull/28), [\#49](https://github.com/arkworks-rs/curves/pull/49) Fix broken documentation links.
- [\#38](https://github.com/arkworks-rs/curves/pull/38) Compile with `panic='abort'` in release mode, for safety of the library across FFI boundaries.
- [\#45](https://github.com/arkworks-rs/curves/pull/45) Fix `ark-ed-on-mnt4-753`.
+- #28 Fix broken documentation links.
+- #38 Compile with `panic='abort'` in release mode, for safety of the library across FFI boundaries.

 ## v0.1.0

--- a/Cargo.toml
+++ b/Cargo.toml
@@ -15,7 +15,6 @@ members = [

    "bls12_381",
    "ed_on_bls12_381",
-    "ed_on_bls12_381_bandersnatch",

    "bn254",
    "ed_on_bn254",
@@ -26,7 +25,7 @@ members = [

    "mnt4_753",
    "mnt6_753",
-    "ed_on_mnt4_753",
+    "ed_on_mnt4_298",

    "pallas",
    "vesta",
@@ -56,6 +55,3 @@ lto = "thin"
 incremental = true
 debug-assertions = true
 debug = true
-
-[patch.crates-io]
-ark-r1cs-std = { git = "https://github.com/arkworks-rs/r1cs-std", branch = "reduce-generics", optional = true, default-features = false }
--- a/README.md
+++ b/README.md
@@ -5,7 +5,6 @@ This repository contains implementations of some popular elliptic curves. The cu
 ### BLS12-381 and embedded curves
 * [`ark-bls12-381`](bls12_381): Implements the BLS12-381 pairing-friendly curve
 * [`ark-ed-on-bls12-381`](ed_on_bls12_381): Implements a Twisted Edwards curve atop the scalar field of BLS12-381
-* [`ark-ed-on-bls12-381-bandersnatch`](ed_on_bls12_381_bandersnatch): Implements Bandersnatch, another Twisted Edwards curve atop the scalar field of BLS12-381

 ### BLS12-377 and related curves
 * [`ark-bls12-377`](bls12_377): Implements the BLS12-377 pairing-friendly curve
--- a/bls12_377/Cargo.toml
+++ b/bls12_377/Cargo.toml
@@ -1,27 +1,27 @@
 [package]
 name = "ark-bls12-377"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The BLS12-377 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-bls12-377/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-std = { git = "https://github.com/arkworks-rs/utils", 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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
@@ -31,4 +31,4 @@ std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
 curve = [ "scalar_field", "base_field" ]
 scalar_field = []
 base_field = []
-r1cs = [ "base_field", "ark-r1cs-std" ]
+r1cs = [ "base_field", "ark-r1cs-std" ]
--- a/bls12_377/src/constraints/curves.rs
+++ b/bls12_377/src/constraints/curves.rs
@@ -16,8 +16,14 @@ pub type G2PreparedVar = bls12::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
    use ark_ec::models::bls12::Bls12Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as Bls12Parameters>::G1Parameters>()
-        .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as Bls12Parameters>::G2Parameters>()
-        .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as Bls12Parameters>::G1Parameters,
+        G1Var,
+    >()
+    .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as Bls12Parameters>::G2Parameters,
+        G2Var,
+    >()
+    .unwrap();
 }
--- a/bls12_377/src/constraints/mod.rs
+++ b/bls12_377/src/constraints/mod.rs
@@ -130,17 +130,17 @@
 //! let pairing_result_native = Bls12_377::pairing(a_native, b_native);
 //!
 //! // Prepare `a` and `b` for pairing.
-//! let a_prep = Bls12_377::prepare_g1(&a)?;
-//! let b_prep = Bls12_377::prepare_g2(&b)?;
-//! let pairing_result = Bls12_377::pairing_gadget(a_prep, b_prep)?;
+//! let a_prep = constraints::PairingVar::prepare_g1(&a)?;
+//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! 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);
 //!
 //! // Check that operations on variables and constants are equivalent.
-//! let a_prep_const = Bls12_377::prepare_g1(&a_const)?;
-//! let b_prep_const = Bls12_377::prepare_g2(&b_const)?;
-//! let pairing_result_const = Bls12_377::pairing_gadget(a_prep_const, b_prep_const)?;
+//! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;
--- a/bls12_377/src/constraints/pairing.rs
+++ b/bls12_377/src/constraints/pairing.rs
@@ -1,8 +1,10 @@
+use crate::Parameters;
+
 /// Specifies the constraints for computing a pairing in the BLS12-377 bilinear group.
-pub use crate::Bls12_377;
+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>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<Bls12_377, PairingVar>().unwrap()
 }
--- a/bls12_377/src/fields/fq2.rs
+++ b/bls12_377/src/fields/fq2.rs
@@ -25,6 +25,7 @@ impl Fp2Parameters for Fq2Parameters {
        field_new!(Fq, "-1"),
    ];

+    // Mul by -5
    #[inline(always)]
    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
        let original = fe;
@@ -32,6 +33,35 @@ impl Fp2Parameters for Fq2Parameters {
        fe.double_in_place();
        fe - original
    }
+
+    // x + -5 * y, computed as x - 5*y
+    #[inline(always)]
+    fn add_and_mul_fp_by_nonresidue(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        // c becomes 5 * y
+        let mut c = y.double();
+        c.double_in_place();
+        c += y;
+        *x - c
+    }
+
+    // x + y + (-5 * y), computed as x - 4*y
+    #[inline(always)]
+    fn add_and_mul_fp_by_nonresidue_plus_one(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        // c becomes 4 * y
+        let mut c = y.double();
+        c.double_in_place();
+        *x - c
+    }
+
+    // x - (-5 * y), computed as x + 5*y
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        // c becomes 5 * y
+        let mut c = y.double();
+        c.double_in_place();
+        c += y;
+        *x + c
+    }
 }

 pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
--- a/bls12_377/src/fields/fr.rs
+++ b/bls12_377/src/fields/fr.rs
@@ -1,24 +1,3 @@
-///! Bls12-377 scalar field.
-///
-/// Roots of unity computed from modulus and R using this sage code:
-///
-/// ```ignore
-/// q = 8444461749428370424248824938781546531375899335154063827935233455917409239041
-/// R = 6014086494747379908336260804527802945383293308637734276299549080986809532403 # Montgomery R
-/// s = 47
-/// o = q - 1
-/// F = GF(q)
-/// g = F.multiplicative_generator()
-/// g = F.multiplicative_generator()
-/// assert g.multiplicative_order() == o
-/// g2 = g ** (o/2**s)
-/// assert g2.multiplicative_order() == 2**s
-/// def into_chunks(val, width, n):
-///     return [int(int(val) // (2 ** (width * i)) % 2 ** width) for i in range(n)]
-/// print("Gen: ", g * R % q)
-/// 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::*};

 pub type Fr = Fp256<FrParameters>;
@@ -33,10 +12,10 @@ impl FftParameters for FrParameters {

    #[rustfmt::skip]
    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        12646347781564978760u64,
-        6783048705277173164u64,
-        268534165941069093u64,
-        1121515446318641358u64,
+        0x3c3d3ca739381fb2,
+        0x9a14cda3ec99772b,
+        0xd7aacc7c59724826,
+        0xd1ba211c5cc349c,
    ]);
 }
 impl FpParameters for FrParameters {
@@ -74,15 +53,15 @@ impl FpParameters for FrParameters {

    const INV: u64 = 725501752471715839u64;

-    /// GENERATOR = 22
+    /// GENERATOR = 11
    /// Encoded in Montgomery form, so the value is
-    /// (22 * R) % q = 5642976643016801619665363617888466827793962762719196659561577942948671127251
+    /// (11 * R) % q = 7043719196222586021957094278335006679584931048936630243748405699433040183146
    #[rustfmt::skip]
    const GENERATOR: BigInteger = BigInteger([
-        2984901390528151251u64,
-        10561528701063790279u64,
-        5476750214495080041u64,
-        898978044469942640u64,
+        1855201571499933546u64,
+        8511318076631809892u64,
+        6222514765367795509u64,
+        1122129207579058019u64,
    ]);

    /// (r - 1)/2 =
--- a/bls12_377/src/lib.rs
+++ b/bls12_377/src/lib.rs
@@ -8,7 +8,7 @@
 )]
 #![forbid(unsafe_code)]

-//! This library implements the BLS12_377 curve generated in [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
+//! 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.
--- a/bls12_381/Cargo.toml
+++ b/bls12_381/Cargo.toml
@@ -1,25 +1,25 @@
 [package]
 name = "ark-bls12-381"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The BLS12-381 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-bls12-381/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", 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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }

 [features]
 default = [ "curve" ]
--- a/bls12_381/src/fields/fq2.rs
+++ b/bls12_381/src/fields/fq2.rs
@@ -29,6 +29,18 @@ impl Fp2Parameters for Fq2Parameters {
    fn mul_fp_by_nonresidue(fp: &Self::Fp) -> Self::Fp {
        -(*fp)
    }
+
+    // x + -1 * y, computed as x - y
+    #[inline(always)]
+    fn add_and_mul_fp_by_nonresidue(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        *x - y
+    }
+
+    // x - (-1 * y), computed as x + y
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        *x + y
+    }
 }

 pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
--- a/bn254/Cargo.toml
+++ b/bn254/Cargo.toml
@@ -1,25 +1,25 @@
 [package]
 name = "ark-bn254"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The BN254 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-bn254/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", 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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }

 [features]
 default = [ "curve" ]
--- a/bn254/src/curves/mod.rs
+++ b/bn254/src/curves/mod.rs
@@ -21,6 +21,8 @@ impl BnParameters for Parameters {
        0, 1, 1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 1, 0,
        -1, 0, 0, 1, 0, 1, 1,
    ];
+    /// `ate_loop_count` is positive.
+    const ATE_LOOP_COUNT_IS_NEGATIVE: bool = false;

    const TWIST_MUL_BY_Q_X: Fq2 = field_new!(
        Fq2,
--- a/bn254/src/fields/fq.rs
+++ b/bn254/src/fields/fq.rs
@@ -19,7 +19,7 @@ impl FftParameters for FqParameters {
    ]);
 }
 impl FpParameters for FqParameters {
-    /// MODULUS = 21888242871839275222246405745257275088696311157297823662689037894645226208583
+    /// MODULUS = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
    #[rustfmt::skip]
    const MODULUS: BigInteger = BigInteger([
        0x3c208c16d87cfd47,
@@ -82,7 +82,7 @@ impl FpParameters for FqParameters {
    ]);

    // (T - 1) // 2 =
-    // 5472060717959818805561601436314318772174077789324455915672259473661306552145
+    // 1837921289030710838195067919506396475074392872918698035817074744121558668640693829665401097909504529
    #[rustfmt::skip]
    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
        0x4f082305b61f3f51,
--- a/bn254/src/fields/fq2.rs
+++ b/bn254/src/fields/fq2.rs
@@ -32,6 +32,18 @@ impl Fp2Parameters for Fq2Parameters {
    fn mul_fp_by_nonresidue(fe: &Self::Fp) -> Self::Fp {
        -(*fe)
    }
+
+    // x + -1 * y, computed as x - y
+    #[inline(always)]
+    fn add_and_mul_fp_by_nonresidue(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        *x - y
+    }
+
+    // x - (-1 * y), computed as x + y
+    #[inline(always)]
+    fn sub_and_mul_fp_by_nonresidue(x: &Self::Fp, y: &Self::Fp) -> Self::Fp {
+        *x + y
+    }
 }

 pub const FQ2_ZERO: Fq2 = field_new!(Fq2, FQ_ZERO, FQ_ZERO);
--- a/bn254/src/fields/fr.rs
+++ b/bn254/src/fields/fr.rs
@@ -34,8 +34,6 @@ impl FpParameters for FrParameters {

    const REPR_SHAVE_BITS: u32 = 2;

-    /// R = pow(2, 320) % MODULUS
-    ///   = 6350874878119819312338956282401532410528162663560392320966563075034087161851
    #[rustfmt::skip]
    const R: BigInteger = BigInteger([
        12436184717236109307u64,
@@ -44,8 +42,6 @@ impl FpParameters for FrParameters {
        1011752739694698287u64,
    ]);

-    /// R2 = R * R % MODULUS
-    ///    = 944936681149208446651664254269745548490766851729442924617792859073125903783
    #[rustfmt::skip]
    const R2: BigInteger = BigInteger([
        1997599621687373223u64,
@@ -54,10 +50,9 @@ impl FpParameters for FrParameters {
        150537098327114917u64,
    ]);

-    /// INV = (-MODULUS) ^ {-1} % pow(2, 64) = 14042775128853446655
    const INV: u64 = 14042775128853446655u64;

