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

@@ -12,9 +12,6 @@
     /// 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)

@@ -3,7 +3,7 @@ fields::*, generate_field_serialization_test, generate_field_test,
 };
 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 @@ cmp::Ordering,
     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;);
@@ -144,26 +144,6 @@ let mut m1 = -Fq2::one();
     assert_eq!(QuadraticResidue, m1.legendre());
     m1 = Fq6Config::mul_fp2_by_nonresidue(&m1);
     assert_eq!(QuadraticNonResidue, m1.legendre());
-}
-
-#[test]
-fn test_fq2_mul_nonresidue() {
-    let mut rng = test_rng();
-
-    let nqr = Fq2::new(Fq::zero(), Fq::one());
-
-    let quadratic_non_residue = Fq2::new(
-        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]

@@ -12,9 +12,6 @@
     /// 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)

@@ -12,9 +12,6 @@
     /// 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)

@@ -1,6 +1,6 @@
 use ark_ff::{
     fields::fp2::{Fp2, Fp2Config},
-    MontFp, QuadExt,
+    MontFp,
 };
 
 use crate::{Fq, FQ_ONE};
@@ -15,11 +15,6 @@
     /// The quadratic non-residue (17) used to construct the extension is
     /// 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]`

@@ -1,6 +1,6 @@
 use ark_ff::{
     fields::fp2::{Fp2, Fp2Config},
-    MontFp, QuadExt,
+    MontFp,
 };
 
 use crate::{Fq, FQ_ONE};
@@ -14,9 +14,6 @@ type Fp = Fq;
 
     // 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]