Fix doctests

CHANGELOG.md

@@ -2,16 +2,12 @@
 
 ## Pending
 
-- [\#76](https://github.com/arkworks-rs/curves/pull/76) twisted Edwards parameters for bls12-377
-
 ### Breaking changes
 
 ### Features
 
 ### Improvements
 
-- [\#74](https://github.com/arkworks-rs/curves/pull/74) Use Scott's subgroup membership tests for `G1` and `G2` of BLS12-381.
-
 ### Bug fixes
 
 ## v0.3.0 

Cargo.toml

@@ -57,8 +57,5 @@ incremental = true
 debug-assertions = true
 debug = true
 
-# To be removed in the new release.
 [patch.crates-io]
-ark-ec = { git = "https://github.com/arkworks-rs/algebra" }
+ark-r1cs-std = { git = "https://github.com/arkworks-rs/r1cs-std", branch = "reduce-generics", optional = true, default-features = false }
-ark-ff = { git = "https://github.com/arkworks-rs/algebra" }
-ark-serialize = { git = "https://github.com/arkworks-rs/algebra" }

bls12_377/Cargo.toml

@@ -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" ]

bls12_377/src/constraints/curves.rs

@@ -1,22 +1,11 @@
 use crate::Parameters;
-use ark_ec::bls12::Bls12Parameters;
+use ark_r1cs_std::groups::bls12;
-use ark_ec::ModelParameters;
-use ark_r1cs_std::{
-    fields::fp::FpVar,
-    groups::{bls12, curves::twisted_edwards::AffineVar as TEAffineVar},
-};
 
 /// An element of G1 in the BLS12-377 bilinear group.
 pub type G1Var = bls12::G1Var<Parameters>;
 /// An element of G2 in the BLS12-377 bilinear group.
 pub type G2Var = bls12::G2Var<Parameters>;
 
-/// An element of G1 (in TE Affine form) in the BLS12-377 bilinear group.
-pub type G1TEAffineVar = TEAffineVar<
-    <Parameters as Bls12Parameters>::G1Parameters,
-    FpVar<<<Parameters as Bls12Parameters>::G1Parameters as ModelParameters>::BaseField>,
->;
-
 /// Represents the cached precomputation that can be performed on a G1 element
 /// which enables speeding up pairing computation.
 pub type G1PreparedVar = bls12::G1PreparedVar<Parameters>;
@@ -27,19 +16,8 @@ pub type G2PreparedVar = bls12::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
     use ark_ec::models::bls12::Bls12Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as Bls12Parameters>::G1Parameters>()
-        <Parameters as Bls12Parameters>::G1Parameters,
+        .unwrap();
-        G1Var,
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as Bls12Parameters>::G2Parameters>()
-    >()
+        .unwrap();
-    .unwrap();
-    ark_curve_constraint_tests::curves::te_test::<
-        <Parameters as Bls12Parameters>::G1Parameters,
-        G1TEAffineVar,
-    >()
-    .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<
-        <Parameters as Bls12Parameters>::G2Parameters,
-        G2Var,
-    >()
-    .unwrap();
 }

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 = constraints::PairingVar::prepare_g1(&a)?;
+//! let a_prep = Bls12_377::prepare_g1(&a)?;
-//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! let b_prep = Bls12_377::prepare_g2(&b)?;
-//! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
+//! let pairing_result = Bls12_377::pairing_gadget(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 = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let a_prep_const = Bls12_377::prepare_g1(&a_const)?;
-//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let b_prep_const = Bls12_377::prepare_g2(&b_const)?;
-//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
+//! let pairing_result_const = Bls12_377::pairing_gadget(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;

bls12_377/src/constraints/pairing.rs

@@ -1,10 +1,8 @@
-use crate::Parameters;
-
 /// Specifies the constraints for computing a pairing in the BLS12-377 bilinear group.
-pub type PairingVar = ark_r1cs_std::pairing::bls12::PairingVar<Parameters>;
+pub use crate::Bls12_377;
 
 #[test]
 fn test() {
     use crate::Bls12_377;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<Bls12_377, PairingVar>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<Bls12_377>().unwrap()
 }

bls12_377/src/curves/g1.rs

@@ -1,11 +1,5 @@
-use ark_ec::models::{
+use ark_ec::models::{ModelParameters, SWModelParameters};
-    twisted_edwards_extended::{
-        GroupAffine as TEGroupAffine, GroupProjective as TEGroupProjective,
-    },
-    ModelParameters, MontgomeryModelParameters, SWModelParameters, TEModelParameters,
-};
 use ark_ff::{field_new, Zero};
-use core::ops::Neg;
 
 use crate::{
     fields::{FQ_ONE, FQ_ZERO},
@@ -46,129 +40,6 @@ impl SWModelParameters for Parameters {
     }
 }
 
-pub type G1TEAffine = TEGroupAffine<Parameters>;
-pub type G1TEProjective = TEGroupProjective<Parameters>;
-
-/// Bls12_377::G1 also has a twisted Edwards form.
-/// It can be obtained via the following script, implementing
-/// 1. SW -> Montgomery -> TE1 transformation: <https://en.wikipedia.org/wiki/Montgomery_curve>
-/// 2. TE1 -> TE2 normalization (enforcing `a = -1`)
-/// ``` sage
-///
-/// # modulus
-/// p = 0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001
-/// Fp = Zmod(p)
-///
-/// #####################################################
-/// # Weierstrass curve: y² = x³ + A * x + B
-/// #####################################################
-/// # curve y^2 = x^3 + 1
-/// WA = Fp(0)
-/// WB = Fp(1)
-///
-/// #####################################################
-/// # Montgomery curve: By² = x³ + A * x² + x
-/// #####################################################
-/// # root for x^3 + 1 = 0
-/// alpha = -1
-/// # s = 1 / (sqrt(3alpha^2 + a))
-/// s = 1/(Fp(3).sqrt())
-///
-/// # MA = 3 * alpha * s
-/// MA = Fp(228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384)
-/// # MB = s
-/// MB = Fp(10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931)
-///
-/// # #####################################################
-/// # # Twisted Edwards curve 1: a * x² + y² = 1 + d * x² * y²
-/// # #####################################################
-/// # We first convert to TE form obtaining a curve with a != -1, and then
-/// # apply a transformation to obtain a TE curve with a = -1.
-/// # a = (MA+2)/MB
-/// TE1a = Fp(61134141799337779744243169579317764548490943457438569789767076791016838392692895365021181670618017873462480451583)
-/// # b = (MA-2)/MB
-/// TE1d = Fp(197530284213631314266409564115575768987902569297476090750117185875703629955647927409947706468955342250977841006588)
-///
-/// # #####################################################
-/// # # Twisted Edwards curve 2: a * x² + y² = 1 + d * x² * y²
-/// # #####################################################
-/// # a = -1
-/// TE2a = Fp(-1)
-/// # b = -TE1d/TE1a
-/// TE2d = Fp(122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179)
-///
-/// ```
-impl TEModelParameters for Parameters {
-    /// COEFF_A = -1
-    const COEFF_A: Fq = field_new!(Fq, "-1");
-
-    /// COEFF_D = 122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179 mod q
-    #[rustfmt::skip]
-    const COEFF_D: Fq = field_new!(Fq, "122268283598675559488486339158635529096981886914877139579534153582033676785385790730042363341236035746924960903179");
-
-    /// COFACTOR = (x - 1)^2 / 3  = 30631250834960419227450344600217059328
-    const COFACTOR: &'static [u64] = &[0x0, 0x170b5d4430000000];
-
-    /// COFACTOR_INV = COFACTOR^{-1} mod r
-    /// = 5285428838741532253824584287042945485047145357130994810877
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "5285428838741532253824584287042945485047145357130994810877");
-
-    /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (TE_GENERATOR_X, TE_GENERATOR_Y);
-
-    type MontgomeryModelParameters = Parameters;
-
-    /// Multiplication by `a` is multiply by `-1`.
-    #[inline(always)]
-    fn mul_by_a(elem: &Self::BaseField) -> Self::BaseField {
-        elem.neg()
-    }
-}
-
-// BLS12-377::G1 also has a Montgomery form.
-// BLS12-377::G1 also has a twisted Edwards form.
-// It can be obtained via the following script, implementing
-// SW -> Montgomery transformation: <https://en.wikipedia.org/wiki/Montgomery_curve>
-// ``` sage
-//
-// # modulus
-// p=0x1ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001
-// Fp=Zmod(p)
-//
-// #####################################################
-// # Weierstrass curve: y² = x³ + A * x + B
-// #####################################################
-// # curve y^2 = x^3 + 1
-// WA=Fp(0)
-// WB=Fp(1)
-//
-// #####################################################
-// # Montgomery curve: By² = x³ + A * x² + x
-// #####################################################
-// # root for x^3 + 1 = 0
-// alpha = -1
-// # s = 1 / (sqrt(3alpha^2 + a))
-// s = 1/(Fp(3).sqrt())
-//
-// # MA = 3 * alpha * s
-// MA=Fp(228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384)
-// # MB = s
-// MB=Fp(10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931)
-// ```
-impl MontgomeryModelParameters for Parameters {
-    /// COEFF_A = 228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384
-    #[rustfmt::skip]
-    const COEFF_A: Fq = field_new!(Fq, "228097355113300204138531148905234651262148041026195375645000724271212049151994375092458297304264351187709081232384");
-
-    /// COEFF_B = 10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931
-    #[rustfmt::skip]
-    const COEFF_B: Fq = field_new!(Fq, "10189023633222963290707194929886294091415157242906428298294512798502806398782149227503530278436336312243746741931");
-
-    type TEModelParameters = Parameters;
-}
-
 /// G1_GENERATOR_X =
 /// 81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695
 #[rustfmt::skip]
@@ -178,56 +49,3 @@ pub const G1_GENERATOR_X: Fq = field_new!(Fq, "819379993731509642399382555734659
 /// 241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030
 #[rustfmt::skip]
 pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030");
-
-// The generator for twisted Edward form is the same SW generator converted into the normalized TE form (TE2).
-// ``` sage
-// # following scripts in previous section
-// #####################################################
-// # Weierstrass curve generator
-// #####################################################
-// Wx = Fp(81937999373150964239938255573465948239988671502647976594219695644855304257327692006745978603320413799295628339695)
-// Wy = Fp(241266749859715473739788878240585681733927191168601896383759122102112907357779751001206799952863815012735208165030)
-//
-// assert(Wy^2 - Wx^3 - WA * Wx - WB == 0)
-//
-// #####################################################
-// # Montgomery curve generator
-// #####################################################
-// # x = s * (x - alpha)
-// Mx = Fp(251803586774461569862800610331871502335378228972505599912537082323947581271784390797244487924068052270360793200630)
-// # y = s * y
-// My = Fp(77739247071951651095607889637653357561348174979132042929587539214321586851215673796661346812932566642719051699820)
-//
-// assert(MB * My^2 == Mx^3+ MA * Mx^2 + Mx)
-//
-// # #####################################################
-// # # Twisted Edwards curve 1 generator
-// # #####################################################
-// # x = Mx/My
-// TE1x = Fp(82241236807150726090333472814441006963902378430536027612759193445733851062772474760677400112551677454953925168208)
-// # y = (Mx - 1)/(Mx+1)
-// TE1y = Fp(6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235)
-//
-// assert( TE1a * TE1x^2 + TE1y^2 == 1 + TE1d * TE1x^2 * TE1y^2 )
-//
-//
-// # #####################################################
-// # # Twisted Edwards curve 2 generator
-// # #####################################################
-// beta = (-TE1a).sqrt()
-// # x = TE1x * sqrt(-TE1a)
-// TE2x = Fp(71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393)
-// # y = TE1y
-// TE2y = Fp(6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235)
-//
-// assert( TE2a * TE2x^2 + TE2y^2 == 1 + TE2d * TE2x^2 * TE2y^2 )
-// ```
-/// TE_GENERATOR_X =
-/// 71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393
-#[rustfmt::skip]
-pub const TE_GENERATOR_X: Fq = field_new!(Fq, "71222569531709137229370268896323705690285216175189308202338047559628438110820800641278662592954630774340654489393");
-
-/// TE_GENERATOR_Y =
-/// 6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235
-#[rustfmt::skip]
-pub const TE_GENERATOR_Y: Fq = field_new!(Fq, "6177051365529633638563236407038680211609544222665285371549726196884440490905471891908272386851767077598415378235");