-    /// GENERATOR = 5
+    // GENERATOR = 5
    #[rustfmt::skip]
    const GENERATOR: BigInteger = BigInteger([
        1949230679015292902u64,
@@ -66,7 +61,7 @@ impl FpParameters for FrParameters {
        1571765431670520771u64,
    ]);

-    /// (MODULUS - 1)/2 =
+    /// (r - 1)/2 =
    /// 10944121435919637611123202872628637544274182200208017171849102093287904247808
    #[rustfmt::skip]
    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
@@ -78,7 +73,7 @@ impl FpParameters for FrParameters {

    // T and T_MINUS_ONE_DIV_TWO, where r - 1 = 2^s * t

-    /// T = (MODULUS - 1) / 2^s =
+    /// t = (r - 1) / 2^s =
    /// 81540058820840996586704275553141814055101440848469862132140264610111
    #[rustfmt::skip]
    const T: BigInteger = BigInteger([
@@ -88,7 +83,7 @@ impl FpParameters for FrParameters {
        0x30644e72e,
    ]);

-    /// (T - 1) / 2 =
+    /// (t - 1) / 2 =
    /// 40770029410420498293352137776570907027550720424234931066070132305055
    #[rustfmt::skip]
    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
--- a/bn254/src/lib.rs
+++ b/bn254/src/lib.rs
@@ -8,7 +8,7 @@
 )]
 #![forbid(unsafe_code)]

-//! This library implements the BN254 curve that was sampled as part of the [\[BCTV14\]](https://eprint.iacr.org/2013/879.pdf) paper .
+//! This library implements the BN254 curve that was sampled as part of the [[BCTV14]][https://eprint.iacr.org/2013/879.pdf] paper .
 //! The name denotes that it is a Barreto--Naehrig curve of embedding degree 12,
 //! defined over a 254-bit (prime) field. The scalar field is highly 2-adic.
 //!
@@ -26,7 +26,7 @@
 //! * 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)
+//!    * B = 3/(u+9) where Fq2[u]=Fq/u+1
 //!        = Fq2(19485874751759354771024239261021720505790618469301721065564631296452457478373, 266929791119991161246907387137283842545076965332900288569378510910307636690)

 #[cfg(feature = "curve")]
--- a/bw6_761/Cargo.toml
+++ b/bw6_761/Cargo.toml
@@ -1,26 +1,26 @@
 [package]
 name = "ark-bw6-761"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The BW6-761 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-bw6-761/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-bls12-377 = { 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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }

 [features]
 default = []
--- a/bw6_761/src/fields/fq3.rs
+++ b/bw6_761/src/fields/fq3.rs
@@ -16,7 +16,7 @@ impl Fp3Parameters for Fq3Parameters {
    type Fp = Fq;

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

--- a/bw6_761/src/lib.rs
+++ b/bw6_761/src/lib.rs
@@ -8,7 +8,7 @@
 )]
 #![forbid(unsafe_code)]

-//! This library implements the BW6_761 curve generated in [\[EG20\]](https://eprint.iacr.org/2020/351).
+//! 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.
--- a/cp6_782/Cargo.toml
+++ b/cp6_782/Cargo.toml
@@ -1,26 +1,28 @@
 [package]
 name = "ark-cp6-782"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The CP6-782 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-cp6-782/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-bls12-377 = { 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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+rand = { version = "0.7", default-features = false }
+rand_xorshift = "0.2"

 [features]
 default = []
--- a/cp6_782/src/lib.rs
+++ b/cp6_782/src/lib.rs
@@ -8,7 +8,7 @@
 )]
 #![forbid(unsafe_code)]

-//! This library implements the CP6_782 curve generated in [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
+//! 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.
 //!
--- a/curve-benches/Cargo.toml
+++ b/curve-benches/Cargo.toml
@@ -1,20 +1,19 @@
 [package]
 name = "ark-curve-benches"
-version = "0.3.0"
+version = "0.1.1-alpha.0"
 authors = [
    "Sean Bowe",
    "Alessandro Chiesa",
    "Matthew Green",
    "Ian Miers",
    "Pratyush Mishra",
-    "Howard Wu",
-    "Daira Hopwood"
+    "Howard Wu"
 ]
 description = "A benchmark library for finite fields and elliptic curves"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/algebra/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves", "pairing"]
+keywords = ["cryptography", "finite fields", "elliptic curves", "pairing"]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
@@ -28,10 +27,10 @@ build = "build.rs"
 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-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }

 ark-mnt4-298 = { path = "../mnt4_298" }
 ark-mnt6-298 = { path = "../mnt6_298" }
@@ -43,8 +42,6 @@ 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"]
@@ -103,13 +100,3 @@ harness = false
 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/pallas.rs
+++ b/curve-benches/benches/pallas.rs
@@ -1,19 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_ec::ProjectiveCurve;
-use ark_ff::{
-    biginteger::{BigInteger256 as FrRepr, BigInteger256 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-use ark_pallas::{fq::Fq, fr::Fr, Affine as GAffine, Projective as G};
-
-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/vesta.rs
+++ b/curve-benches/benches/vesta.rs
@@ -1,19 +0,0 @@
-use ark_curve_benches::*;
-use ark_std::ops::{AddAssign, MulAssign, SubAssign};
-
-use ark_ec::ProjectiveCurve;
-use ark_ff::{
-    biginteger::{BigInteger256 as FrRepr, BigInteger256 as FqRepr},
-    BigInteger, Field, PrimeField, SquareRootField, UniformRand,
-};
-use ark_vesta::{fq::Fq, fr::Fr, Affine as GAffine, Projective as G};
-
-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-constraint-tests/Cargo.toml
+++ b/curve-constraint-tests/Cargo.toml
@@ -1,24 +1,24 @@
 [package]
 name = "ark-curve-constraint-tests"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A library for testing constraints for finite fields, elliptic curves, and pairings"
 homepage = "https://arkworks.rs"
 repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-curve-constraint-tests/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves", "r1cs" ]
+keywords = ["cryptography", "finite fields", "elliptic curves", "r1cs" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [dependencies]
-ark-std = { version = "^0.3.0", default-features = false }
-ark-serialize = { version = "^0.3.0", default-features = false }
-ark-ff = { version = "^0.3.0", default-features = false }
-ark-relations = { version = "^0.3.0", default-features = false }
-ark-r1cs-std = { version = "^0.3.0", default-features = false }
-ark-ec = { version = "^0.3.0", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-relations = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }

 [features]
 default = []
--- a/curve-constraint-tests/src/lib.rs
+++ b/curve-constraint-tests/src/lib.rs
@@ -233,8 +233,7 @@ pub mod fields {
 pub mod curves {
    use ark_ec::{
        short_weierstrass_jacobian::GroupProjective as SWProjective,
-        twisted_edwards_extended::GroupProjective as TEProjective, ModelParameters,
-        ProjectiveCurve,
+        twisted_edwards_extended::GroupProjective as TEProjective, ProjectiveCurve,
    };
    use ark_ff::{BitIteratorLE, Field, FpParameters, One, PrimeField};
    use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
@@ -242,13 +241,12 @@ pub mod curves {

    use ark_r1cs_std::prelude::*;

-    type ConstraintF<P> = <<P as ModelParameters>::BaseField as Field>::BasePrimeField;
-
-    pub fn group_test<C, ConstraintF>() -> Result<(), SynthesisError>
+    pub fn group_test<C, ConstraintF, GG>() -> Result<(), SynthesisError>
    where
-        C: CurveWithVar<ConstraintF>,
+        C: ProjectiveCurve,
        ConstraintF: Field,
-        for<'a> &'a C::Var: GroupOpsBounds<'a, C, C::Var>,
+        GG: CurveVar<C, ConstraintF>,
+        for<'a> &'a GG: GroupOpsBounds<'a, C, GG>,
    {
        let modes = [
            AllocationMode::Input,
@@ -261,14 +259,12 @@ pub mod curves {
            let mut rng = test_rng();
            let a_native = C::rand(&mut rng);
            let b_native = C::rand(&mut rng);
-            let a =
-                C::Var::new_variable(ark_relations::ns!(cs, "generate_a"), || Ok(a_native), mode)
-                    .unwrap();
-            let b =
-                C::Var::new_variable(ark_relations::ns!(cs, "generate_b"), || Ok(b_native), mode)
-                    .unwrap();
+            let a = GG::new_variable(ark_relations::ns!(cs, "generate_a"), || Ok(a_native), mode)
+                .unwrap();
+            let b = GG::new_variable(ark_relations::ns!(cs, "generate_b"), || Ok(b_native), mode)
+                .unwrap();

-            let zero = C::Var::zero();
+            let zero = GG::zero();
            assert_eq!(zero.value()?, zero.value()?);

            // a == a
@@ -277,14 +273,14 @@ pub mod curves {
            assert_eq!((&a + &zero).value()?, a.value()?);
            // a - 0 = a
            assert_eq!((&a - &zero).value()?, a.value()?);
+            // a - a = 0
+            assert_eq!((&a - &a).value()?, zero.value()?);
            // a + b = b + a
            let a_b = &a + &b;
            let b_a = &b + &a;
            assert_eq!(a_b.value()?, b_a.value()?);
            a_b.enforce_equal(&b_a)?;
            assert!(cs.is_satisfied().unwrap());
-            // a - a = 0
-            assert_eq!((&a - &a).value()?, zero.value()?);

            // (a + b) + a = a + (b + a)
            let ab_a = &a_b + &a;
@@ -384,15 +380,13 @@ pub mod curves {
        Ok(())
    }

-    type SWVar<P> = <SWProjective<P> as CurveWithVar<ConstraintF<P>>>::Var;
-
-    pub fn sw_test<P>() -> Result<(), SynthesisError>
+    pub fn sw_test<P, GG>() -> Result<(), SynthesisError>
    where
        P: ark_ec::SWModelParameters,
-        SWProjective<P>: CurveWithVar<ConstraintF<P>> + ProjectiveCurve,
-        for<'a> &'a SWVar<P>: GroupOpsBounds<'a, SWProjective<P>, SWVar<P>>,
+        GG: CurveVar<SWProjective<P>, <P::BaseField as Field>::BasePrimeField>,
+        for<'a> &'a GG: GroupOpsBounds<'a, SWProjective<P>, GG>,
    {
-        group_test::<SWProjective<P>, _>()?;
+        group_test::<SWProjective<P>, _, GG>()?;
        let modes = [
            AllocationMode::Input,
            AllocationMode::Witness,
@@ -411,12 +405,14 @@ pub mod curves {
            let b_affine = b.into_affine();

            let ns = ark_relations::ns!(cs, "allocating variables");
-            let mut gadget_a = SWVar::<P>::new_variable(cs.clone(), || Ok(a), mode)?;
-            let gadget_b = SWVar::<P>::new_variable(cs.clone(), || Ok(b), mode)?;
-            let zero = SWVar::<P>::zero();
+            let mut gadget_a = GG::new_variable(cs.clone(), || Ok(a), mode)?;
+            let gadget_b = GG::new_variable(cs.clone(), || Ok(b), mode)?;
+            let zero = GG::zero();
            drop(ns);
-            assert_eq!(gadget_a.value()?.into_affine(), a_affine);
-            assert_eq!(gadget_b.value()?.into_affine(), b_affine);
+            assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
+            assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
+            assert_eq!(gadget_b.value()?.into_affine().x, b_affine.x);
+            assert_eq!(gadget_b.value()?.into_affine().y, b_affine.y);
            assert_eq!(cs.which_is_unsatisfied().unwrap(), None);

            // Check addition
@@ -457,15 +453,13 @@ pub mod curves {
        Ok(())
    }

-    type TEVar<P> = <TEProjective<P> as CurveWithVar<ConstraintF<P>>>::Var;
-
-    pub fn te_test<P>() -> Result<(), SynthesisError>
+    pub fn te_test<P, GG>() -> Result<(), SynthesisError>
    where
        P: ark_ec::TEModelParameters,
-        TEProjective<P>: CurveWithVar<ConstraintF<P>> + ProjectiveCurve,
-        for<'a> &'a TEVar<P>: GroupOpsBounds<'a, TEProjective<P>, TEVar<P>>,
+        GG: CurveVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField>,
+        for<'a> &'a GG: GroupOpsBounds<'a, TEProjective<P>, GG>,
    {
-        group_test::<TEProjective<P>, _>()?;
+        group_test::<TEProjective<P>, _, GG>()?;
        let modes = [
            AllocationMode::Input,
            AllocationMode::Witness,
@@ -484,12 +478,14 @@ pub mod curves {
            let b_affine = b.into_affine();

            let ns = ark_relations::ns!(cs, "allocating variables");
-            let mut gadget_a = TEVar::<P>::new_variable(cs.clone(), || Ok(a), mode)?;
-            let gadget_b = TEVar::<P>::new_variable(cs.clone(), || Ok(b), mode)?;
+            let mut gadget_a = GG::new_variable(cs.clone(), || Ok(a), mode)?;
+            let gadget_b = GG::new_variable(cs.clone(), || Ok(b), mode)?;
            drop(ns);

