`QUADRATIC_NONRESIDUE` is never used, remove (#104)

* `QUADRATIC_NONRESIDUE` is never used, remove

* Update CHANGELOG.md

* Remove unused imports

CHANGELOG.md

@@ -7,6 +7,8 @@
 
 ### Breaking changes
 
+- [\#104](https://github.com/arkworks-rs/curves/pull/104) Remove `QUADRATIC_NONRESIDUE` parameter from implementors of `Fp2Config`.
+ 
 ### Features
 
 ### Improvements

bls12_377/src/fields/fq2.rs

@@ -12,9 +12,6 @@ impl Fp2Config for Fq2Config {
     /// NONRESIDUE = -5
     const NONRESIDUE: Fq = MontFp!(Fq, "-5");
 
-    /// QUADRATIC_NONRESIDUE = U
-    const QUADRATIC_NONRESIDUE: Fq2 = QuadExt!(FQ_ZERO, FQ_ONE);
-
     /// Coefficients for the Frobenius automorphism.
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // NONRESIDUE**(((q^0) - 1) / 2)

bls12_377/src/fields/tests.rs

@@ -3,7 +3,7 @@ use ark_algebra_test_templates::{
 };
 use ark_ff::{
     biginteger::{BigInt, BigInteger, BigInteger384},
-    fields::{FftField, Field, Fp2Config, Fp6Config, PrimeField, SquareRootField},
+    fields::{FftField, Field, Fp6Config, PrimeField, SquareRootField},
     One, UniformRand, Zero,
 };
 use ark_serialize::{buffer_bit_byte_size, CanonicalSerialize};
@@ -13,7 +13,7 @@ use core::{
     ops::{AddAssign, MulAssign, SubAssign},
 };
 
-use crate::{Fq, Fq12, Fq2, Fq2Config, Fq6, Fq6Config, FqConfig, Fr, FrConfig};
+use crate::{Fq, Fq12, Fq2, Fq6, Fq6Config, FqConfig, Fr, FrConfig};
 
 generate_field_test!(bls12_377; fq2; fq6; fq12; mont(6, 4); );
 generate_field_serialization_test!(bls12_377; fq2; fq6; fq12;);
@@ -146,26 +146,6 @@ fn test_fq2_legendre() {
     assert_eq!(QuadraticNonResidue, m1.legendre());
 }
 
-#[test]
-fn test_fq2_mul_nonresidue() {
-    let mut rng = test_rng();
-
-    let nqr = Fq2::new(Fq::zero(), Fq::one());
-
-    let quadratic_non_residue = Fq2::new(
-        Fq2Config::QUADRATIC_NONRESIDUE.c0,
-        Fq2Config::QUADRATIC_NONRESIDUE.c1,
-    );
-    for _ in 0..1000 {
-        let mut a = Fq2::rand(&mut rng);
-        let mut b = a;
-        a = quadratic_non_residue * &a;
-        b.mul_assign(&nqr);
-
-        assert_eq!(a, b);
-    }
-}
-
 #[test]
 fn test_fq6_mul_by_1() {
     let mut rng = test_rng();

bls12_381/src/fields/fq2.rs

@@ -12,9 +12,6 @@ impl Fp2Config for Fq2Config {
     /// NONRESIDUE = -1
     const NONRESIDUE: Fq = MontFp!(Fq, "-1");
 
-    /// QUADRATIC_NONRESIDUE = (U + 1)
-    const QUADRATIC_NONRESIDUE: Fq2 = QuadExt!(FQ_ONE, FQ_ONE);
-
     /// Coefficients for the Frobenius automorphism.
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // Fq(-1)**(((q^0) - 1) / 2)

bn254/src/fields/fq2.rs

@@ -12,9 +12,6 @@ impl Fp2Config for Fq2Config {
     /// NONRESIDUE = -1
     const NONRESIDUE: Fq = MontFp!(Fq, "-1");
 
-    /// QUADRATIC_NONRESIDUE = U+2
-    const QUADRATIC_NONRESIDUE: Fq2 = QuadExt!(MontFp!(Fq, "2"), MontFp!(Fq, "1"));
-
     /// Coefficients for the Frobenius automorphism.
     const FROBENIUS_COEFF_FP2_C1: &'static [Fq] = &[
         // NONRESIDUE**(((q^0) - 1) / 2)

mnt4_298/src/fields/fq2.rs

@@ -1,6 +1,6 @@
 use ark_ff::{
     fields::fp2::{Fp2, Fp2Config},
-    MontFp, QuadExt,
+    MontFp,
 };
 
 use crate::{Fq, FQ_ONE};
@@ -16,11 +16,6 @@ impl Fp2Config for Fq2Config {
     /// the same as that used in [`libff`](https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L102).
     const NONRESIDUE: Fq = MontFp!(Fq, "17");
 
-    /// The quadratic non-residue in F<sub>p</sub><sup>2</sup> that is used
-    /// in the computation of square roots is (8, 1), the same as that in
-    /// [`libff`](https://github.com/scipr-lab/libff/blob/c927821ebe02e0a24b5e0f9170cec5e211a35f08/libff/algebra/curves/mnt/mnt4/mnt4_init.cpp#L103)
-    const QUADRATIC_NONRESIDUE: Fq2 = QuadExt!(MontFp!(Fq, "8"), FQ_ONE);
-
     /// Precomputed coefficients:
     /// `[1, 475922286169261325753349249653048451545124879242694725395555128576210262817955800483758080]`
     const FROBENIUS_COEFF_FP2_C1: &'static [Self::Fp] = &[

mnt4_753/src/fields/fq2.rs

@@ -1,6 +1,6 @@
 use ark_ff::{
     fields::fp2::{Fp2, Fp2Config},
-    MontFp, QuadExt,
+    MontFp,
 };
 
 use crate::{Fq, FQ_ONE};
@@ -15,9 +15,6 @@ impl Fp2Config for Fq2Config {
     // non_residue = 13
     const NONRESIDUE: Fq = MontFp!(Fq, "13");
 
-    // qnr = (8, 1)
-    const QUADRATIC_NONRESIDUE: Fq2 = QuadExt!(MontFp!(Fq, "8"), FQ_ONE);
-
     // Coefficients:
     // [1, 41898490967918953402344214791240637128170709919953949071783502921025352812571106773058893763790338921418070971888253786114353726529584385201591605722013126468931404347949840543007986327743462853720628051692141265303114721689600]
     // see https://github.com/o1-labs/snarky/blob/2cf5ef3a14989e57c17518832b3c52590068fc48/src/camlsnark_c/libsnark-caml/depends/libff/libff/algebra/curves/mnt753/mnt4753/mnt4753_init.cpp