bls12_377/src/curves/mod.rs

@@ -31,5 +31,3 @@ pub type G1Affine = bls12::G1Affine<Parameters>;
 pub type G1Projective = bls12::G1Projective<Parameters>;
 pub type G2Affine = bls12::G2Affine<Parameters>;
 pub type G2Projective = bls12::G2Projective<Parameters>;
-
-pub use g1::{G1TEAffine, G1TEProjective};

bls12_377/src/curves/tests.rs

@@ -1,22 +1,19 @@
 #![allow(unused_imports)]
-use crate::{
-    g1, g2, Bls12_377, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G1TEProjective, G2Affine,
-    G2Projective,
-};
-use ark_ec::{
-    models::SWModelParameters, short_weierstrass_jacobian, AffineCurve, PairingEngine,
-    ProjectiveCurve,
-};
 use ark_ff::{
     fields::{Field, FpParameters, PrimeField, SquareRootField},
     One, Zero,
 };
 use ark_serialize::CanonicalSerialize;
-use ark_std::{rand::Rng, test_rng};
+use ark_std::test_rng;
+
+use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
+use ark_std::rand::Rng;
 use core::ops::{AddAssign, MulAssign};
 
+use crate::{g1, g2, Bls12_377, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
+
 use ark_algebra_test_templates::{
-    curves::{curve_tests, edwards_tests, sw_tests},
+    curves::{curve_tests, sw_tests},
     groups::group_test,
 };
 
@@ -25,7 +22,6 @@ fn test_g1_projective_curve() {
     curve_tests::<G1Projective>();
 
     sw_tests::<g1::Parameters>();
-    edwards_tests::<g1::Parameters>();
 }
 
 #[test]
@@ -34,10 +30,6 @@ fn test_g1_projective_group() {
     let a: G1Projective = rng.gen();
     let b: G1Projective = rng.gen();
     group_test(a, b);
-
-    let c = rng.gen();
-    let d = rng.gen();
-    group_test::<G1TEProjective>(c, d);
 }
 
 #[test]

bls12_377/src/fields/fr.rs

@@ -1,4 +1,4 @@
-//! Bls12-377 scalar field.
+///! Bls12-377 scalar field.
 ///
 /// Roots of unity computed from modulus and R using this sage code:
 ///
@@ -76,8 +76,7 @@ impl FpParameters for FrParameters {
 
     /// GENERATOR = 22
     /// Encoded in Montgomery form, so the value is
-    /// (22 * R) % q =
+    /// (22 * R) % q = 5642976643016801619665363617888466827793962762719196659561577942948671127251
-    /// 5642976643016801619665363617888466827793962762719196659561577942948671127251
     #[rustfmt::skip]
     const GENERATOR: BigInteger = BigInteger([
         2984901390528151251u64,

bls12_377/src/fields/tests.rs

@@ -7,7 +7,8 @@ use ark_ff::{
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
-use ark_std::{rand::Rng, test_rng};
+use ark_std::rand::Rng;
+use ark_std::test_rng;
 use core::{
     cmp::Ordering,
     ops::{AddAssign, MulAssign, SubAssign},

bls12_381/src/curves/g1.rs

@@ -1,13 +1,9 @@
 use crate::*;
 use ark_ec::{
     bls12,
-    bls12::Bls12Parameters,
     models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::GroupAffine,
-    AffineCurve, ProjectiveCurve,
 };
-use ark_ff::{biginteger::BigInteger256, field_new, Zero};
+use ark_ff::{field_new, Zero};
-use ark_std::ops::Neg;
 
 pub type G1Affine = bls12::G1Affine<crate::Parameters>;
 pub type G1Projective = bls12::G1Projective<crate::Parameters>;
@@ -44,25 +40,6 @@ impl SWModelParameters for Parameters {
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
-
-    fn is_in_correct_subgroup_assuming_on_curve(p: &GroupAffine<Parameters>) -> bool {
-        // Algorithm from Section 6 of https://eprint.iacr.org/2021/1130.
-        //
-        // Check that endomorphism_p(P) == -[X^2]P
-
-        let x = BigInteger256::new([crate::Parameters::X[0], 0, 0, 0]);
-
-        // An early-out optimization described in Section 6.
-        // If uP == P but P != point of infinity, then the point is not in the right subgroup.
-        let x_times_p = p.mul(x);
-        if x_times_p.eq(p) && !p.infinity {
-            return false;
-        }
-
-        let minus_x_squared_times_p = x_times_p.mul(x).neg();
-        let endomorphism_p = endomorphism(p);
-        minus_x_squared_times_p.eq(&endomorphism_p)
-    }
 }
 