-            assert_eq!(gadget_a.value()?.into_affine(), a_affine);
-            assert_eq!(gadget_b.value()?.into_affine(), b_affine);
+            assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
+            assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
+            assert_eq!(gadget_b.value()?.into_affine().x, b_affine.x);
+            assert_eq!(gadget_b.value()?.into_affine().y, b_affine.y);
            assert_eq!(cs.which_is_unsatisfied()?, None);

            // Check addition
@@ -531,21 +527,16 @@ pub mod curves {
 pub mod pairing {
    use ark_ec::{PairingEngine, ProjectiveCurve};
    use ark_ff::{BitIteratorLE, Field, PrimeField};
-    use ark_r1cs_std::{fields::fp::FpVar, prelude::*};
+    use ark_r1cs_std::prelude::*;
    use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
    use ark_std::{test_rng, vec::Vec, UniformRand};

    #[allow(dead_code)]
-    pub fn bilinearity_test<P: PairingGadget>() -> Result<(), SynthesisError>
+    pub fn bilinearity_test<E: PairingEngine, P: PairingVar<E>>() -> Result<(), SynthesisError>
    where
-        for<'a> &'a P::G1Var: GroupOpsBounds<'a, P::G1Projective, P::G1Var>,
-        for<'a> &'a P::G2Var: GroupOpsBounds<'a, P::G2Projective, P::G2Var>,
-        for<'a> &'a P::GTVar: FieldOpsBounds<'a, P::Fqk, P::GTVar>,
-        P::Fq: FieldWithVar<Var = FpVar<P::Fq>>,
-        P::Fqe: FieldWithVar,
-        P::Fqk: FieldWithVar<Var = P::GTVar>,
-        P::G1Projective: CurveWithVar<P::Fq, Var = P::G1Var>,
-        P::G2Projective: CurveWithVar<P::Fq, Var = P::G2Var>,
+        for<'a> &'a P::G1Var: GroupOpsBounds<'a, E::G1Projective, P::G1Var>,
+        for<'a> &'a P::G2Var: GroupOpsBounds<'a, E::G2Projective, P::G2Var>,
+        for<'a> &'a P::GTVar: FieldOpsBounds<'a, E::Fqk, P::GTVar>,
    {
        let modes = [
            AllocationMode::Input,
@@ -553,12 +544,12 @@ pub mod pairing {
            AllocationMode::Constant,
        ];
        for &mode in &modes {
-            let cs = ConstraintSystem::<P::Fq>::new_ref();
+            let cs = ConstraintSystem::<E::Fq>::new_ref();

            let mut rng = test_rng();
-            let a = P::G1Projective::rand(&mut rng);
-            let b = P::G2Projective::rand(&mut rng);
-            let s = P::Fr::rand(&mut rng);
+            let a = E::G1Projective::rand(&mut rng);
+            let b = E::G2Projective::rand(&mut rng);
+            let s = E::Fr::rand(&mut rng);

            let mut sa = a;
            sa *= s;
@@ -580,16 +571,16 @@ pub mod pairing {

            let (ans1_g, ans1_n) = {
                let _ml_constraints = cs.num_constraints();
-                let ml_g = P::miller_loop_gadget(&[sa_prep_g], &[b_prep_g.clone()])?;
+                let ml_g = P::miller_loop(&[sa_prep_g], &[b_prep_g.clone()])?;
                let _fe_constraints = cs.num_constraints();
-                let ans_g = P::final_exponentiation_gadget(&ml_g)?;
-                let ans_n = <P as PairingEngine>::pairing(sa, b);
+                let ans_g = P::final_exponentiation(&ml_g)?;
+                let ans_n = E::pairing(sa, b);
                (ans_g, ans_n)
            };

            let (ans2_g, ans2_n) = {
-                let ans_g = P::pairing_gadget(a_prep_g.clone(), sb_prep_g)?;
-                let ans_n = <P as PairingEngine>::pairing(a, sb);
+                let ans_g = P::pairing(a_prep_g.clone(), sb_prep_g)?;
+                let ans_n = E::pairing(a, sb);
                (ans_g, ans_n)
            };

@@ -598,8 +589,8 @@ pub mod pairing {
                    .map(Boolean::constant)
                    .collect::<Vec<_>>();

-                let mut ans_g = P::pairing_gadget(a_prep_g, b_prep_g)?;
-                let mut ans_n = <P as PairingEngine>::pairing(a, b);
+                let mut ans_g = P::pairing(a_prep_g, b_prep_g)?;
+                let mut ans_n = E::pairing(a, b);
                ans_n = ans_n.pow(s.into_repr());
                ans_g = ans_g.pow_le(&s_iter)?;

--- a/ed_on_bls12_377/Cargo.toml
+++ b/ed_on_bls12_377/Cargo.toml
@@ -1,29 +1,31 @@
 [package]
 name = "ark-ed-on-bls12-377"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the BLS12-377 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-bls12-377/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-bls12-377 = { version = "^0.3.0", path = "../bls12_377", default-features = false, features = [ "scalar_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-bls12-377 = { path = "../bls12_377", default-features = false, features = [ "scalar_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
+rand = { version = "0.7", default-features = false }
+rand_xorshift = "0.2"

 [features]
 default = []
--- a/ed_on_bls12_377/src/constraints/curves.rs
+++ b/ed_on_bls12_377/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;

+use crate::constraints::FqVar;
+
 /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
+pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
 }
--- a/ed_on_bls12_377/src/lib.rs
+++ b/ed_on_bls12_377/src/lib.rs
@@ -11,7 +11,7 @@
 //! This library implements a twisted Edwards curve whose base field is the scalar field of the
 //! curve BLS12-377.  This allows defining cryptographic primitives that use elliptic curves over
 //! the scalar field of the latter curve. This curve was generated as part of the paper
-//! [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
+//! [[BCGMMW20, “Zexe”]](https://eprint.iacr.org/2018/962).
 //!
 //! Curve information:
 //! * Base field: q = 8444461749428370424248824938781546531375899335154063827935233455917409239041
--- a/ed_on_bls12_381/Cargo.toml
+++ b/ed_on_bls12_381/Cargo.toml
@@ -1,28 +1,28 @@
 [package]
 name = "ark-ed-on-bls12-381"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the BLS12-381 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-bls12-381/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-bls12-381 = { version = "^0.3.0", path = "../bls12_381", default-features = false, features = [ "scalar_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-bls12-381 = { path = "../bls12_381", default-features = false, features = [ "scalar_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/ed_on_bls12_381/src/constraints/curves.rs
+++ b/ed_on_bls12_381/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;

+use crate::constraints::FqVar;
+
 /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
+pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<_, EdwardsVar>().unwrap();
 }
--- a/ed_on_bls12_381/src/lib.rs
+++ b/ed_on_bls12_381/src/lib.rs
@@ -9,7 +9,7 @@
 #![forbid(unsafe_code)]

 //! This library implements a twisted Edwards curve whose base field is the scalar field of the
-//! curve BLS12-381. This allows defining cryptographic primitives that use elliptic curves over
+//! curve BLS12-377. This allows defining cryptographic primitives that use elliptic curves over
 //! the scalar field of the latter curve. This curve was generated by Sean Bowe, and is also known
 //! as [Jubjub](https://github.com/zkcrypto/jubjub).
 //!
--- a/ed_on_bls12_381_bandersnatch/Cargo.toml
+++ b/ed_on_bls12_381_bandersnatch/Cargo.toml
@@ -1,34 +0,0 @@
-[package]
-name = "ark-ed-on-bls12-381-bandersnatch"
-version = "0.1.0"
-authors = [ "zhenfei zhang", "arkworks contributors" ]
-description = "Bandersnatch: a curve defined over the scalar field of the BLS12-381 curve"
-repository = "https://github.com/zhenfeizhang/bandersnatch-rust"
-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"
-
-[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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-bls12-381 = { version = "^0.3.0", default-features = false, features = [ "scalar_field" ] }
-
-[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-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }
-
-[features]
-default = []
-std = [ 
-    "ark-std/std", 
-    "ark-ff/std", 
-    "ark-ec/std", 
-    "ark-bls12-381/std" 
-]
-r1cs = ["ark-r1cs-std"]
--- a/ed_on_bls12_381_bandersnatch/src/constraints/curves.rs
+++ b/ed_on_bls12_381_bandersnatch/src/constraints/curves.rs
@@ -1,10 +0,0 @@
-use crate::*;
-use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;
-
-/// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
-
-#[test]
-fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
-}
--- a/ed_on_bls12_381_bandersnatch/src/constraints/fields.rs
+++ b/ed_on_bls12_381_bandersnatch/src/constraints/fields.rs
@@ -1,9 +0,0 @@
-use ark_r1cs_std::fields::fp::FpVar;
-
-/// A variable that is the R1CS equivalent of `crate::Fq`.
-pub type FqVar = FpVar<crate::Fq>;
-
-#[test]
-fn test() {
-    ark_curve_constraint_tests::fields::field_test::<_, _, FqVar>().unwrap();
-}
--- a/ed_on_bls12_381_bandersnatch/src/constraints/mod.rs
+++ b/ed_on_bls12_381_bandersnatch/src/constraints/mod.rs
@@ -1,107 +0,0 @@
-//! This module implements the R1CS equivalent of `ark_bandersnatch`.
-//!
-//! It implements field variables for `crate::Fq`,
-//! and group variables for `crate::GroupProjective`.
-//!
-//! The field underlying these constraints is `crate::Fq`.
-//!
-//! # Examples
-//!
-//! One can perform standard algebraic operations on `FqVar`:
-//!
-//! ```
-//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
-//! use ark_std::UniformRand;
-//! use ark_relations::r1cs::*;
-//! use ark_r1cs_std::prelude::*;
-//! use ark_ed_on_bls12_381_bandersnatch::{*, constraints::*};
-//!
-//! let cs = ConstraintSystem::<Fq>::new_ref();
-//! // This rng is just for test purposes; do not use it
-//! // in real applications.
-//! let mut rng = ark_std::test_rng();
-//!
-//! // Generate some random `Fq` elements.
-//! let a_native = Fq::rand(&mut rng);
-//! let b_native = Fq::rand(&mut rng);
-//!
-//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
-//! let a = FqVar::new_witness(ark_relations::ns!(cs, "generate_a"), || Ok(a_native))?;
-//! let b = FqVar::new_witness(ark_relations::ns!(cs, "generate_b"), || Ok(b_native))?;
-//!
-//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
-//! // constraints or variables.
-//! let a_const = FqVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
-//! let b_const = FqVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
-//!
-//! let one = FqVar::one();
-//! let zero = FqVar::zero();
-//!
-//! // Sanity check one + one = two
-//! let two = &one + &one + &zero;
-//! two.enforce_equal(&one.double()?)?;
-//!
-//! assert!(cs.is_satisfied()?);
-//!
-//! // Check that the value of &a + &b is correct.
-//! assert_eq!((&a + &b).value()?, a_native + &b_native);
-//!
-//! // Check that the value of &a * &b is correct.
-//! assert_eq!((&a * &b).value()?, a_native * &b_native);
-//!
-//! // Check that operations on variables and constants are equivalent.
-//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
-//! assert!(cs.is_satisfied()?);
-//! # Ok(())
-//! # }
-//! ```
-//!
-//! One can also perform standard algebraic operations on `EdwardsVar`:
-//!
-//! ```
-//! # fn main() -> Result<(), ark_relations::r1cs::SynthesisError> {
-//! # use ark_std::UniformRand;
-//! # use ark_relations::r1cs::*;
-//! # use ark_r1cs_std::prelude::*;
-//! # use ark_ed_on_bls12_381_bandersnatch::{*, constraints::*};
-//!
-//! # let cs = ConstraintSystem::<Fq>::new_ref();
-//! # let mut rng = ark_std::test_rng();
-//!
-//! // Generate some random `Edwards` elements.
-//! let a_native = EdwardsProjective::rand(&mut rng);
-//! let b_native = EdwardsProjective::rand(&mut rng);
-//!
-//! // Allocate `a_native` and `b_native` as witness variables in `cs`.
-//! let a = EdwardsVar::new_witness(ark_relations::ns!(cs, "a"), || Ok(a_native))?;
-//! let b = EdwardsVar::new_witness(ark_relations::ns!(cs, "b"), || Ok(b_native))?;
-//!
-//! // Allocate `a_native` and `b_native` as constants in `cs`. This does not add any
-//! // constraints or variables.
-//! let a_const = EdwardsVar::new_constant(ark_relations::ns!(cs, "a_as_constant"), a_native)?;
-//! let b_const = EdwardsVar::new_constant(ark_relations::ns!(cs, "b_as_constant"), b_native)?;
-//!
-//! // This returns the identity of `Edwards`.
-//! let zero = EdwardsVar::zero();
-//!
-//! // Sanity check one + one = two
-//! let two_a = &a + &a + &zero;
-//! two_a.enforce_equal(&a.double()?)?;
-//!
-//! assert!(cs.is_satisfied()?);
-//!
-//! // Check that the value of &a + &b is correct.
-//! assert_eq!((&a + &b).value()?, a_native + &b_native);
-//!
-//! // Check that operations on variables and constants are equivalent.
-//! (&a + &b).enforce_equal(&(&a_const + &b_const))?;
-//! assert!(cs.is_satisfied()?);
-//! # Ok(())
-//! # }
-//! ```
-
-mod curves;
-mod fields;
-
-pub use curves::*;
-pub use fields::*;
--- a/ed_on_bls12_381_bandersnatch/src/curves/mod.rs
+++ b/ed_on_bls12_381_bandersnatch/src/curves/mod.rs
@@ -1,94 +0,0 @@
-use crate::{Fq, Fr};
-use ark_ec::{
-    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    twisted_edwards_extended::{GroupAffine, GroupProjective},
-};
-use ark_ff::{field_new, Field};
-#[cfg(test)]
-mod tests;
-
-pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
-
-/// `banersnatch` is a twisted Edwards curve. These curves have equations of the
-/// form: ax² + y² = 1 - dx²y².
-/// over some base finite field Fq.
-///
-/// banersnatch's curve equation: -5x² + y² = 1 - dx²y²
-///
-/// q = 52435875175126190479447740508185965837690552500527637822603658699938581184513.
-///
-/// a = 52435875175126190479447740508185965837690552500527637822603658699938581184508.
-/// d = (138827208126141220649022263972958607803/
-/// 171449701953573178309673572579671231137) mod q
-///   = 45022363124591815672509500913686876175488063829319466900776701791074614335719.
-///
-/// Sage script to calculate these:
-///
-/// ```text
-/// q = 52435875175126190479447740508185965837690552500527637822603658699938581184513
-/// Fq = GF(q)
-/// d = (Fq(138827208126141220649022263972958607803)/Fq(171449701953573178309673572579671231137))
-/// ```
-/// These parameters and the sage script obtained from:
-/// <https://github.com/asanso/Bandersnatch/>
-#[derive(Clone, Default, PartialEq, Eq)]
-pub struct EdwardsParameters;
-
-impl ModelParameters for EdwardsParameters {
-    type BaseField = Fq;
-    type ScalarField = Fr;
-}
-
-impl TEModelParameters for EdwardsParameters {
-    /// COEFF_A = -5
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "-5");
-
-    /// COEFF_D = (138827208126141220649022263972958607803/
-    /// 171449701953573178309673572579671231137) mod q
-    #[rustfmt::skip]
-    const COEFF_D: Fq = field_new!(Fq, "45022363124591815672509500913686876175488063829319466900776701791074614335719");
-
-    /// COFACTOR = 4
-    const COFACTOR: &'static [u64] = &[4];
-
-    /// COFACTOR^(-1) mod r =
-    /// 9831726595336160714896451345284868594481866920080427688839802480047265754601
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "9831726595336160714896451345284868594481866920080427688839802480047265754601");
-
-    /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
-
-    type MontgomeryModelParameters = EdwardsParameters;
-
-    /// Multiplication by `a` is multiply by `-5`.
-    #[inline(always)]
-    fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
-        let t = (*elem).double().double();
-        -(t + *elem)
-    }
-}
-
-impl MontgomeryModelParameters for EdwardsParameters {
-    /// COEFF_A = 29978822694968839326280996386011761570173833766074948509196803838190355340952
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "29978822694968839326280996386011761570173833766074948509196803838190355340952");
-    /// COEFF_B = 25465760566081946422412445027709227188579564747101592991722834452325077642517
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "25465760566081946422412445027709227188579564747101592991722834452325077642517");
-
-    type TEModelParameters = EdwardsParameters;
-}
-
-// using the generator from bench.py (in affine form)
-// P = BandersnatchPoint(
-//      13738737789055671334382939318077718462576533426798874551591468520593954805549,
-//      11575885077368931610486103676191793534029821920164915325066801506752632626968,
-//      14458123306641001284399433086015669988340559992755622870694102351476334505845,
-//      C)
-#[rustfmt::skip]
-const GENERATOR_X: Fq = field_new!(Fq, "29627151942733444043031429156003786749302466371339015363120350521834195802525");
-#[rustfmt::skip]
-const GENERATOR_Y: Fq = field_new!(Fq, "27488387519748396681411951718153463804682561779047093991696427532072116857978");
--- a/ed_on_bls12_381_bandersnatch/src/curves/tests.rs
+++ b/ed_on_bls12_381_bandersnatch/src/curves/tests.rs
@@ -1,103 +0,0 @@
-use crate::*;
-use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_ff::{bytes::FromBytes, Zero};
-use ark_std::{rand::Rng, str::FromStr, test_rng};
-
-#[test]
-fn test_projective_curve() {
-    curve_tests::<EdwardsProjective>();
-
-    edwards_tests::<EdwardsParameters>();
-}
-
-#[test]
-fn test_projective_group() {
-    let mut rng = test_rng();
-    let a = rng.gen();
-    let b = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsProjective>(a, b);
-    }
-}
-
-#[test]
-fn test_affine_group() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    for _i in 0..100 {
-        group_test::<EdwardsAffine>(a, b);
-    }
-}
-
-#[test]
-fn test_generator() {
-    let generator = EdwardsAffine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_conversion() {
-    let mut rng = test_rng();
-    let a: EdwardsAffine = rng.gen();
-    let b: EdwardsAffine = rng.gen();
-    let a_b = {
-        use ark_ec::group::Group;
-        (a + &b).double().double()
-    };
-    let a_b2 = (a.into_projective() + &b.into_projective())
-        .double()
-        .double();
-    assert_eq!(a_b, a_b2.into_affine());
-    assert_eq!(a_b.into_projective(), a_b2);
-}
-
-#[test]
-fn test_scalar_multiplication() {
-    let f1 = Fr::from_str(
-        "4257185345094557079734489188109952172285839137338142340240392707284963971010",
-    )
-    .unwrap();
-    let f2 = Fr::from_str(
-        "1617998875791656082457755819308421023664764572929977389209373068350490665160",
-    )
-    .unwrap();
-
-    let g = EdwardsAffine::from_str(
-        "(29627151942733444043031429156003786749302466371339015363120350521834195802525, \
-         27488387519748396681411951718153463804682561779047093991696427532072116857978)",
-    )
-    .unwrap();
-    let f1f2g = EdwardsAffine::from_str(
-        "(16530491029447613915334753043669938793793987372416328257719459807614119987301, \
-         42481140308370805476764840229335460092474682686441442216596889726548353970772)",
-    )
-    .unwrap();
-
-    assert!(!g.is_zero());
-    assert!(!f1f2g.is_zero());
-
-    let f1g = g.mul(f1).into_affine();
-    assert_eq!(g.mul(f1 * &f2).into_affine(), f1f2g);
-    assert_eq!(f1g.mul(f2).into_affine(), f1f2g);
-}
-
-#[test]
-fn test_bytes() {
-    let g_from_repr = EdwardsAffine::from_str(
-        "(29627151942733444043031429156003786749302466371339015363120350521834195802525, \
-         27488387519748396681411951718153463804682561779047093991696427532072116857978)",
-    )
-    .unwrap();
-
-    let g_bytes = ark_ff::to_bytes![g_from_repr].unwrap();
-    let g = EdwardsAffine::read(g_bytes.as_slice()).unwrap();
-    assert_eq!(g_from_repr, g);
-}
-
-#[test]
-fn test_montgomery_conversion() {
-    montgomery_conversion_test::<EdwardsParameters>();
-}
--- a/ed_on_bls12_381_bandersnatch/src/fields/fq.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/fq.rs
@@ -1 +0,0 @@
-pub use ark_bls12_381::{Fr as Fq, FrParameters as FqParameters};
--- a/ed_on_bls12_381_bandersnatch/src/fields/fr.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/fr.rs
@@ -1,115 +0,0 @@
-use ark_ff::{
-    biginteger::BigInteger256 as BigInteger,
-    fields::{FftParameters, Fp256, Fp256Parameters, FpParameters},
-};
-
-pub type Fr = Fp256<FrParameters>;
-
-pub struct FrParameters;
-
-impl Fp256Parameters for FrParameters {}
-impl FftParameters for FrParameters {
-    type BigInt = BigInteger;
-
-    /// Let `N` be the size of the multiplicative group defined by the field.
-    /// Then `TWO_ADICITY` is the two-adicity of `N`, i.e. the integer `s`
-    /// such that `N = 2^s * t` for some odd integer `t`.
-    const TWO_ADICITY: u32 = 5;
-
-    /// 2^s root of unity computed by GENERATOR^t
-    /// 4740934665446857387895054948191089665295030226009829406950782728666658007874
-    #[rustfmt::skip]
-    const TWO_ADIC_ROOT_OF_UNITY: BigInteger = BigInteger([
-        0xa4dcdba087826b42,
-        0x6e4ab162f57f862a,
-        0xabc5492749348d6a,
-        0xa7b462035f8c169,
-    ]);
-}
-impl FpParameters for FrParameters {
-    /// The modulus of the field.
-    /// MODULUS = 13108968793781547619861935127046491459309155893440570251786403306729687672801.
-    #[rustfmt::skip]
-    const MODULUS: BigInteger = BigInteger([
-        0x74fd06b52876e7e1,
-        0xff8f870074190471,
-        0x0cce760202687600,
-        0x1cfb69d4ca675f52,
-    ]);
-
-    /// The number of bits needed to represent the `Self::MODULUS`.
-    const MODULUS_BITS: u32 = 253;
-
-    /// The number of bits that can be reliably stored.
-    /// (Should equal `SELF::MODULUS_BITS - 1`)
-    const CAPACITY: u32 = Self::MODULUS_BITS - 1;
-
-    /// The number of bits that must be shaved from the beginning of
-    /// the representation when randomly sampling.
-    const REPR_SHAVE_BITS: u32 = 4;
-
-    /// Let `M` be the power of 2^64 nearest to `Self::MODULUS_BITS`. Then
-    /// `R = M % Self::MODULUS`.
-    /// R = 10920338887063814464675503992315976178796737518116002025166357554075628257528
-    #[rustfmt::skip]
-    const R: BigInteger = BigInteger([
-        0x5817ca56bc48c0f8,
-        0x0383c7fc5f37dc74,
-        0x998c4fefecbc4ff8,
-        0x1824b159acc5056f,
-    ]);
-
-    /// R2 = R^2 % Self::MODULUS
-    /// R2 = 4932290691328759802879919559207542894238895193980447506221046538067943049163
-    #[rustfmt::skip]
-    const R2: BigInteger = BigInteger([
-        0xdbb4f5d658db47cb,
-        0x40fa7ca27fecb938,
-        0xaa9e6daec0055cea,
-        0xae793ddb14aec7d
-    ]);
-
-    /// INV = -MODULUS^{-1} mod 2^64
-    /// INV = 17410672245482742751
-    const INV: u64 = 0xf19f22295cc063df;