 /// G1_GENERATOR_X =
@@ -74,14 +51,3 @@ pub const G1_GENERATOR_X: Fq = field_new!(Fq, "368541675371338701678108831518307
 /// 1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569
 #[rustfmt::skip]
 pub const G1_GENERATOR_Y: Fq = field_new!(Fq, "1339506544944476473020471379941921221584933875938349620426543736416511423956333506472724655353366534992391756441569");
-
-/// BETA is a non-trivial cubic root of unity in Fq.
-pub const BETA: Fq = field_new!(Fq, "793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350");
-
-pub fn endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
-    // Endomorphism of the points on the curve.
-    // endomorphism_p(x,y) = (BETA * x, y) where BETA is a non-trivial cubic root of unity in Fq.
-    let mut res = (*p).clone();
-    res.x *= BETA;
-    res
-}

bls12_381/src/curves/g2.rs

@@ -1,12 +1,9 @@
 use crate::*;
-use ark_ec::bls12::Bls12Parameters;
 use ark_ec::{
     bls12,
     models::{ModelParameters, SWModelParameters},
-    short_weierstrass_jacobian::GroupAffine,
-    AffineCurve,
 };
-use ark_ff::{biginteger::BigInteger256, field_new, Field, Zero};
+use ark_ff::{field_new, Zero};
 
 pub type G2Affine = bls12::G2Affine<crate::Parameters>;
 pub type G2Projective = bls12::G2Projective<crate::Parameters>;
@@ -54,21 +51,6 @@ impl SWModelParameters for Parameters {
     fn mul_by_a(_: &Self::BaseField) -> Self::BaseField {
         Self::BaseField::zero()
     }
-
-    fn is_in_correct_subgroup_assuming_on_curve(point: &GroupAffine<Parameters>) -> bool {
-        // Algorithm from Section 4 of https://eprint.iacr.org/2021/1130.
-        //
-        // Checks that [p]P = [X]P
-
-        let mut x_times_point = point.mul(BigInteger256([crate::Parameters::X[0], 0, 0, 0]));
-        if crate::Parameters::X_IS_NEGATIVE {
-            x_times_point = -x_times_point;
-        }
-
-        let p_times_point = p_power_endomorphism(point);
-
-        x_times_point.eq(&p_times_point)
-    }
 }
 
 pub const G2_GENERATOR_X: Fq2 = field_new!(Fq2, G2_GENERATOR_X_C0, G2_GENERATOR_X_C1);
@@ -93,52 +75,3 @@ pub const G2_GENERATOR_Y_C0: Fq = field_new!(Fq, "198515060228729193556805452117
 /// 927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582
 #[rustfmt::skip]
 pub const G2_GENERATOR_Y_C1: Fq = field_new!(Fq, "927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582");
-
-// psi(x,y) = (x**p * PSI_X, y**p * PSI_Y) is the Frobenius composed
-// with the quadratic twist and its inverse
-
-// PSI_X = 1/(u+1)^((p-1)/3)
-pub const P_POWER_ENDOMORPHISM_COEFF_0 : Fq2 = field_new!(
-    Fq2,
-    FQ_ZERO,
-    field_new!(
-       Fq,
-       "4002409555221667392624310435006688643935503118305586438271171395842971157480381377015405980053539358417135540939437"
-    )
-);
-
-// PSI_Y = 1/(u+1)^((p-1)/2)
-pub const P_POWER_ENDOMORPHISM_COEFF_1: Fq2 = field_new!(
-    Fq2,
-    field_new!(
-       Fq,
-       "2973677408986561043442465346520108879172042883009249989176415018091420807192182638567116318576472649347015917690530"),
-    field_new!(
-       Fq,
-       "1028732146235106349975324479215795277384839936929757896155643118032610843298655225875571310552543014690878354869257")
-);
-
-pub fn p_power_endomorphism(p: &GroupAffine<Parameters>) -> GroupAffine<Parameters> {
-    // The p-power endomorphism for G2 is defined as follows:
-    // 1. Note that G2 is defined on curve E': y^2 = x^3 + 4(u+1). To map a point (x, y) in E' to (s, t) in E,
-    //    one set s = x / ((u+1) ^ (1/3)), t = y / ((u+1) ^ (1/2)), because E: y^2 = x^3 + 4.
-    // 2. Apply the Frobenius endomorphism (s, t) => (s', t'), another point on curve E,
-    //    where s' = s^p, t' = t^p.
-    // 3. Map the point from E back to E'; that is,
-    //    one set x' = s' * ((u+1) ^ (1/3)), y' = t' * ((u+1) ^ (1/2)).
-    //
-    // To sum up, it maps
-    // (x,y) -> (x^p / ((u+1)^((p-1)/3)), y^p / ((u+1)^((p-1)/2)))
-    // as implemented in the code as follows.
-
-    let mut res = *p;
-    res.x.frobenius_map(1);
-    res.y.frobenius_map(1);
-
-    let tmp_x = res.x.clone();
-    res.x.c0 = -P_POWER_ENDOMORPHISM_COEFF_0.c1 * &tmp_x.c1;
-    res.x.c1 = P_POWER_ENDOMORPHISM_COEFF_0.c1 * &tmp_x.c0;
-    res.y *= P_POWER_ENDOMORPHISM_COEFF_1;
-
-    res
-}

bls12_381/src/curves/tests.rs

@@ -1,12 +1,8 @@
 #![allow(unused_imports)]
-use ark_ec::{
+use ark_ec::{models::SWModelParameters, AffineCurve, PairingEngine, ProjectiveCurve};
-    models::SWModelParameters,
-    short_weierstrass_jacobian::{GroupAffine, GroupProjective},
-    AffineCurve, PairingEngine, ProjectiveCurve,
-};
 use ark_ff::{
     fields::{Field, FpParameters, PrimeField, SquareRootField},
-    BitIteratorBE, One, UniformRand, Zero,
+    One, Zero,
 };
 use ark_serialize::CanonicalSerialize;
 use ark_std::rand::Rng;
@@ -15,7 +11,6 @@ use core::ops::{AddAssign, MulAssign};
 
 use crate::{g1, g2, Bls12_381, Fq, Fq12, Fq2, Fr, G1Affine, G1Projective, G2Affine, G2Projective};
 use ark_algebra_test_templates::{curves::*, groups::*};
-use ark_ec::group::Group;
 
 #[test]
 fn test_g1_projective_curve() {
@@ -120,54 +115,3 @@ fn test_g1_generator_raw() {
         x.add_assign(&Fq::one());
     }
 }
-
-#[test]
-fn test_g1_endomorphism_beta() {
-    assert!(g1::BETA.pow(&[3u64]).is_one());
-}
-
-#[test]
-fn test_g1_subgroup_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    let generator = G1Projective::rand(&mut rng).into_affine();
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g1_subgroup_non_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    loop {
-        let x = Fq::rand(&mut rng);
-        let greatest = rng.gen();
-
-        if let Some(p) = G1Affine::get_point_from_x(x, greatest) {
-            if !p.into_projective().mul(Fr::characteristic()).is_zero() {
-                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-                return;
-            }
-        }
-    }
-}
-
-#[test]
-fn test_g2_subgroup_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    let generator = G2Projective::rand(&mut rng).into_affine();
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-}
-
-#[test]
-fn test_g2_subgroup_non_membership_via_endomorphism() {
-    let mut rng = test_rng();
-    loop {
-        let x = Fq2::rand(&mut rng);
-        let greatest = rng.gen();
-
-        if let Some(p) = G2Affine::get_point_from_x(x, greatest) {
-            if !p.into_projective().mul(Fr::characteristic()).is_zero() {
-                assert!(!p.is_in_correct_subgroup_assuming_on_curve());
-                return;
-            }
-        }
-    }
-}

bls12_381/src/fields/tests.rs

@@ -1004,7 +1004,7 @@ fn test_fq_repr_num_bits() {
 }
 
 #[test]
-fn test_fq_repr_sub_ret_borrow() {
+fn test_fq_repr_sub_noborrow() {
     let mut rng = ark_std::test_rng();
 
     let mut t = BigInteger384([
@@ -1015,7 +1015,7 @@ fn test_fq_repr_sub_ret_borrow() {
         0xad0eb3948a5c34fd,
         0xd56f7b5ab8b5ce8,
     ]);
-    t.sub_ret_borrow(&BigInteger384([
+    t.sub_noborrow(&BigInteger384([
         0xc7867917187ca02b,
         0x5d75679d4911ffef,
         0x8c5b3e48b1a71c15,
@@ -1050,12 +1050,12 @@ fn test_fq_repr_sub_ret_borrow() {
         assert!(b < c);
 
         let mut csub_ba = c;
-        csub_ba.sub_ret_borrow(&b);
+        csub_ba.sub_noborrow(&b);
-        csub_ba.sub_ret_borrow(&a);
+        csub_ba.sub_noborrow(&a);
 
         let mut csub_ab = c;
-        csub_ab.sub_ret_borrow(&a);
+        csub_ab.sub_noborrow(&a);
-        csub_ab.sub_ret_borrow(&b);
+        csub_ab.sub_noborrow(&b);
 
         assert_eq!(csub_ab, csub_ba);
     }
@@ -1069,7 +1069,7 @@ fn test_fq_repr_sub_ret_borrow() {
         0x4b1ba7b6434bacd7,
         0x1a0111ea397fe69a,
     ]);
-    qplusone.sub_ret_borrow(&BigInteger384([
+    qplusone.sub_noborrow(&BigInteger384([
         0xb9feffffffffaaac,
         0x1eabfffeb153ffff,
         0x6730d2a0f6b0f624,
@@ -1091,7 +1091,7 @@ fn test_fq_repr_sub_ret_borrow() {
 }
 