-
-    /// A multiplicative generator of the field.
-    /// `Self::GENERATOR` is an element having multiplicative order
-    /// `Self::MODULUS - 1`.
-    /// n = 9962557815892774795293348142308860067333132192265356416788884706064406244838
-    #[rustfmt::skip]
-    const GENERATOR: BigInteger = BigInteger([
-        0x56b6f3ab7b616de6,
-        0x114f419d6c9083e5,
-        0xbf518d217780c4b9,
-        0x16069b9f45dbce7f,
-    ]);
-
-    /// (Self::MODULUS - 1) / 2
-    /// 6554484396890773809930967563523245729654577946720285125893201653364843836400
-    const MODULUS_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xba7e835a943b73f0,
-        0x7fc7c3803a0c8238,
-        0x06673b0101343b00,
-        0xe7db4ea6533afa9,
-    ]);
-
-    /// t for 2^s * t = MODULUS - 1, and t coprime to 2.
-    /// t = 409655274805673363120685472720202858103411121670017820368325103335302739775
-    ///   = (modulus-1)/2^5
-    const T: BigInteger = BigInteger([
-        0x8ba7e835a943b73f,
-        0x07fc7c3803a0c823,
-        0x906673b0101343b0,
-        0xe7db4ea6533afa,
-    ]);
-
-    /// (t - 1) / 2
-    ///  = 204827637402836681560342736360101429051705560835008910184162551667651369887
-    const T_MINUS_ONE_DIV_TWO: BigInteger = BigInteger([
-        0xc5d3f41ad4a1db9f,
-        0x03fe3e1c01d06411,
-        0x483339d80809a1d8,
-        0x73eda753299d7d,
-    ]);
-}
--- a/ed_on_bls12_381_bandersnatch/src/fields/mod.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/mod.rs
@@ -1,8 +0,0 @@
-pub mod fq;
-pub mod fr;
-
-pub use fq::*;
-pub use fr::*;
-
-#[cfg(all(feature = "ed_on_bls12_381_bandersnatch", test))]
-mod tests;
--- a/ed_on_bls12_381_bandersnatch/src/fields/tests.rs
+++ b/ed_on_bls12_381_bandersnatch/src/fields/tests.rs
@@ -1,423 +0,0 @@
-use crate::{Fq, Fr};
-use ark_algebra_test_templates::fields::*;
-use ark_ff::{
-    biginteger::BigInteger256 as BigInteger,
-    bytes::{FromBytes, ToBytes},
-    fields::{Field, LegendreSymbol::*, SquareRootField},
-    One, Zero,
-};
-use ark_std::{rand::Rng, str::FromStr, test_rng};
-
-#[test]
-fn test_fr() {
-    let mut rng = test_rng();
-    let a: Fr = rng.gen();
-    let b: Fr = rng.gen();
-    field_test(a, b);
-    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>();
-}
-
-#[test]
-fn test_fq_add() {
-    let f1 = Fq::from_str(
-        "18386742314266644595564329008376577163854043021652781768352795308532764650733",
-    )
-    .unwrap();
-    let f2 = Fq::from_str(
-        "39786307610986038981023499868190793548353538256264351797285876981647142458383",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "5737174750126493097140088368381404874517028777389495743035013590241325924603",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f2.is_zero());
-    assert!(!f3.is_zero());
-    assert_eq!(f1 + &f2, f3);
-}
-
-#[test]
-fn test_fq_add_one() {
-    let f1 = Fq::from_str(
-        "4946875394261337176810256604189376311946643975348516311606738923340201185904",
-    )
-    .unwrap();
-    let f2 = Fq::from_str(
-        "4946875394261337176810256604189376311946643975348516311606738923340201185905",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f2.is_zero());
-    assert_eq!(f1 + &Fq::one(), f2);
-}
-
-#[test]
-fn test_fq_mul() {
-    let f1 = Fq::from_str(
-        "24703123148064348394273033316595937198355721297494556079070134653139656190956",
-    )
-    .unwrap();
-    let f2 = Fq::from_str(
-        "38196797080882758914424853878212529985425118523754343117256179679117054302131",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "38057113854472161555556064369220825628027487067886761874351491955834635348140",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f2.is_zero());
-    assert!(!f3.is_zero());
-    assert_eq!(f1 * &f2, f3);
-}
-
-#[test]
-fn test_fq_triple_mul() {
-    let f1 = Fq::from_str(
-        "23834398828139479510988224171342199299644042568628082836691700490363123893905",
-    )
-    .unwrap();
-    let f2 = Fq::from_str(
-        "48343809612844640454129919255697536258606705076971130519928764925719046689317",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "22704845471524346880579660022678666462201713488283356385810726260959369106033",
-    )
-    .unwrap();
-    let f4 = Fq::from_str(
-        "18897508522635316277030308074760673440128491438505204942623624791502972539393",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f2.is_zero());
-    assert!(!f3.is_zero());
-    assert_eq!(f1 * &f2 * &f3, f4);
-}
-
-#[test]
-fn test_fq_div() {
-    let f1 = Fq::from_str(
-        "31892744363926593013886463524057935370302352424137349660481695792871889573091",
-    )
-    .unwrap();
-    let f2 = Fq::from_str(
-        "47695868328933459965610498875668250916462767196500056002116961816137113470902",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "29049672724678710659792141917402891276693777283079976086581207190825261000580",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f2.is_zero());
-    assert!(!f3.is_zero());
-    assert_eq!(f1 / &f2, f3);
-}
-
-#[test]
-fn test_fq_sub() {
-    let f1 = Fq::from_str(
-        "18695869713129401390241150743745601908470616448391638969502807001833388904079",
-    )
-    .unwrap();
-    let f2 = Fq::from_str(
-        "10105476028534616828778879109836101003805485072436929139123765141153277007373",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "8590393684594784561462271633909500904665131375954709830379041860680111896706",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f2.is_zero());
-    assert!(!f3.is_zero());
-    assert_eq!(f1 - &f2, f3);
-}
-
-#[test]
-fn test_fq_double_in_place() {
-    let mut f1 = Fq::from_str(
-        "29729289787452206300641229002276778748586801323231253291984198106063944136114",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "7022704399778222121834717496367591659483050145934868761364737512189307087715",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f3.is_zero());
-    f1.double_in_place();
-    assert_eq!(f1, f3);
-}
-
-#[test]
-fn test_fq_double_in_place_thrice() {
-    let mut f1 = Fq::from_str(
-        "32768907806651393940832831055386272949401004221411141755415956893066040832473",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "52407761752706389608871686410346320244445823769178582752913020344774001921732",
-    )
-    .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f3.is_zero());
-    f1.double_in_place();
-    f1.double_in_place();
-    f1.double_in_place();
-    assert_eq!(f1, f3);
-}
-
-#[test]
-fn test_fq_generate_random_ed_on_bls12_381_point() {
-    let d = Fq::from_str(
-        "19257038036680949359750312669786877991949435402254120286184196891950884077233",
-    )
-    .unwrap();
-    let y = Fq::from_str(
-        "20269054604167148422407276086932743904275456233139568486008667107872965128512",
-    )
-    .unwrap();
-    let x2 = Fq::from_str(
-        "35041048504708632193693740149219726446678304552734087046982753200179718192840",
-    )
-    .unwrap();
-
-    let computed_y2 = y.square();
-    let y2 = Fq::from_str(
-        "22730681238307918419349440108285755984465605552827817317611903495170775437833",
-    )
-    .unwrap();
-    assert_eq!(y2, computed_y2);
-
-    let computed_dy2 = d * &computed_y2;
-    let dy2 = Fq::from_str(
-        "24720347560552809545835752815204882739669031262711919770503096707526812943411",
-    )
-    .unwrap();
-    assert_eq!(dy2, computed_dy2);
-
-    let computed_divisor = computed_dy2 + &Fq::one();
-    let divisor = Fq::from_str(
-        "24720347560552809545835752815204882739669031262711919770503096707526812943412",
-    )
-    .unwrap();
-    assert_eq!(divisor, computed_divisor);
-
-    let computed_x2 = (computed_y2 - &Fq::one()) / &computed_divisor;
-    assert_eq!(x2, computed_x2);
-
-    let x = Fq::from_str(
-        "15337652609730546173818014678723269532482775720866471265774032070871608223361",
-    )
-    .unwrap();
-    let computed_x = computed_x2.sqrt().unwrap();
-    assert_eq!(computed_x.square(), x2);
-    assert_eq!(x, computed_x);
-
-    fn add<'a>(curr: (Fq, Fq), other: &'a (Fq, Fq)) -> (Fq, Fq) {
-        let y1y2 = curr.1 * &other.1;
-        let x1x2 = curr.0 * &other.0;
-        let d = Fq::from_str(
-            "19257038036680949359750312669786877991949435402254120286184196891950884077233",
-        )
-        .unwrap();
-        let dx1x2y1y2 = d * &y1y2 * &x1x2;
-
-        let d1 = Fq::one() + &dx1x2y1y2;
-        let d2 = Fq::one() - &dx1x2y1y2;
-
-        let x1y2 = curr.0 * &other.1;
-        let y1x2 = curr.1 * &other.0;
-
-        let x = (x1y2 + &y1x2) / &d1;
-        let y = (y1y2 + &x1x2) / &d2;
-
-        (x, y)
-    }
-
-    let result = add((x, y), &(x, y));
-    let result = add(result, &result);
-    let result = add(result, &result);
-
-    let point_x = Fq::from_str(
-        "47259664076168047050113154262636619161204477920503059672059915868534495873964",
-    )
-    .unwrap();
-    let point_y = Fq::from_str(
-        "19016409245280491801573912449420132838852726543024859389273314249842195919690",
-    )
-    .unwrap();
-    assert_eq!((point_x, point_y), result);
-}
-
-#[test]
-fn test_fq_square_in_place() {
-    let mut f1 = Fq::from_str(
-        "34864651240005695523200639428464570946052769938774601449735727714436878540682",
-    )
-    .unwrap();
-    let f3 =
-        Fq::from_str("213133100629336594719108316042277780359104840987226496279264105585804377948")
-            .unwrap();
-    assert!(!f1.is_zero());
-    assert!(!f3.is_zero());
-    f1.square_in_place();
-    assert_eq!(f1, f3);
-}
-
-#[test]
-fn test_fq_sqrt() {
-    let f1 = Fq::from_str(
-        "10875927553327821418567659853801220899541454800710193788767706167237535308235",
-    )
-    .unwrap();
-    let f3 = Fq::from_str(
-        "10816221372957505053219354782681292880545918527618367765651802809826238616708",
-    )
-    .unwrap();
-    assert_eq!(f1.sqrt().unwrap(), f3);
-}
-
-#[test]
-fn test_fq_from_str() {
-    let f1_from_repr = Fq::from(BigInteger([
-        0xab8a2535947d1a77,
-        0x9ba74cbfda0bbcda,
-        0xe928b59724d60baf,
-        0x1cccaaeb9bb1680a,
-    ]));
-    let f1 = Fq::from_str(
-        "13026376210409056429264774981357153555336288129100724591327877625017068755575",
-    )
-    .unwrap();
-    let f2_from_repr = Fq::from(BigInteger([
-        0x97e9103775d2f35c,
-        0xbe6756b6c587544b,
-        0x6ee38c3afd88ef4b,
-        0x2bacd150f540c677,
-    ]));
-    let f2 = Fq::from_str(
-        "19754794831832707859764530223239420866832328728734160755396495950822165902172",
-    )
-    .unwrap();
-    assert_eq!(f1_from_repr, f1);
-    assert_eq!(f2_from_repr, f2);
-}
-
-#[test]
-fn test_fq_legendre() {
-    assert_eq!(QuadraticResidue, Fq::one().legendre());
-    assert_eq!(Zero, Fq::zero().legendre());
-
-    let e = BigInteger([
-        0x0dbc5349cd5664da,
-        0x8ac5b6296e3ae29d,
-        0x127cb819feceaa3b,
-        0x3a6b21fb03867191,
-    ]);
-    assert_eq!(QuadraticResidue, Fq::from(e).legendre());
-    let e = BigInteger([
-        0x96341aefd047c045,
-        0x9b5f4254500a4d65,
-        0x1ee08223b68ac240,
-        0x31d9cd545c0ec7c6,
-    ]);
-    assert_eq!(QuadraticNonResidue, Fq::from(e).legendre());
-}
-
-#[test]
-fn test_fq_bytes() {
-    let f1_from_repr = Fq::from(BigInteger([
-        0xab8a2535947d1a77,
-        0x9ba74cbfda0bbcda,
-        0xe928b59724d60baf,
-        0x1cccaaeb9bb1680a,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fq::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
-}
-
-#[test]
-fn test_fr_add() {
-    let f1 = Fr::from(BigInteger([
-        0xc81265fb4130fe0c,
-        0xb308836c14e22279,
-        0x699e887f96bff372,
-        0x84ecc7e76c11ad,
-    ]));
-    let f2 = Fr::from(BigInteger([
-        0x71875719b422efb8,
-        0x0043658e68a93612,
-        0x9fa756be2011e833,
-        0xaa2b2cb08dac497,
-    ]));
-    let f3 = Fr::from(BigInteger([
-        0x3999bd14f553edc4,
-        0xb34be8fa7d8b588c,
-        0x0945df3db6d1dba5,
-        0xb279f92f046d645,
-    ]));
-    assert_eq!(f1 + &f2, f3);
-}
-
-#[test]
-fn test_fr_mul() {
-    let f1 = Fr::from(BigInteger([
-        0xc81265fb4130fe0c,
-        0xb308836c14e22279,
-        0x699e887f96bff372,
-        0x84ecc7e76c11ad,
-    ]));
-    let f2 = Fr::from(BigInteger([
-        0x71875719b422efb8,
-        0x43658e68a93612,
-        0x9fa756be2011e833,
-        0xaa2b2cb08dac497,
-    ]));
-    let f3 = Fr::from(BigInteger([
-        0xbe3e50c164fe3381,
-        0x5ac45bc180974585,
-        0x1c234ad6dcdc70c9,
-        0x15a75fba99bc8ad,
-    ]));
-    assert_eq!(f1 * &f2, f3);
-}
-
-#[test]
-fn test_fr_bytes() {
-    let f1_from_repr = Fr::from(BigInteger([
-        0xc81265fb4130fe0c,
-        0xb308836c14e22279,
-        0x699e887f96bff372,
-        0x84ecc7e76c11ad,
-    ]));
-
-    let mut f1_bytes = [0u8; 32];
-    f1_from_repr.write(f1_bytes.as_mut()).unwrap();
-
-    let f1 = Fr::read(f1_bytes.as_ref()).unwrap();
-    assert_eq!(f1_from_repr, f1);
-}
-
-#[test]
-fn test_fr_from_str() {
-    let f100_from_repr = Fr::from(BigInteger([0x64, 0, 0, 0]));
-    let f100 = Fr::from_str("100").unwrap();
-    assert_eq!(f100_from_repr, f100);
-}
--- a/ed_on_bls12_381_bandersnatch/src/lib.rs
+++ b/ed_on_bls12_381_bandersnatch/src/lib.rs
@@ -1,37 +0,0 @@
-#![cfg_attr(not(feature = "std"), no_std)]
-#![deny(
-    warnings,
-    unused,
-    future_incompatible,
-    nonstandard_style,
-    rust_2018_idioms
-)]
-#![forbid(unsafe_code)]
-
-//! This library implements the Bendersnatch curve, a twisted Edwards curve
-//! whose base field is the scalar field of the curve BLS12-381. This allows
-//! defining cryptographic primitives that use elliptic curves over the scalar
-//! field of the latter curve. This curve was generated by Simon Masson from Anoma,
-//! and Antonio Sanso from Ethereum Foundation, and is also known as [bandersnatch](https://ethresear.ch/t/introducing-bandersnatch-a-fast-elliptic-curve-built-over-the-bls12-381-scalar-field/9957).
-//!
-//! See [here](https://github.com/asanso/Bandersnatch/blob/main/README.md) for the specification of the curve.
-//! There was also a Python implementation [here](https://github.com/asanso/Bandersnatch/).
-//!
-//! Curve information:
-//! * Base field: q =
-//!   52435875175126190479447740508185965837690552500527637822603658699938581184513
-//! * Scalar field: r =
-//!   13108968793781547619861935127046491459309155893440570251786403306729687672801
-//! * Valuation(q - 1, 2) = 32
-//! * Valuation(r - 1, 2) = 5
-//! * Curve equation: ax^2 + y^2 =1 + dx^2y^2, where
-//!    * a = -5
-//!    * d = 45022363124591815672509500913686876175488063829319466900776701791074614335719
-
-#[cfg(feature = "r1cs")]
-pub mod constraints;
-mod curves;
-mod fields;
-
-pub use curves::*;
-pub use fields::*;
--- a/ed_on_bn254/Cargo.toml
+++ b/ed_on_bn254/Cargo.toml
@@ -1,31 +1,31 @@
 [package]
 name = "ark-ed-on-bn254"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the BN254 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-bn254/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-bn254 = { version = "^0.3.0", path = "../bn254", default-features = false, features = [ "scalar_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-bn254 = { path = "../bn254", default-features = false, features = [ "scalar_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-bn254/std" ]
-r1cs = ["ark-r1cs-std"]
+r1cs = ["ark-r1cs-std"]
--- a/ed_on_bn254/src/constraints/curves.rs
+++ b/ed_on_bn254/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;

+use crate::constraints::FqVar;
+
 /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
+pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<_, EdwardsVar>().unwrap();
 }
--- a/ed_on_bw6_761/Cargo.toml
+++ b/ed_on_bw6_761/Cargo.toml
@@ -1,25 +1,25 @@
 [package]
 name = "ark-ed-on-bw6-761"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the BW6-761 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-bw6-761/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [dependencies]
-ark-ed-on-cp6-782 = { version = "^0.3.0", path = "../ed_on_cp6_782", default-features = false }
+ark-ed-on-cp6-782 = { path = "../ed_on_cp6_782", default-features = false }

 [dev-dependencies]
-ark-relations = { version = "^0.3.0", default-features = false }
-ark-r1cs-std = { version = "^0.3.0", default-features = false }
-ark-ff = { version = "^0.3.0", default-features = false }
-ark-std = { version = "^0.3.0", default-features = false }
+ark-relations = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }

 [features]
 default = []
--- a/ed_on_bw6_761/src/lib.rs
+++ b/ed_on_bw6_761/src/lib.rs
@@ -4,7 +4,7 @@
 //! curve BW6_761.  *It is the same curve as that in `ark-ed_on_cp6_782`.*
 //! This allows defining cryptographic primitives that use elliptic curves over the scalar field of
 //! the latter curve.  This curve was generated as part of the paper
-//! [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
+//! [[BCGMMW20, “Zexe”]](https://eprint.iacr.org/2018/962).
 //!
 //! Curve information:
 //! * Base field: q = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
--- a/ed_on_cp6_782/Cargo.toml
+++ b/ed_on_cp6_782/Cargo.toml
@@ -1,28 +1,28 @@
 [package]
 name = "ark-ed-on-cp6-782"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the CP6-782 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-cp6-782/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-bls12-377 = { version = "^0.3.0", path = "../bls12_377", default-features = false, features = [ "base_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-bls12-377 = { path = "../bls12_377", default-features = false, features = [ "base_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/ed_on_cp6_782/src/constraints/curves.rs
+++ b/ed_on_cp6_782/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;

+use crate::constraints::FqVar;
+
 /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
+pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
 }
--- a/ed_on_cp6_782/src/lib.rs
+++ b/ed_on_cp6_782/src/lib.rs
@@ -10,7 +10,7 @@

 //! This library implements a twisted Edwards curve whose base field is the scalar field of the curve CP6.
 //! This allows defining cryptographic primitives that use elliptic curves over the scalar field of the latter curve.
-//! This curve was generated as part of the paper [\[BCGMMW20, “Zexe”\]](https://eprint.iacr.org/2018/962).
+//! This curve was generated as part of the paper [[BCGMMW20, “Zexe”]](https://eprint.iacr.org/2018/962).
 //!
 //! Curve information:
 //! * Base field: q = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177
--- a/ed_on_mnt4_298/Cargo.toml
+++ b/ed_on_mnt4_298/Cargo.toml
@@ -1,28 +1,28 @@
 [package]
 name = "ark-ed-on-mnt4-298"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the MNT4-298 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-mnt4-298/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-mnt4-298 = { version = "^0.3.0", path = "../mnt4_298", default-features = false, features = [ "scalar_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-mnt4-298 = { path = "../mnt4_298", default-features = false, features = [ "scalar_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/ed_on_mnt4_298/src/constraints/curves.rs
+++ b/ed_on_mnt4_298/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;

+use crate::constraints::fields::FqVar;
+
 /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
+pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
 }
--- a/ed_on_mnt4_753/Cargo.toml
+++ b/ed_on_mnt4_753/Cargo.toml
@@ -1,31 +1,31 @@
 [package]
 name = "ark-ed-on-mnt4-753"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "A Twisted Edwards curve defined over the scalar field of the MNT4-753 curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-ed-on-mnt4-753/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+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"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-mnt4-753 = { version = "^0.3.0", path = "../mnt4_753", default-features = false, features = [ "scalar_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-mnt4-753 = { path = "../mnt4_753", default-features = false, features = [ "scalar_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std", "ark-mnt4-753/std" ]
-r1cs = ["ark-r1cs-std"]
+r1cs = ["ark-r1cs-std"]
--- a/ed_on_mnt4_753/src/constraints/curves.rs
+++ b/ed_on_mnt4_753/src/constraints/curves.rs
@@ -1,10 +1,12 @@
-use crate::*;
 use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;
+use crate::*;
+
+use crate::constraints::fields::FqVar;

 /// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<EdwardsParameters>;
+pub type EdwardsVar = AffineVar<EdwardsParameters, FqVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
 }
--- a/ed_on_mnt4_753/src/constraints/fields.rs
+++ b/ed_on_mnt4_753/src/constraints/fields.rs
@@ -1,5 +1,5 @@
-use crate::fq::Fq;
 use ark_r1cs_std::fields::fp::FpVar;
+use crate::fq::Fq;

 /// A variable that is the R1CS equivalent of `crate::Fq`.
 pub type FqVar = FpVar<Fq>;
--- a/ed_on_mnt4_753/src/curves/mod.rs
+++ b/ed_on_mnt4_753/src/curves/mod.rs
@@ -2,7 +2,7 @@ use ark_ec::{
    models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
    twisted_edwards_extended::{GroupAffine, GroupProjective},
 };
-use ark_ff::field_new;
+use ark_ff::{biginteger::BigInteger768, field_new};

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

@@ -20,22 +20,75 @@ impl ModelParameters for EdwardsParameters {
    type ScalarField = Fr;
 }

+// Many parameters need to be written down in the Montgomery residue form,
+// discussed below. Some useful numbers:
+// R for Fq: 11407975440035778516953587871987109648531742722982233186120790377529569367095961954159305159259556262528904776132787438725571821295685691762729353555475679813615501328617736020411951837995932262333059670631633855898874183380802
+// R for Fr: 933352698056040166367534174176950366489065242993745918174914647273231163953185260894581718311971532174387033963715296372791285468903747270837716556902938133611910788060028435531754797383796835009316018259656953442114538695438
+
 impl TEModelParameters for EdwardsParameters {
    /// COEFF_A = -1
+    /// Needs to be in the Montgomery residue form in Fq
+    /// I.e., -1 * R for Fq
+    ///     = 30490515527883174885390626919253527479638967196971715885662712543495783445475144818899588604530782658889166195755671038597601236195908163306966888299320716352105914996732328421058466299850466207278876048428274308321910292779199
    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "-1");
+    const COEFF_A: Fq = field_new!(Fq, BigInteger768([
+        2265581976117350591u64,
+        18442012872391748519u64,
+        3807704300793525789u64,
+        12280644139289115082u64,
+        10655371227771325282u64,
+        1346491763263331896u64,
+        7477357615964975877u64,
+        12570239403004322603u64,
+        2180620924574446161u64,
+        12129628062772479841u64,
+        8853285699251153944u64,
+        362282887012814u64,
+    ]));

    /// COEFF_D = 317690
+    /// Needs to be in the Montgomery residue form in Fq
+    /// I.e., 317690 * R for Fq
+    ///     = 22147310944926701613095824060993292411108298129020138512675871596899298127988454048404371067902679066037332245471578749765607461010546427833106841035248048771826362113332201923280907352099197626899000000763383579702914883060881
    #[rustfmt::skip]
-    const COEFF_D: Fq = field_new!(Fq, "317690");
+    const COEFF_D: Fq = field_new!(Fq, BigInteger768([
+        17599538631181665425u64,
+        541385733032329781u64,
+        10984951882154109942u64,
+        6745898816867096302u64,
+        8606788232777167026u64,
+        17697068798460151905u64,
+        7726746940317276687u64,
+        16708084840201435716u64,
+        10141323747759975110u64,
+        6527904409415579649u64,
+        18367733563217133340u64,
+        263150412834478u64,
+    ]));

    /// COFACTOR = 8
    const COFACTOR: &'static [u64] = &[8];

    /// COFACTOR_INV (mod r) =
    /// 4582647449616135528381398492791944685893671397494963179726320631987147963874964803303316505414568319530101512550297775574042810022553679071007001162683923594233560231270043634777390699589793776691858866199511300853468155295505
+    /// Needs to be in the Montgomery residue form in Fr
+    /// I.e., COFACTOR_INV * R for Fr
+    ///     = 1425996930004472314619198483998388706066467840372779148265098797191196170886995244269913144907444532816113097116978062210611142118628305286285286330379702579339648914584658878663580978127201397716695606910888919424112361707074
    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "4582647449616135528381398492791944685893671397494963179726320631987147963874964803303316505414568319530101512550297775574042810022553679071007001162683923594233560231270043634777390699589793776691858866199511300853468155295505");
+    const COFACTOR_INV: Fr = field_new!(Fr, BigInteger768([
+        18349096995079034434u64,
+        12232096963923221952u64,
+        10313403112747203584u64,
+        7266093872567585103u64,
+        9102010985112647012u64,
+        11539789563873699451u64,
+        5062476400815403157u64,
+        3112383580531982668u64,
+        9803941911066678468u64,
+        11670110706913295633u64,
+        5956199581925454898u64,
+        16943442107464u64,
+    ]));