 #[test]
-fn test_fq_repr_add_ret_carry() {
+fn test_fq_repr_add_nocarry() {
     let mut rng = ark_std::test_rng();
 
     let mut t = BigInteger384([
@@ -1102,7 +1102,7 @@ fn test_fq_repr_add_ret_carry() {
         0xad0eb3948a5c34fd,
         0xd56f7b5ab8b5ce8,
     ]);
-    t.add_ret_carry(&BigInteger384([
+    t.add_nocarry(&BigInteger384([
         0xc7867917187ca02b,
         0x5d75679d4911ffef,
         0x8c5b3e48b1a71c15,
@@ -1133,28 +1133,28 @@ fn test_fq_repr_add_ret_carry() {
         c.0[5] >>= 3;
 
         let mut abc = a;
-        abc.add_ret_carry(&b);
+        abc.add_nocarry(&b);
-        abc.add_ret_carry(&c);
+        abc.add_nocarry(&c);
 
         let mut acb = a;
-        acb.add_ret_carry(&c);
+        acb.add_nocarry(&c);
-        acb.add_ret_carry(&b);
+        acb.add_nocarry(&b);
 
         let mut bac = b;
-        bac.add_ret_carry(&a);
+        bac.add_nocarry(&a);
-        bac.add_ret_carry(&c);
+        bac.add_nocarry(&c);
 
         let mut bca = b;
-        bca.add_ret_carry(&c);
+        bca.add_nocarry(&c);
-        bca.add_ret_carry(&a);
+        bca.add_nocarry(&a);
 
         let mut cab = c;
-        cab.add_ret_carry(&a);
+        cab.add_nocarry(&a);
-        cab.add_ret_carry(&b);
+        cab.add_nocarry(&b);
 
         let mut cba = c;
-        cba.add_ret_carry(&b);
+        cba.add_nocarry(&b);
-        cba.add_ret_carry(&a);
+        cba.add_nocarry(&a);
 
         assert_eq!(abc, acb);
         assert_eq!(abc, bac);
@@ -1172,7 +1172,7 @@ fn test_fq_repr_add_ret_carry() {
         0xffffffffffffffff,
         0xffffffffffffffff,
     ]);
-    x.add_ret_carry(&BigInteger384::from(1));
+    x.add_nocarry(&BigInteger384::from(1));
     assert!(x.is_zero());
 }
 

curve-benches/src/macros/ec.rs

@@ -196,32 +196,6 @@ macro_rules! ec_bench {
             });
         }
 
-        fn deser_uncompressed(b: &mut $crate::bencher::Bencher) {
-            use ark_ec::ProjectiveCurve;
-            use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
-            const SAMPLES: usize = 1000;
-
-            let mut rng = ark_std::test_rng();
-
-            let mut num_bytes = 0;
-            let tmp = <$projective>::rand(&mut rng).into_affine();
-            let v: Vec<_> = (0..SAMPLES)
-                .flat_map(|_| {
-                    let mut bytes = Vec::with_capacity(1000);
-                    tmp.serialize_uncompressed(&mut bytes).unwrap();
-                    num_bytes = bytes.len();
-                    bytes
-                })
-                .collect();
-
-            let mut count = 0;
-            b.iter(|| {
-                count = (count + 1) % SAMPLES;
-                let index = count * num_bytes;
-                <$affine>::deserialize_uncompressed(&v[index..(index + num_bytes)]).unwrap()
-            });
-        }
-
         fn msm_131072(b: &mut $crate::bencher::Bencher) {
             use ark_serialize::{CanonicalDeserialize, CanonicalSerialize};
             const SAMPLES: usize = 131072;
@@ -250,7 +224,6 @@ macro_rules! ec_bench {
             deser,
             ser_unchecked,
             deser_unchecked,
-            deser_uncompressed,
             msm_131072,
         );
     };

curve-benches/src/macros/field.rs

@@ -24,8 +24,8 @@ macro_rules! f_bench {
                 // sqrt field stuff
                 sqrt,
                 // prime field stuff
-                repr_add_ret_carry,
+                repr_add_nocarry,
-                repr_sub_ret_borrow,
+                repr_sub_noborrow,
                 repr_num_bits,
                 repr_mul2,
                 repr_div2,
@@ -322,7 +322,7 @@ macro_rules! sqrt {
 #[macro_export]
 macro_rules! prime_field {
     ($f:ident, $f_type:ty, $f_repr:ident, $f_repr_type:ty) => {
-        fn repr_add_ret_carry(b: &mut $crate::bencher::Bencher) {
+        fn repr_add_nocarry(b: &mut $crate::bencher::Bencher) {
             const SAMPLES: usize = 1000;
 
             let mut rng = ark_std::test_rng();
@@ -343,13 +343,13 @@ macro_rules! prime_field {
             let mut count = 0;
             b.iter(|| {
                 let mut tmp = v[count].0;
-                n_fold!(tmp, v, add_ret_carry, count);
+                n_fold!(tmp, v, add_nocarry, count);
                 count = (count + 1) % SAMPLES;
                 tmp
             });
         }
 
-        fn repr_sub_ret_borrow(b: &mut $crate::bencher::Bencher) {
+        fn repr_sub_noborrow(b: &mut $crate::bencher::Bencher) {
             const SAMPLES: usize = 1000;
 
             let mut rng = ark_std::test_rng();
@@ -369,7 +369,7 @@ macro_rules! prime_field {
             let mut count = 0;
             b.iter(|| {
                 let mut tmp = v[count].0;
-                n_fold!(tmp, v, sub_ret_borrow, count);
+                n_fold!(tmp, v, sub_noborrow, count);
                 count = (count + 1) % SAMPLES;
                 tmp;
             });
@@ -448,7 +448,7 @@ macro_rules! prime_field {
             let mut count = 0;
             b.iter(|| {
                 count = (count + 1) % SAMPLES;
-                let _ = $f::from(v[count]);
+                $f::from(v[count]);
             });
         }
     };

curve-constraint-tests/src/lib.rs

@@ -233,7 +233,8 @@ pub mod fields {
 pub mod curves {
     use ark_ec::{
         short_weierstrass_jacobian::GroupProjective as SWProjective,
-        twisted_edwards_extended::GroupProjective as TEProjective, ProjectiveCurve,
+        twisted_edwards_extended::GroupProjective as TEProjective, ModelParameters,
+        ProjectiveCurve,
     };
     use ark_ff::{BitIteratorLE, Field, FpParameters, One, PrimeField};
     use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
@@ -241,12 +242,13 @@ pub mod curves {
 
     use ark_r1cs_std::prelude::*;
 
-    pub fn group_test<C, ConstraintF, GG>() -> Result<(), SynthesisError>
+    type ConstraintF<P> = <<P as ModelParameters>::BaseField as Field>::BasePrimeField;
+
+    pub fn group_test<C, ConstraintF>() -> Result<(), SynthesisError>
     where
-        C: ProjectiveCurve,
+        C: CurveWithVar<ConstraintF>,
         ConstraintF: Field,
-        GG: CurveVar<C, ConstraintF>,
+        for<'a> &'a C::Var: GroupOpsBounds<'a, C, C::Var>,
-        for<'a> &'a GG: GroupOpsBounds<'a, C, GG>,
     {
         let modes = [
             AllocationMode::Input,
@@ -259,12 +261,14 @@ pub mod curves {
             let mut rng = test_rng();
             let a_native = C::rand(&mut rng);
             let b_native = C::rand(&mut rng);
-            let a = GG::new_variable(ark_relations::ns!(cs, "generate_a"), || Ok(a_native), mode)
+            let a =
-                .unwrap();
+                C::Var::new_variable(ark_relations::ns!(cs, "generate_a"), || Ok(a_native), mode)
-            let b = GG::new_variable(ark_relations::ns!(cs, "generate_b"), || Ok(b_native), mode)
+                    .unwrap();
-                .unwrap();
+            let b =
+                C::Var::new_variable(ark_relations::ns!(cs, "generate_b"), || Ok(b_native), mode)
+                    .unwrap();
 
-            let zero = GG::zero();
+            let zero = C::Var::zero();
             assert_eq!(zero.value()?, zero.value()?);
 
             // a == a
@@ -273,14 +277,14 @@ 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;
@@ -380,13 +384,15 @@ pub mod curves {
         Ok(())
     }
 