    /// Generated randomly
    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
@@ -51,22 +104,85 @@ impl TEModelParameters for EdwardsParameters {

 impl MontgomeryModelParameters for EdwardsParameters {
    /// COEFF_A = 40212480635445336270302172549278415015971955924352275480357619589919378421241453024646804979794897776496091377551124233752850182852486874251193367187677349266115879541798515219680194853352256809837126277708211496794264654247419
+    /// Needs to be in the Montgomery residue form in Fq
+    /// I.e., COEFF_A * R for Fq
+    ///     = 30548714567617468394128273134168309733495884043859854416819409495212098575586848195824755026287273763308450716502830186864520759966983420083939453225231731740328282532297868204762840705631404761799649264638732114864775402781225
    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "40212480635445336270302172549278415015971955924352275480357619589919378421241453024646804979794897776496091377551124233752850182852486874251193367187677349266115879541798515219680194853352256809837126277708211496794264654247419");
-
+    const COEFF_A: Fq = field_new!(Fq, BigInteger768([
+        4717325759818398249u64,
+        9984799932299155706u64,
+        1320735555238925850u64,
+        17027346723122076572u64,
+        2632519042034336982u64,
+        15439824589583270152u64,
+        8351651296737343223u64,
+        11351622927160584696u64,
+        3108522085485690820u64,
+        6958456540352275598u64,
+        16034686916204205245u64,
+        362974397660347u64,
+    ]));
    /// COEFF_B = 1686010332473617132042042241962222112198753995601673591425883331105974391329653748412088783995441144921979594337334243570322874639106980818502874667119046899605536783551549221790223284494141659774809441351696667426519821912580
+    /// Needs to be in the Montgomery residue form in Fq
+    //  I.e., COEFF_B * R for Fq
+    //      = 30432316488148881376652980704338745225782050350083577354506015591779468315363441441974422182774291554469881675008511890330681712424832906529994323373409700963883547461166788637354091894069527652758102832217816501779045182777173
    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "1686010332473617132042042241962222112198753995601673591425883331105974391329653748412088783995441144921979594337334243570322874639106980818502874667119046899605536783551549221790223284494141659774809441351696667426519821912580");
+    const COEFF_B: Fq = field_new!(Fq, BigInteger768([
+        18260582266125854549u64,
+        8452481738774789715u64,
+        6294673046348125729u64,
+        7533941555456153592u64,
+        231479339798761966u64,
+        5699903010652945257u64,
+        6603063935192608530u64,
+        13788855878848060510u64,
+        1252719763663201502u64,
+        17300799585192684084u64,
+        1671884482298102643u64,
+        361591376365281u64,
+    ]));

    type TEModelParameters = EdwardsParameters;
 }

 /// GENERATOR_X =
 /// 41126137307536311801428235632419266329480236393691483739251051053325519918069469184425962602019877935619960143044210127218431046103600632347238890180171944971817510488009355627861577881883236134824745174469522277738875418206826
+/// Needs to be in the Montgomery residue form in Fq
+/// I.e., GENERATOR_X * R for Fq
+///     = 17458296603084005843875564204476809882690765950143935590811069375604430769391871724158635621148427226413334766092842987247361751645959801401160673759590522483750685475882467271029344718076741595831312033991612062403782328664175
 #[rustfmt::skip]
-const GENERATOR_X: Fq = field_new!(Fq, "41126137307536311801428235632419266329480236393691483739251051053325519918069469184425962602019877935619960143044210127218431046103600632347238890180171944971817510488009355627861577881883236134824745174469522277738875418206826");
+const GENERATOR_X: Fq = field_new!(Fq, BigInteger768([
+    13391543849638641775u64,
+    1472718285337442467u64,
+    1704796371472020786u64,
+    1309193942690519845u64,
+    11187264906425773918u64,
+    11963130799714018220u64,
+    10821241385017749516u64,
+    4661882526685671286u64,
+    8328914571224024668u64,
+    17202160931109725769u64,
+    4708938015393622850u64,
+    207436377712515u64,
+]));

 /// GENERATOR_Y =
 /// 18249602579663240810999977712212098844157230095713722119136881953011435881503578209163288529034825612841855863913294174196656077002578342108932925693640046298989762289691399012056048139253937882385653600831389370198228562812681
+/// Needs to be in the Montgomery residue form in Fq
+/// I.e., GENERATOR_Y * R for Fq
+///     = 9017791529346511307345374145466037779022974291216533108328228023141994468888559894991603799439817566592668010556604996318161436165296215592281656017954181737938978992370627048110847574165717052386876801764386102664064737203581
 #[rustfmt::skip]
-const GENERATOR_Y: Fq = field_new!(Fq, "18249602579663240810999977712212098844157230095713722119136881953011435881503578209163288529034825612841855863913294174196656077002578342108932925693640046298989762289691399012056048139253937882385653600831389370198228562812681");
+const GENERATOR_Y: Fq = field_new!(Fq, BigInteger768([
+    16764059510974436733u64,
+    10694630934032454957u64,
+    15899992550979352399u64,
+    17663221529566141065u64,
+    3780246386961240559u64,
+    6062186621379836072u64,
+    11042203340250178810u64,
+    1263100291243127914u64,
+    14407501552666806512u64,
+    13385165116432280059u64,
+    11978187531853934313u64,
+    107147796394053u64,
+]));
--- a/ed_on_mnt4_753/src/curves/tests.rs
+++ b/ed_on_mnt4_753/src/curves/tests.rs
@@ -1,6 +1,6 @@
 use ark_ec::{AffineCurve, ProjectiveCurve};
-use ark_std::rand::Rng;
 use ark_std::test_rng;
+use ark_std::rand::Rng;

 use crate::*;

--- a/ed_on_mnt4_753/src/fields/tests.rs
+++ b/ed_on_mnt4_753/src/fields/tests.rs
@@ -1,5 +1,5 @@
-use ark_std::rand::Rng;
 use ark_std::test_rng;
+use ark_std::rand::Rng;

 use crate::{Fq, Fr};
 use ark_algebra_test_templates::fields::*;
--- a/ed_on_mnt4_753/src/lib.rs
+++ b/ed_on_mnt4_753/src/lib.rs
@@ -21,10 +21,10 @@
 //!    * a = -1
 //!    * d = 317690 mod q

-#[cfg(feature = "r1cs")]
-pub mod constraints;
 mod curves;
 mod fields;
+#[cfg(feature = "r1cs")]
+pub mod constraints;

 pub use curves::*;
 pub use fields::*;
--- a/mnt4_298/Cargo.toml
+++ b/mnt4_298/Cargo.toml
@@ -1,27 +1,27 @@
 [package]
 name = "ark-mnt4-298"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The MNT4-298 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-mnt4-298/"
-keywords = ["cryptography", "finite-fields" ]
+keywords = ["cryptography", "finite fields" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/mnt4_298/src/constraints/curves.rs
+++ b/mnt4_298/src/constraints/curves.rs
@@ -16,8 +16,14 @@ pub type G2PreparedVar = mnt4::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
    use ark_ec::models::mnt4::MNT4Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G1Parameters>()
-        .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G2Parameters>()
-        .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT4Parameters>::G1Parameters,
+        G1Var,
+    >()
+    .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT4Parameters>::G2Parameters,
+        G2Var,
+    >()
+    .unwrap();
 }
--- a/mnt4_298/src/constraints/mod.rs
+++ b/mnt4_298/src/constraints/mod.rs
@@ -130,17 +130,17 @@
 //! let pairing_result_native = MNT4_298::pairing(a_native, b_native);
 //!
 //! // Prepare `a` and `b` for pairing.
-//! let a_prep = MNT4_298::prepare_g1(&a)?;
-//! let b_prep = MNT4_298::prepare_g2(&b)?;
-//! let pairing_result = MNT4_298::pairing_gadget(a_prep, b_prep)?;
+//! let a_prep = constraints::PairingVar::prepare_g1(&a)?;
+//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! 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);
 //!
 //! // Check that operations on variables and constants are equivalent.
-//! let a_prep_const = MNT4_298::prepare_g1(&a_const)?;
-//! let b_prep_const = MNT4_298::prepare_g2(&b_const)?;
-//! let pairing_result_const = MNT4_298::pairing_gadget(a_prep_const, b_prep_const)?;
+//! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;
--- a/mnt4_298/src/constraints/pairing.rs
+++ b/mnt4_298/src/constraints/pairing.rs
@@ -1,8 +1,10 @@
+use crate::Parameters;
+
 /// Specifies the constraints for computing a pairing in the MNT4-298 bilinear group.
-pub use crate::MNT4_298;
+pub type PairingVar = ark_r1cs_std::pairing::mnt4::PairingVar<Parameters>;

 #[test]
 fn test() {
    use crate::MNT4_298;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_298>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_298, PairingVar>().unwrap()
 }
--- a/mnt4_298/src/curves/g1.rs
+++ b/mnt4_298/src/curves/g1.rs
@@ -19,12 +19,12 @@ impl ModelParameters for Parameters {

 impl SWModelParameters for Parameters {
    /// COEFF_A = 2
-    /// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L116>
+    /// Reference: https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L116
    #[rustfmt::skip]
    const COEFF_A: Fq = field_new!(Fq, "2");

    /// COEFF_B = 423894536526684178289416011533888240029318103673896002803341544124054745019340795360841685
-    /// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L117>
+    /// Reference: https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L117
    #[rustfmt::skip]
    const COEFF_B: Fq = field_new!(Fq, "423894536526684178289416011533888240029318103673896002803341544124054745019340795360841685");

@@ -45,11 +45,11 @@ impl SWModelParameters for Parameters {
 // X = 60760244141852568949126569781626075788424196370144486719385562369396875346601926534016838,
 // Y = 363732850702582978263902770815145784459747722357071843971107674179038674942891694705904306,
 /// G1_GENERATOR_X
-/// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L137>
+/// Reference: https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L137
 #[rustfmt::skip]
 pub const G1_GENERATOR_X: Fq = field_new!(Fq, "60760244141852568949126569781626075788424196370144486719385562369396875346601926534016838");

 /// G1_GENERATOR_Y
-/// Reference: <https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L138>
+/// Reference: https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L138
 #[rustfmt::skip]
 pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "363732850702582978263902770815145784459747722357071843971107674179038674942891694705904306");
--- a/mnt4_298/src/lib.rs
+++ b/mnt4_298/src/lib.rs
@@ -9,7 +9,7 @@
 #![forbid(unsafe_code)]

 //! This library implements the MNT4_298 curve generated by
-//! [\[BCTV14\]](https://eprint.iacr.org/2014/595).  The name denotes that it is a
+//! [[BCTV14]](https://eprint.iacr.org/2014/595).  The name denotes that it is a
 //! Miyaji--Nakabayashi--Takano curve of embedding degree 4, defined over a 298-bit (prime) field.
 //! The main feature of this curve is that its scalar field and base field respectively equal the
 //! base field and scalar field of MNT6_298.
--- a/mnt4_753/Cargo.toml
+++ b/mnt4_753/Cargo.toml
@@ -1,27 +1,27 @@
 [package]
 name = "ark-mnt4-753"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The MNT4-753 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-mnt4-753/"
-keywords = ["cryptography", "finite-fields" ]
+keywords = ["cryptography", "finite fields" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/mnt4_753/src/constraints/curves.rs
+++ b/mnt4_753/src/constraints/curves.rs
@@ -16,8 +16,14 @@ pub type G2PreparedVar = mnt4::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
    use ark_ec::models::mnt4::MNT4Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G1Parameters>()
-        .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G2Parameters>()
-        .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT4Parameters>::G1Parameters,
+        G1Var,
+    >()
+    .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT4Parameters>::G2Parameters,
+        G2Var,
+    >()
+    .unwrap();
 }
--- a/mnt4_753/src/constraints/mod.rs
+++ b/mnt4_753/src/constraints/mod.rs
@@ -130,17 +130,17 @@
 //! let pairing_result_native = MNT4_753::pairing(a_native, b_native);
 //!
 //! // Prepare `a` and `b` for pairing.
-//! let a_prep = MNT4_753::prepare_g1(&a)?;
-//! let b_prep = MNT4_753::prepare_g2(&b)?;
-//! let pairing_result = MNT4_753::pairing_gadget(a_prep, b_prep)?;
+//! let a_prep = constraints::PairingVar::prepare_g1(&a)?;
+//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! 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);
 //!
 //! // Check that operations on variables and constants are equivalent.
-//! let a_prep_const = MNT4_753::prepare_g1(&a_const)?;
-//! let b_prep_const = MNT4_753::prepare_g2(&b_const)?;
-//! let pairing_result_const = MNT4_753::pairing_gadget(a_prep_const, b_prep_const)?;
+//! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;
--- a/mnt4_753/src/constraints/pairing.rs
+++ b/mnt4_753/src/constraints/pairing.rs
@@ -1,8 +1,10 @@
+use crate::Parameters;
+
 /// Specifies the constraints for computing a pairing in the MNT4-753 bilinear group.
-pub use crate::MNT4_753;
+pub type PairingVar = ark_r1cs_std::pairing::mnt4::PairingVar<Parameters>;

 #[test]
 fn test() {
    use crate::MNT4_753;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_753>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_753, PairingVar>().unwrap()
 }
--- a/mnt4_753/src/lib.rs
+++ b/mnt4_753/src/lib.rs
@@ -9,7 +9,7 @@
 #![forbid(unsafe_code)]