-    pub fn sw_test<P, GG>() -> Result<(), SynthesisError>
+    type SWVar<P> = <SWProjective<P> as CurveWithVar<ConstraintF<P>>>::Var;
+
+    pub fn sw_test<P>() -> Result<(), SynthesisError>
     where
         P: ark_ec::SWModelParameters,
-        GG: CurveVar<SWProjective<P>, <P::BaseField as Field>::BasePrimeField>,
+        SWProjective<P>: CurveWithVar<ConstraintF<P>> + ProjectiveCurve,
-        for<'a> &'a GG: GroupOpsBounds<'a, SWProjective<P>, GG>,
+        for<'a> &'a SWVar<P>: GroupOpsBounds<'a, SWProjective<P>, SWVar<P>>,
     {
-        group_test::<SWProjective<P>, _, GG>()?;
+        group_test::<SWProjective<P>, _>()?;
         let modes = [
             AllocationMode::Input,
             AllocationMode::Witness,
@@ -405,14 +411,12 @@ pub mod curves {
             let b_affine = b.into_affine();
 
             let ns = ark_relations::ns!(cs, "allocating variables");
-            let mut gadget_a = GG::new_variable(cs.clone(), || Ok(a), mode)?;
+            let mut gadget_a = SWVar::<P>::new_variable(cs.clone(), || Ok(a), mode)?;
-            let gadget_b = GG::new_variable(cs.clone(), || Ok(b), mode)?;
+            let gadget_b = SWVar::<P>::new_variable(cs.clone(), || Ok(b), mode)?;
-            let zero = GG::zero();
+            let zero = SWVar::<P>::zero();
             drop(ns);
-            assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
+            assert_eq!(gadget_a.value()?.into_affine(), a_affine);
-            assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
+            assert_eq!(gadget_b.value()?.into_affine(), b_affine);
-            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
@@ -453,13 +457,15 @@ pub mod curves {
         Ok(())
     }
 
-    pub fn te_test<P, GG>() -> Result<(), SynthesisError>
+    type TEVar<P> = <TEProjective<P> as CurveWithVar<ConstraintF<P>>>::Var;
+
+    pub fn te_test<P>() -> Result<(), SynthesisError>
     where
         P: ark_ec::TEModelParameters,
-        GG: CurveVar<TEProjective<P>, <P::BaseField as Field>::BasePrimeField>,
+        TEProjective<P>: CurveWithVar<ConstraintF<P>> + ProjectiveCurve,
-        for<'a> &'a GG: GroupOpsBounds<'a, TEProjective<P>, GG>,
+        for<'a> &'a TEVar<P>: GroupOpsBounds<'a, TEProjective<P>, TEVar<P>>,
     {
-        group_test::<TEProjective<P>, _, GG>()?;
+        group_test::<TEProjective<P>, _>()?;
         let modes = [
             AllocationMode::Input,
             AllocationMode::Witness,
@@ -478,14 +484,12 @@ pub mod curves {
             let b_affine = b.into_affine();
 
             let ns = ark_relations::ns!(cs, "allocating variables");
-            let mut gadget_a = GG::new_variable(cs.clone(), || Ok(a), mode)?;
+            let mut gadget_a = TEVar::<P>::new_variable(cs.clone(), || Ok(a), mode)?;
-            let gadget_b = GG::new_variable(cs.clone(), || Ok(b), mode)?;
+            let gadget_b = TEVar::<P>::new_variable(cs.clone(), || Ok(b), mode)?;
             drop(ns);
 
-            assert_eq!(gadget_a.value()?.into_affine().x, a_affine.x);
+            assert_eq!(gadget_a.value()?.into_affine(), a_affine);
-            assert_eq!(gadget_a.value()?.into_affine().y, a_affine.y);
+            assert_eq!(gadget_b.value()?.into_affine(), b_affine);
-            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
@@ -527,16 +531,21 @@ pub mod curves {
 pub mod pairing {
     use ark_ec::{PairingEngine, ProjectiveCurve};
     use ark_ff::{BitIteratorLE, Field, PrimeField};
-    use ark_r1cs_std::prelude::*;
+    use ark_r1cs_std::{fields::fp::FpVar, prelude::*};
     use ark_relations::r1cs::{ConstraintSystem, SynthesisError};
     use ark_std::{test_rng, vec::Vec, UniformRand};
 
     #[allow(dead_code)]
-    pub fn bilinearity_test<E: PairingEngine, P: PairingVar<E>>() -> Result<(), SynthesisError>
+    pub fn bilinearity_test<P: PairingGadget>() -> Result<(), SynthesisError>
     where
-        for<'a> &'a P::G1Var: GroupOpsBounds<'a, E::G1Projective, P::G1Var>,
+        for<'a> &'a P::G1Var: GroupOpsBounds<'a, P::G1Projective, P::G1Var>,
-        for<'a> &'a P::G2Var: GroupOpsBounds<'a, E::G2Projective, P::G2Var>,
+        for<'a> &'a P::G2Var: GroupOpsBounds<'a, P::G2Projective, P::G2Var>,
-        for<'a> &'a P::GTVar: FieldOpsBounds<'a, E::Fqk, P::GTVar>,
+        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>,
     {
         let modes = [
             AllocationMode::Input,
@@ -544,12 +553,12 @@ pub mod pairing {
             AllocationMode::Constant,
         ];
         for &mode in &modes {
-            let cs = ConstraintSystem::<E::Fq>::new_ref();
+            let cs = ConstraintSystem::<P::Fq>::new_ref();
 
             let mut rng = test_rng();
-            let a = E::G1Projective::rand(&mut rng);
+            let a = P::G1Projective::rand(&mut rng);
-            let b = E::G2Projective::rand(&mut rng);
+            let b = P::G2Projective::rand(&mut rng);
-            let s = E::Fr::rand(&mut rng);
+            let s = P::Fr::rand(&mut rng);
 
             let mut sa = a;
             sa *= s;
@@ -571,16 +580,16 @@ pub mod pairing {
 
             let (ans1_g, ans1_n) = {
                 let _ml_constraints = cs.num_constraints();
-                let ml_g = P::miller_loop(&[sa_prep_g], &[b_prep_g.clone()])?;
+                let ml_g = P::miller_loop_gadget(&[sa_prep_g], &[b_prep_g.clone()])?;
                 let _fe_constraints = cs.num_constraints();
-                let ans_g = P::final_exponentiation(&ml_g)?;
+                let ans_g = P::final_exponentiation_gadget(&ml_g)?;
-                let ans_n = E::pairing(sa, b);
+                let ans_n = <P as PairingEngine>::pairing(sa, b);
                 (ans_g, ans_n)
             };
 
             let (ans2_g, ans2_n) = {
-                let ans_g = P::pairing(a_prep_g.clone(), sb_prep_g)?;
+                let ans_g = P::pairing_gadget(a_prep_g.clone(), sb_prep_g)?;
-                let ans_n = E::pairing(a, sb);
+                let ans_n = <P as PairingEngine>::pairing(a, sb);
                 (ans_g, ans_n)
             };
 
@@ -589,8 +598,8 @@ pub mod pairing {
                     .map(Boolean::constant)
                     .collect::<Vec<_>>();
 
-                let mut ans_g = P::pairing(a_prep_g, b_prep_g)?;
+                let mut ans_g = P::pairing_gadget(a_prep_g, b_prep_g)?;
-                let mut ans_n = E::pairing(a, b);
+                let mut ans_n = <P as PairingEngine>::pairing(a, b);
                 ans_n = ans_n.pow(s.into_repr());
                 ans_g = ans_g.pow_le(&s_iter)?;
 

ed_on_bls12_377/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
 }

ed_on_bls12_381/src/constraints/curves.rs

@@ -1,17 +1,10 @@
 use crate::*;
-use ark_r1cs_std::groups::curves::{short_weierstrass::ProjectiveVar, twisted_edwards::AffineVar};
+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<JubjubParameters, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
-
-/// A variable that is the R1CS equivalent of `crate::SWProjective`
-pub type SWVar = ProjectiveVar<JubjubParameters, FqVar>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<_, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<_, SWVar>().unwrap();
-    ark_curve_constraint_tests::curves::group_test::<_, Fq, EdwardsVar>().unwrap();
 }

ed_on_bls12_381/src/curves/mod.rs

@@ -1,21 +1,15 @@
 use crate::{Fq, Fr};
 use ark_ec::{
     models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    short_weierstrass_jacobian::{
-        GroupAffine as SWGroupAffine, GroupProjective as SWGroupProjective,
-    },
     twisted_edwards_extended::{GroupAffine, GroupProjective},
-    SWModelParameters,
 };
 use ark_ff::field_new;
 
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<JubjubParameters>;
+pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<JubjubParameters>;
+pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
-pub type SWAffine = SWGroupAffine<JubjubParameters>;
-pub type SWProjective = SWGroupProjective<JubjubParameters>;
 
 /// `JubJub` is a twisted Edwards curve. These curves have equations of the
 /// form: ax² + y² = 1 - dx²y².
@@ -38,29 +32,15 @@ pub type SWProjective = SWGroupProjective<JubjubParameters>;
 /// ```
 /// These parameters and the sage script obtained from:
 /// <https://github.com/zcash/zcash/issues/2230#issuecomment-317182190>
-///
-///
-/// `jubjub` also has a short Weierstrass curve form, following the
-/// form: y² = x³ + A * x + B
-/// where
-///
-/// A = 52296097456646850916096512823759002727550416093741407922227928430486925478210
-/// B = 48351165704696163914533707656614864561753505123260775585269522553028192119009
-///
-/// We can use the script available
-/// [here](https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/jubjub.sage)
-/// to convert between the different representations.
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct JubjubParameters;
+pub struct EdwardsParameters;
-pub type EdwardsParameters = JubjubParameters;
-pub type SWParameters = JubjubParameters;
 
-impl ModelParameters for JubjubParameters {
+impl ModelParameters for EdwardsParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 }
 
-impl TEModelParameters for JubjubParameters {
+impl TEModelParameters for EdwardsParameters {
     /// COEFF_A = -1
     #[rustfmt::skip]
     const COEFF_A: Fq = field_new!(Fq, "-1");
@@ -80,7 +60,7 @@ impl TEModelParameters for JubjubParameters {
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
     const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
 
-    type MontgomeryModelParameters = JubjubParameters;
+    type MontgomeryModelParameters = EdwardsParameters;
 
     /// Multiplication by `a` is simply negation here.
     #[inline(always)]
@@ -89,7 +69,7 @@ impl TEModelParameters for JubjubParameters {
     }
 }
 
-impl MontgomeryModelParameters for JubjubParameters {
+impl MontgomeryModelParameters for EdwardsParameters {
     /// COEFF_A = 40962
     #[rustfmt::skip]
     const COEFF_A: Fq = field_new!(Fq, "40962");
@@ -97,39 +77,10 @@ impl MontgomeryModelParameters for JubjubParameters {
     #[rustfmt::skip]
     const COEFF_B: Fq = field_new!(Fq, "-40964");
 
-    type TEModelParameters = JubjubParameters;
+    type TEModelParameters = EdwardsParameters;
 }
 
 #[rustfmt::skip]
 const GENERATOR_X: Fq = field_new!(Fq, "8076246640662884909881801758704306714034609987455869804520522091855516602923");
 #[rustfmt::skip]
 const GENERATOR_Y: Fq = field_new!(Fq, "13262374693698910701929044844600465831413122818447359594527400194675274060458");
-
-impl SWModelParameters for JubjubParameters {
-    /// COEFF_A = 52296097456646850916096512823759002727550416093741407922227928430486925478210
-    #[rustfmt::skip]
-    const COEFF_A: Self::BaseField = field_new!(Fq, "52296097456646850916096512823759002727550416093741407922227928430486925478210");
-
-    /// COEFF_B = 48351165704696163914533707656614864561753505123260775585269522553028192119009
-    #[rustfmt::skip]
-    const COEFF_B: Self::BaseField = field_new!(Fq, "48351165704696163914533707656614864561753505123260775585269522553028192119009");
-
-    /// COFACTOR = 8
-    const COFACTOR: &'static [u64] = &[8];
-
-    /// COFACTOR^(-1) mod r =
-    /// 819310549611346726241370945440405716213240158234039660170669895299022906775
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "819310549611346726241370945440405716213240158234039660170669895299022906775");
-
-    /// generators
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (SW_GENERATOR_X, SW_GENERATOR_Y);
-}
-
-/// x coordinate for SW curve generator
-#[rustfmt::skip]
-const SW_GENERATOR_X: Fq = field_new!(Fq, "33835869156188682335217394949746694649676633840125476177319971163079011318731");
-/// y coordinate for SW curve generator
-#[rustfmt::skip]
-const SW_GENERATOR_Y: Fq = field_new!(Fq, "43777270878440091394432848052353307184915192688165709016756678962558652055320");

ed_on_bls12_381/src/curves/tests.rs

@@ -1,6 +1,8 @@
 use ark_ec::{AffineCurve, ProjectiveCurve};
 use ark_ff::{bytes::FromBytes, Zero};
-use ark_std::{rand::Rng, str::FromStr, test_rng};
+use ark_std::rand::Rng;
+use ark_std::str::FromStr;
+use ark_std::test_rng;
 
 use crate::*;
 
@@ -10,9 +12,7 @@ use ark_algebra_test_templates::{curves::*, groups::*};
 fn test_projective_curve() {
     curve_tests::<EdwardsProjective>();
 
-    edwards_tests::<JubjubParameters>();
+    edwards_tests::<EdwardsParameters>();
-    montgomery_conversion_test::<JubjubParameters>();
-    sw_tests::<JubjubParameters>();
 }
 
 #[test]
@@ -20,13 +20,8 @@ fn test_projective_group() {
     let mut rng = test_rng();
     let a = rng.gen();
     let b = rng.gen();
-
-    let c = rng.gen();
-    let d = rng.gen();
-
     for _i in 0..100 {
         group_test::<EdwardsProjective>(a, b);
-        group_test::<SWProjective>(c, d);
     }
 }
 
@@ -42,15 +37,9 @@ fn test_affine_group() {
 
 #[test]
 fn test_generator() {
-    // edward curve
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-
-    // weierstrass curve
-    let generator = SWAffine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }
 
 #[test]
@@ -114,5 +103,5 @@ fn test_bytes() {
 
 #[test]
 fn test_montgomery_conversion() {
-    montgomery_conversion_test::<JubjubParameters>();
+    montgomery_conversion_test::<EdwardsParameters>();
 }

ed_on_bls12_381/src/fields/tests.rs

@@ -9,7 +9,8 @@ use ark_std::test_rng;
 
 use ark_algebra_test_templates::fields::*;
 
-use ark_std::{rand::Rng, str::FromStr};
+use ark_std::rand::Rng;
+use ark_std::str::FromStr;
 
 #[test]
 fn test_fr() {

ed_on_bls12_381/src/lib.rs

@@ -8,16 +8,14 @@
 )]
 #![forbid(unsafe_code)]
 
-//! This library implements a twisted Edwards curve whose base field is the
+//! This library implements a twisted Edwards curve whose base field is the scalar field of the
-//! scalar field of the curve BLS12-381. This allows defining cryptographic
+//! curve BLS12-381. This allows defining cryptographic primitives that use elliptic curves over
-//! primitives that use elliptic curves over the scalar field of the latter
+//! the scalar field of the latter curve. This curve was generated by Sean Bowe, and is also known
-//! curve. This curve was generated by Sean Bowe, and is also known as [Jubjub](https://github.com/zkcrypto/jubjub).
+//! as [Jubjub](https://github.com/zkcrypto/jubjub).
 //!
 //! Curve information:
-//! * Base field: q =
+//! * Base field: q = 52435875175126190479447740508185965837690552500527637822603658699938581184513
-//!   52435875175126190479447740508185965837690552500527637822603658699938581184513
+//! * Scalar field: r = 6554484396890773809930967563523245729705921265872317281365359162392183254199
-//! * Scalar field: r =
-//!   6554484396890773809930967563523245729705921265872317281365359162392183254199
 //! * Valuation(q - 1, 2) = 32
 //! * Valuation(r - 1, 2) = 1
 //! * Curve equation: ax^2 + y^2 =1 + dx^2y^2, where

ed_on_bls12_381_bandersnatch/src/constraints/curves.rs

@@ -1,15 +1,10 @@
-use crate::{constraints::FqVar, *};
+use crate::*;
-use ark_r1cs_std::groups::curves::{short_weierstrass::ProjectiveVar, twisted_edwards::AffineVar};
+use ark_r1cs_std::groups::curves::twisted_edwards::AffineVar;
 
-/// A variable that is the R1CS equivalent of `crate::BandersnatchParameters`.
+/// A variable that is the R1CS equivalent of `crate::EdwardsAffine`.
-pub type EdwardsVar = AffineVar<BandersnatchParameters, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
-
-/// A variable that is the R1CS equivalent of `crate::SWProjective`
-pub type SWVar = ProjectiveVar<BandersnatchParameters, FqVar>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<_, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<_, SWVar>().unwrap();
-    ark_curve_constraint_tests::curves::group_test::<_, Fq, EdwardsVar>().unwrap();
 }

ed_on_bls12_381_bandersnatch/src/curves/mod.rs

@@ -1,34 +1,26 @@
 use crate::{Fq, Fr};
 use ark_ec::{
     models::{ModelParameters, MontgomeryModelParameters, TEModelParameters},
-    short_weierstrass_jacobian::{
-        GroupAffine as SWGroupAffine, GroupProjective as SWGroupProjective,
-    },
     twisted_edwards_extended::{GroupAffine, GroupProjective},
-    SWModelParameters,
 };
 use ark_ff::{field_new, Field};
-
 #[cfg(test)]
 mod tests;
 