 //! This library implements the MNT4_753 curve generated in
-//! [\[BCTV14\]](https://eprint.iacr.org/2014/595). The name denotes that it is a
+//! [[BCTV14]](https://eprint.iacr.org/2014/595). The name denotes that it is a
 //! Miyaji--Nakabayashi--Takano curve of embedding degree 4, defined over a 753-bit (prime) field.
 //! The main feature of this curve is that its scalar field and base field respectively equal the
 //! base field and scalar field of MNT6_753.
--- a/mnt6_298/Cargo.toml
+++ b/mnt6_298/Cargo.toml
@@ -1,28 +1,28 @@
 [package]
 name = "ark-mnt6-298"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The MNT6-298 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-mnt6-298/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves"]
+keywords = ["cryptography", "finite fields" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [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-r1cs-std = { version = "^0.3.0", default-features = false, optional = true }
-ark-mnt4-298 = { version = "^0.3.0", path = "../mnt4_298", default-features = false, features = [ "scalar_field", "base_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-mnt4-298 = { path = "../mnt4_298", default-features = false, features = [ "scalar_field", "base_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/mnt6_298/src/constraints/curves.rs
+++ b/mnt6_298/src/constraints/curves.rs
@@ -16,8 +16,14 @@ pub type G2PreparedVar = mnt6::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
    use ark_ec::models::mnt6::MNT6Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G1Parameters>()
-        .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G2Parameters>()
-        .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT6Parameters>::G1Parameters,
+        G1Var,
+    >()
+    .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT6Parameters>::G2Parameters,
+        G2Var,
+    >()
+    .unwrap();
 }
--- a/mnt6_298/src/constraints/mod.rs
+++ b/mnt6_298/src/constraints/mod.rs
@@ -130,17 +130,17 @@
 //! let pairing_result_native = MNT6_298::pairing(a_native, b_native);
 //!
 //! // Prepare `a` and `b` for pairing.
-//! let a_prep = MNT6_298::prepare_g1(&a)?;
-//! let b_prep = MNT6_298::prepare_g2(&b)?;
-//! let pairing_result = MNT6_298::pairing_gadget(a_prep, b_prep)?;
+//! let a_prep = constraints::PairingVar::prepare_g1(&a)?;
+//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! 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);
 //!
 //! // Check that operations on variables and constants are equivalent.
-//! let a_prep_const = MNT6_298::prepare_g1(&a_const)?;
-//! let b_prep_const = MNT6_298::prepare_g2(&b_const)?;
-//! let pairing_result_const = MNT6_298::pairing_gadget(a_prep_const, b_prep_const)?;
+//! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;
--- a/mnt6_298/src/constraints/pairing.rs
+++ b/mnt6_298/src/constraints/pairing.rs
@@ -1,8 +1,10 @@
+use crate::Parameters;
+
 /// Specifies the constraints for computing a pairing in the MNT6-298 bilinear group.
-pub use crate::MNT6_298;
+pub type PairingVar = ark_r1cs_std::pairing::mnt6::PairingVar<Parameters>;

 #[test]
 fn test() {
    use crate::MNT6_298;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_298>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_298, PairingVar>().unwrap()
 }
--- a/mnt6_298/src/lib.rs
+++ b/mnt6_298/src/lib.rs
@@ -9,7 +9,7 @@
 #![forbid(unsafe_code)]

 //! This library implements the MNT6_298 curve generated in
-//! [\[BCTV14\]](https://eprint.iacr.org/2014/595).  The name denotes that it is a
+//! [[BCTV14]](https://eprint.iacr.org/2014/595).  The name denotes that it is a
 //! Miyaji--Nakabayashi--Takano curve of embedding degree 6, defined over a 298-bit (prime) field.
 //! The main feature of this curve is that its scalar field and base field respectively equal the
 //! base field and scalar field of MNT4_298.
--- a/mnt6_753/Cargo.toml
+++ b/mnt6_753/Cargo.toml
@@ -1,31 +1,31 @@
 [package]
 name = "ark-mnt6-753"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "arkworks contributors" ]
 description = "The MNT6-753 pairing-friendly elliptic curve"
 homepage = "https://arkworks.rs"
-repository = "https://github.com/arkworks-rs/curves"
+repository = "https://github.com/arkworks-rs/algebra"
 documentation = "https://docs.rs/ark-mnt6-753/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+keywords = ["cryptography", "finite fields" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src", "README.md", "LICENSE-APACHE", "LICENSE-MIT"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [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-r1cs-std = {  version = "^0.3.0", default-features = false, optional = true }
-ark-mnt4-753 = { version = "^0.3.0", path = "../mnt4_753", default-features = false, features = [ "scalar_field", "base_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-mnt4-753 = { path = "../mnt4_753", default-features = false, features = [ "scalar_field", "base_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
 default = []
 std = [ "ark-std/std", "ark-ff/std", "ark-ec/std" ]
-r1cs = ["ark-r1cs-std"]
+r1cs = ["ark-r1cs-std"]
--- a/mnt6_753/src/constraints/curves.rs
+++ b/mnt6_753/src/constraints/curves.rs
@@ -16,8 +16,14 @@ pub type G2PreparedVar = mnt6::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
    use ark_ec::models::mnt6::MNT6Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G1Parameters>()
-        .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G2Parameters>()
-        .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT6Parameters>::G1Parameters,
+        G1Var,
+    >()
+    .unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<
+        <Parameters as MNT6Parameters>::G2Parameters,
+        G2Var,
+    >()
+    .unwrap();
 }
--- a/mnt6_753/src/constraints/mod.rs
+++ b/mnt6_753/src/constraints/mod.rs
@@ -130,17 +130,17 @@
 //! let pairing_result_native = MNT6_753::pairing(a_native, b_native);
 //!
 //! // Prepare `a` and `b` for pairing.
-//! let a_prep = MNT6_753::prepare_g1(&a)?;
-//! let b_prep = MNT6_753::prepare_g2(&b)?;
-//! let pairing_result = MNT6_753::pairing_gadget(a_prep, b_prep)?;
+//! let a_prep = constraints::PairingVar::prepare_g1(&a)?;
+//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! 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);
 //!
 //! // Check that operations on variables and constants are equivalent.
-//! let a_prep_const = MNT6_753::prepare_g1(&a_const)?;
-//! let b_prep_const = MNT6_753::prepare_g2(&b_const)?;
-//! let pairing_result_const = MNT6_753::pairing_gadget(a_prep_const, b_prep_const)?;
+//! let a_prep_const = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;
--- a/mnt6_753/src/constraints/pairing.rs
+++ b/mnt6_753/src/constraints/pairing.rs
@@ -1,8 +1,10 @@
+use crate::Parameters;
+
 /// Specifies the constraints for computing a pairing in the MNT6-753 bilinear group.
-pub use crate::MNT6_753;
+pub type PairingVar = ark_r1cs_std::pairing::mnt6::PairingVar<Parameters>;

 #[test]
 fn test() {
    use crate::MNT6_753;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_753>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_753, PairingVar>().unwrap()
 }
--- a/mnt6_753/src/lib.rs
+++ b/mnt6_753/src/lib.rs
@@ -9,7 +9,7 @@
 #![forbid(unsafe_code)]

 //! This library implements the MNT6_753 curve generated in
-//! [\[BCTV14\]](https://eprint.iacr.org/2014/595). The name denotes that it is a
+//! [[BCTV14]](https://eprint.iacr.org/2014/595). The name denotes that it is a
 //! Miyaji--Nakabayashi--Takano curve of embedding degree 6, defined over a 753-bit (prime) field.
 //! The main feature of this curve is that its scalar field and base field respectively equal the
 //! base field and scalar field of MNT4_753.
--- a/pallas/Cargo.toml
+++ b/pallas/Cargo.toml
@@ -1,27 +1,27 @@
 [package]
 name = "ark-pallas"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "Ying Tong Lai", "Daira Hopwood", "O(1) Labs", "arkworks contributors" ]
 description = "The Pallas prime-order elliptic curve"
 homepage = "https://arkworks.rs"
 repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-pallas/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+keywords = ["cryptography", "finite fields", "elliptic curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [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 = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-std = { git = "https://github.com/arkworks-rs/utils", 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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/pallas/src/constraints/curves.rs
+++ b/pallas/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;

+use crate::constraints::FBaseVar;
+
 /// A group element in the Pallas prime-order group.
-pub type GVar = ProjectiveVar<PallasParameters>;
+pub type GVar = ProjectiveVar<PallasParameters, FBaseVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::sw_test::<PallasParameters>().unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<PallasParameters, GVar>().unwrap();
 }
--- a/scripts/linkify_changelog.py
+++ b/scripts/linkify_changelog.py
@@ -1,31 +0,0 @@
-import re
-import sys
-import fileinput
-import os
-
-# Set this to the name of the repo, if you don't want it to be read from the filesystem.
-# It assumes the changelog file is in the root of the repo.
-repo_name = ""
-
-# This script goes through the provided file, and replaces any " \#<number>",
-# with the valid mark down formatted link to it. e.g.
-# " [\#number](https://github.com/arkworks-rs/template/pull/<number>)
-# Note that if the number is for a an issue, github will auto-redirect you when you click the link.
-# It is safe to run the script multiple times in succession. 
-#
-# Example usage $ python3 linkify_changelog.py ../CHANGELOG.md
-if len(sys.argv) < 2:
-    print("Must include path to changelog as the first argument to the script")
-    print("Example Usage: python3 linkify_changelog.py ../CHANGELOG.md")
-    exit()
-
-changelog_path = sys.argv[1]
-if repo_name == "":
-    path = os.path.abspath(changelog_path)
-    components = path.split(os.path.sep)
-    repo_name = components[-2]
-
-for line in fileinput.input(inplace=True):
-    line = re.sub(r"\- #([0-9]*)", r"- [\\#\1](https://github.com/arkworks-rs/" + repo_name + r"/pull/\1)", line.rstrip())
-    # edits the current file
-    print(line)
--- a/vesta/Cargo.toml
+++ b/vesta/Cargo.toml
@@ -1,28 +1,28 @@
 [package]
 name = "ark-vesta"
-version = "0.3.0"
+version = "0.1.0"
 authors = [ "Ying Tong Lai", "Daira Hopwood", "O(1) Labs", "arkworks contributors" ]
 description = "The Vesta prime-order elliptic curve"
 homepage = "https://arkworks.rs"
 repository = "https://github.com/arkworks-rs/curves"
 documentation = "https://docs.rs/ark-vesta/"
-keywords = ["cryptography", "finite-fields", "elliptic-curves" ]
+keywords = ["cryptography", "finite fields", "elliptic curves" ]
 categories = ["cryptography"]
 include = ["Cargo.toml", "src"]
 license = "MIT/Apache-2.0"
 edition = "2018"

 [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-pallas = { version = "^0.3.0", path = "../pallas", default-features = false, features = [ "scalar_field", "base_field" ] }
+ark-ff = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-ec = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-r1cs-std = {  git = "https://github.com/arkworks-rs/r1cs-std", default-features = false, optional = true }
+ark-std = { git = "https://github.com/arkworks-rs/utils", default-features = false }
+ark-pallas = { path = "../pallas", default-features = false, features = [ "scalar_field", "base_field" ] }

 [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 = { git = "https://github.com/arkworks-rs/snark", default-features = false }
+ark-serialize = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
+ark-algebra-test-templates = { git = "https://github.com/arkworks-rs/algebra", default-features = false }
 ark-curve-constraint-tests = { path = "../curve-constraint-tests", default-features = false }

 [features]
--- a/vesta/src/constraints/curves.rs
+++ b/vesta/src/constraints/curves.rs
@@ -1,10 +1,12 @@
 use crate::*;
 use ark_r1cs_std::groups::curves::short_weierstrass::ProjectiveVar;

+use crate::constraints::FBaseVar;
+
 /// A group element in the Vesta prime-order group.
-pub type GVar = ProjectiveVar<VestaParameters>;
+pub type GVar = ProjectiveVar<VestaParameters, FBaseVar>;

 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::sw_test::<VestaParameters>().unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<VestaParameters, GVar>().unwrap();
 }
Author	SHA1	Message	Date
Dev Ojha	53dd4de35b	Merge branch 'master' into fq2_neg_nonresidue	2021-02-06 00:39:52 -06:00
ValarDragon	cd60d33bcb	new add + mul by residue + 1	2021-02-05 20:13:02 -06:00
ValarDragon	64ece6414f	Add optimization for bls12_381 and bn254	2021-02-05 12:48:57 -06:00
ValarDragon	bb033e9949	Use negative non-residue optimization	2021-02-05 11:53:30 -06:00
				`@@ -1 +0,0 @@`
				`pub use ark_bls12_381::{Fr as Fq, FrParameters as FqParameters};`