-pub type EdwardsAffine = GroupAffine<BandersnatchParameters>;
+pub type EdwardsAffine = GroupAffine<EdwardsParameters>;
-pub type EdwardsProjective = GroupProjective<BandersnatchParameters>;
+pub type EdwardsProjective = GroupProjective<EdwardsParameters>;
 
-pub type SWAffine = SWGroupAffine<BandersnatchParameters>;
+/// `banersnatch` is a twisted Edwards curve. These curves have equations of the
-pub type SWProjective = SWGroupProjective<BandersnatchParameters>;
-
-/// `bandersnatch` is a twisted Edwards curve. These curves have equations of the
 /// form: ax² + y² = 1 - dx²y².
 /// over some base finite field Fq.
 ///
-/// bandersnatch's curve equation: -5x² + y² = 1 - dx²y²
+/// banersnatch's curve equation: -5x² + y² = 1 - dx²y²
 ///
 /// q = 52435875175126190479447740508185965837690552500527637822603658699938581184513.
 ///
-/// a = -5.
+/// a = 52435875175126190479447740508185965837690552500527637822603658699938581184508.
 /// d = (138827208126141220649022263972958607803/
-///     171449701953573178309673572579671231137) mod q
+/// 171449701953573178309673572579671231137) mod q
 ///   = 45022363124591815672509500913686876175488063829319466900776701791074614335719.
 ///
 /// Sage script to calculate these:
@@ -40,30 +32,17 @@ pub type SWProjective = SWGroupProjective<BandersnatchParameters>;
 /// ```
 /// These parameters and the sage script obtained from:
 /// <https://github.com/asanso/Bandersnatch/>
-///
-/// bandersnatch also has a short Weierstrass curve form, following the
-/// form: y² = x³ + A * x + B
-/// where
-///
-/// A = 10773120815616481058602537765553212789256758185246796157495669123169359657269
-/// B = 29569587568322301171008055308580903175558631321415017492731745847794083609535
-///
-/// Script to transfer between different curves are available
-/// <https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/bandersnatch.sage>
-///
 #[derive(Clone, Default, PartialEq, Eq)]
-pub struct BandersnatchParameters;
+pub struct EdwardsParameters;
 
-pub type EdwardsParameters = BandersnatchParameters;
+impl ModelParameters for EdwardsParameters {
-pub type SWParameters = BandersnatchParameters;
-
-impl ModelParameters for BandersnatchParameters {
     type BaseField = Fq;
     type ScalarField = Fr;
 }
 
-impl TEModelParameters for BandersnatchParameters {
+impl TEModelParameters for EdwardsParameters {
     /// COEFF_A = -5
+    #[rustfmt::skip]
     const COEFF_A: Fq = field_new!(Fq, "-5");
 
     /// COEFF_D = (138827208126141220649022263972958607803/
@@ -80,10 +59,9 @@ impl TEModelParameters for BandersnatchParameters {
     const COFACTOR_INV: Fr = field_new!(Fr, "9831726595336160714896451345284868594481866920080427688839802480047265754601");
 
     /// AFFINE_GENERATOR_COEFFS = (GENERATOR_X, GENERATOR_Y)
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
+    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) = (GENERATOR_X, GENERATOR_Y);
-        (TE_GENERATOR_X, TE_GENERATOR_Y);
 
-    type MontgomeryModelParameters = BandersnatchParameters;
+    type MontgomeryModelParameters = EdwardsParameters;
 
     /// Multiplication by `a` is multiply by `-5`.
     #[inline(always)]
@@ -93,56 +71,24 @@ impl TEModelParameters for BandersnatchParameters {
     }
 }
 
-impl MontgomeryModelParameters for BandersnatchParameters {
+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 = BandersnatchParameters;
+    type TEModelParameters = EdwardsParameters;
 }
 
-// The TE form generator is generated following Zcash's fashion:
+// using the generator from bench.py (in affine form)
-//  "The generators of G1 and G2 are computed by finding the lexicographically smallest
+// P = BandersnatchPoint(
-//   valid x-coordinate, and its lexicographically smallest y-coordinate and scaling it
+//      13738737789055671334382939318077718462576533426798874551591468520593954805549,
-//   by the cofactor such that the result is not the point at infinity."
+//      11575885077368931610486103676191793534029821920164915325066801506752632626968,
-// The SW form generator is the same TE generator converted into SW form, obtained from the scripts:
+//      14458123306641001284399433086015669988340559992755622870694102351476334505845,
-//   <https://github.com/zhenfeizhang/bandersnatch/blob/main/bandersnatch/script/bandersnatch.sage>
+//      C)
-
-/// x coordinate for TE curve generator
 #[rustfmt::skip]
-const TE_GENERATOR_X: Fq = field_new!(Fq, "18886178867200960497001835917649091219057080094937609519140440539760939937304");
+const GENERATOR_X: Fq = field_new!(Fq, "29627151942733444043031429156003786749302466371339015363120350521834195802525");
-/// y coordinate for TE curve generator
 #[rustfmt::skip]
-const TE_GENERATOR_Y: Fq = field_new!(Fq, "19188667384257783945677642223292697773471335439753913231509108946878080696678");
+const GENERATOR_Y: Fq = field_new!(Fq, "27488387519748396681411951718153463804682561779047093991696427532072116857978");
-/// x coordinate for SW curve generator
-#[rustfmt::skip]
-const SW_GENERATOR_X: Fq = field_new!(Fq, "30900340493481298850216505686589334086208278925799850409469406976849338430199");
-/// y coordinate for SW curve generator
-#[rustfmt::skip]
-const SW_GENERATOR_Y: Fq = field_new!(Fq, "12663882780877899054958035777720958383845500985908634476792678820121468453298");
-
-impl SWModelParameters for BandersnatchParameters {
-    /// COEFF_A = 10773120815616481058602537765553212789256758185246796157495669123169359657269
-    #[rustfmt::skip]
-    const COEFF_A: Self::BaseField = field_new!(Fq, "10773120815616481058602537765553212789256758185246796157495669123169359657269");
-
-    /// COEFF_B = 29569587568322301171008055308580903175558631321415017492731745847794083609535
-    #[rustfmt::skip]
-    const COEFF_B: Self::BaseField = field_new!(Fq, "29569587568322301171008055308580903175558631321415017492731745847794083609535");
-
-    /// COFACTOR = 4
-    const COFACTOR: &'static [u64] = &[4];
-
-    /// COFACTOR^(-1) mod r =
-    /// 9831726595336160714896451345284868594481866920080427688839802480047265754601
-    #[rustfmt::skip]
-    const COFACTOR_INV: Fr = field_new!(Fr, "9831726595336160714896451345284868594481866920080427688839802480047265754601");
-
-    /// generators
-    const AFFINE_GENERATOR_COEFFS: (Self::BaseField, Self::BaseField) =
-        (SW_GENERATOR_X, SW_GENERATOR_Y);
-}

ed_on_bls12_381_bandersnatch/src/curves/tests.rs

@@ -8,9 +8,7 @@ use ark_std::{rand::Rng, str::FromStr, test_rng};
 fn test_projective_curve() {
     curve_tests::<EdwardsProjective>();
 
-    edwards_tests::<BandersnatchParameters>();
+    edwards_tests::<EdwardsParameters>();
-    montgomery_conversion_test::<BandersnatchParameters>();
-    sw_tests::<BandersnatchParameters>();
 }
 
 #[test]
@@ -18,13 +16,8 @@ fn test_projective_group() {
     let mut rng = test_rng();
     let a = rng.gen();
     let b = rng.gen();
-
-    let c = rng.gen();
-    let d = rng.gen();
-
     for _i in 0..100 {
         group_test::<EdwardsProjective>(a, b);
-        group_test::<SWProjective>(c, d);
     }
 }
 
@@ -40,20 +33,13 @@ fn test_affine_group() {
 
 #[test]
 fn test_generator() {
-    // edward curve
     let generator = EdwardsAffine::prime_subgroup_generator();
     assert!(generator.is_on_curve());
     assert!(generator.is_in_correct_subgroup_assuming_on_curve());
-
-    // weierstrass curve
-    let generator = SWAffine::prime_subgroup_generator();
-    assert!(generator.is_on_curve());
-    assert!(generator.is_in_correct_subgroup_assuming_on_curve());
 }
 
 #[test]
 fn test_conversion() {
-    // edward curve
     let mut rng = test_rng();
     let a: EdwardsAffine = rng.gen();
     let b: EdwardsAffine = rng.gen();
@@ -66,14 +52,6 @@ fn test_conversion() {
         .double();
     assert_eq!(a_b, a_b2.into_affine());
     assert_eq!(a_b.into_projective(), a_b2);
-
-    // weierstrass curve
-    let mut rng = test_rng();
-    let a: SWProjective = rng.gen();
-    let b: SWProjective = rng.gen();
-    let a_b = { (a + &b).double().double() };
-    let a_b2 = (a + &b).double().double();
-    assert_eq!(a_b.into_affine(), a_b2.into_affine());
 }
 
 #[test]
@@ -121,5 +99,5 @@ fn test_bytes() {
 
 #[test]
 fn test_montgomery_conversion() {
-    montgomery_conversion_test::<BandersnatchParameters>();
+    montgomery_conversion_test::<EdwardsParameters>();
 }

ed_on_bls12_381_bandersnatch/src/lib.rs

@@ -11,8 +11,8 @@
 //! 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
+//! field of the latter curve. This curve was generated by Simon Masson from Anoma,
-//! 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).
+//! 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/).

ed_on_bn254/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<_, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
 }

ed_on_cp6_782/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
 }

ed_on_mnt4_298/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
 }

ed_on_mnt4_753/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FqVar>;
+pub type EdwardsVar = AffineVar<EdwardsParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters, EdwardsVar>().unwrap();
+    ark_curve_constraint_tests::curves::te_test::<EdwardsParameters>().unwrap();
 }

mnt4_298/src/constraints/curves.rs

@@ -16,14 +16,8 @@ pub type G2PreparedVar = mnt4::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
     use ark_ec::models::mnt4::MNT4Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G1Parameters>()
-        <Parameters as MNT4Parameters>::G1Parameters,
+        .unwrap();
-        G1Var,
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G2Parameters>()
-    >()
+        .unwrap();
-    .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<
-        <Parameters as MNT4Parameters>::G2Parameters,
-        G2Var,
-    >()
-    .unwrap();
 }

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 = constraints::PairingVar::prepare_g1(&a)?;
+//! let a_prep = MNT4_298::prepare_g1(&a)?;
-//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! let b_prep = MNT4_298::prepare_g2(&b)?;
-//! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
+//! let pairing_result = MNT4_298::pairing_gadget(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 = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let a_prep_const = MNT4_298::prepare_g1(&a_const)?;
-//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let b_prep_const = MNT4_298::prepare_g2(&b_const)?;
-//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
+//! let pairing_result_const = MNT4_298::pairing_gadget(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;

mnt4_298/src/constraints/pairing.rs

@@ -1,10 +1,8 @@
-use crate::Parameters;
-
 /// Specifies the constraints for computing a pairing in the MNT4-298 bilinear group.
-pub type PairingVar = ark_r1cs_std::pairing::mnt4::PairingVar<Parameters>;
+pub use crate::MNT4_298;
 
 #[test]
 fn test() {
     use crate::MNT4_298;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_298, PairingVar>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_298>().unwrap()
 }

mnt4_753/src/constraints/curves.rs

@@ -16,14 +16,8 @@ pub type G2PreparedVar = mnt4::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
     use ark_ec::models::mnt4::MNT4Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G1Parameters>()
-        <Parameters as MNT4Parameters>::G1Parameters,
+        .unwrap();
-        G1Var,
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT4Parameters>::G2Parameters>()
-    >()
+        .unwrap();
-    .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<
-        <Parameters as MNT4Parameters>::G2Parameters,
-        G2Var,
-    >()
-    .unwrap();
 }

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 = constraints::PairingVar::prepare_g1(&a)?;
+//! let a_prep = MNT4_753::prepare_g1(&a)?;
-//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! let b_prep = MNT4_753::prepare_g2(&b)?;
-//! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
+//! let pairing_result = MNT4_753::pairing_gadget(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 = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let a_prep_const = MNT4_753::prepare_g1(&a_const)?;
-//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let b_prep_const = MNT4_753::prepare_g2(&b_const)?;
-//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
+//! let pairing_result_const = MNT4_753::pairing_gadget(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;

mnt4_753/src/constraints/pairing.rs

@@ -1,10 +1,8 @@
-use crate::Parameters;
-
 /// Specifies the constraints for computing a pairing in the MNT4-753 bilinear group.
-pub type PairingVar = ark_r1cs_std::pairing::mnt4::PairingVar<Parameters>;
+pub use crate::MNT4_753;
 
 #[test]
 fn test() {
     use crate::MNT4_753;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_753, PairingVar>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT4_753>().unwrap()
 }

mnt6_298/src/constraints/curves.rs

@@ -16,14 +16,8 @@ pub type G2PreparedVar = mnt6::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
     use ark_ec::models::mnt6::MNT6Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G1Parameters>()
-        <Parameters as MNT6Parameters>::G1Parameters,
+        .unwrap();
-        G1Var,
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G2Parameters>()
-    >()
+        .unwrap();
-    .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<
-        <Parameters as MNT6Parameters>::G2Parameters,
-        G2Var,
-    >()
-    .unwrap();
 }

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 = constraints::PairingVar::prepare_g1(&a)?;
+//! let a_prep = MNT6_298::prepare_g1(&a)?;
-//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! let b_prep = MNT6_298::prepare_g2(&b)?;
-//! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
+//! let pairing_result = MNT6_298::pairing_gadget(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 = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let a_prep_const = MNT6_298::prepare_g1(&a_const)?;
-//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let b_prep_const = MNT6_298::prepare_g2(&b_const)?;
-//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
+//! let pairing_result_const = MNT6_298::pairing_gadget(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;

mnt6_298/src/constraints/pairing.rs

@@ -1,10 +1,8 @@
-use crate::Parameters;
-
 /// Specifies the constraints for computing a pairing in the MNT6-298 bilinear group.
-pub type PairingVar = ark_r1cs_std::pairing::mnt6::PairingVar<Parameters>;
+pub use crate::MNT6_298;
 
 #[test]
 fn test() {
     use crate::MNT6_298;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_298, PairingVar>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_298>().unwrap()
 }

mnt6_753/src/constraints/curves.rs

@@ -16,14 +16,8 @@ pub type G2PreparedVar = mnt6::G2PreparedVar<Parameters>;
 #[test]
 fn test() {
     use ark_ec::models::mnt6::MNT6Parameters;
-    ark_curve_constraint_tests::curves::sw_test::<
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G1Parameters>()
-        <Parameters as MNT6Parameters>::G1Parameters,
+        .unwrap();
-        G1Var,
+    ark_curve_constraint_tests::curves::sw_test::<<Parameters as MNT6Parameters>::G2Parameters>()
-    >()
+        .unwrap();
-    .unwrap();
-    ark_curve_constraint_tests::curves::sw_test::<
-        <Parameters as MNT6Parameters>::G2Parameters,
-        G2Var,
-    >()
-    .unwrap();
 }

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 = constraints::PairingVar::prepare_g1(&a)?;
+//! let a_prep = MNT6_753::prepare_g1(&a)?;
-//! let b_prep = constraints::PairingVar::prepare_g2(&b)?;
+//! let b_prep = MNT6_753::prepare_g2(&b)?;
-//! let pairing_result = constraints::PairingVar::pairing(a_prep, b_prep)?;
+//! let pairing_result = MNT6_753::pairing_gadget(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 = constraints::PairingVar::prepare_g1(&a_const)?;
+//! let a_prep_const = MNT6_753::prepare_g1(&a_const)?;
-//! let b_prep_const = constraints::PairingVar::prepare_g2(&b_const)?;
+//! let b_prep_const = MNT6_753::prepare_g2(&b_const)?;
-//! let pairing_result_const = constraints::PairingVar::pairing(a_prep_const, b_prep_const)?;
+//! let pairing_result_const = MNT6_753::pairing_gadget(a_prep_const, b_prep_const)?;
 //! println!("Done here 3");
 //!
 //! pairing_result.enforce_equal(&pairing_result_const)?;

mnt6_753/src/constraints/pairing.rs

@@ -1,10 +1,8 @@
-use crate::Parameters;
-
 /// Specifies the constraints for computing a pairing in the MNT6-753 bilinear group.
-pub type PairingVar = ark_r1cs_std::pairing::mnt6::PairingVar<Parameters>;
+pub use crate::MNT6_753;
 
 #[test]
 fn test() {
     use crate::MNT6_753;
-    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_753, PairingVar>().unwrap()
+    ark_curve_constraint_tests::pairing::bilinearity_test::<MNT6_753>().unwrap()
 }

pallas/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FBaseVar>;
+pub type GVar = ProjectiveVar<PallasParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::sw_test::<PallasParameters, GVar>().unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<PallasParameters>().unwrap();
 }

vesta/src/constraints/curves.rs

@@ -1,12 +1,10 @@
 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, FBaseVar>;
+pub type GVar = ProjectiveVar<VestaParameters>;
 
 #[test]
 fn test() {
-    ark_curve_constraint_tests::curves::sw_test::<VestaParameters, GVar>().unwrap();
+    ark_curve_constraint_tests::curves::sw_test::<VestaParameters>().unwrap();
 }