bug: Added test for FROBENIUS_COEFF_FQ6_C1 and fixed incorrect constant (#1471)

Added a test for the `FROBENIUS_COEFF_FQ6_C1` constant in the pairing
extension. The test checks that the values are the same as those in
`halo2curves_shims` I found that `FREBENIUS_COEFF_FQ6_C1[0]` did not
pass the test. This value is not currently being used in the code, but
for completeness, I updated it to be correct.

Author: Avaneesh-axiom

extensions/pairing/guest/src/bn254/mod.rs

@@ -140,7 +140,7 @@ impl Bn254 {
     pub const FROBENIUS_COEFF_FQ6_C1: [Fp2; 3] = [
         Fp2 {
             c0: Bn254Fp(hex!(
-                "9d0d8fc58d435dd33d0bc7f528eb780a2c4679786fa36e662fdf079ac1770a0e"
+                "0100000000000000000000000000000000000000000000000000000000000000"
             )),
             c1: Bn254Fp(hex!(
                 "0000000000000000000000000000000000000000000000000000000000000000"

extensions/pairing/guest/src/bn254/tests.rs

@@ -1,6 +1,7 @@
 use group::{ff::Field, prime::PrimeCurveAffine};
 use halo2curves_axiom::bn256::{
     Fq, Fq12, Fq2, Fq6, G1Affine, G2Affine, G2Prepared, Gt, FROBENIUS_COEFF_FQ12_C1,
+    FROBENIUS_COEFF_FQ6_C1,
 };
 use num_bigint::BigUint;
 use num_traits::One;
@@ -288,3 +289,16 @@ fn test_bn254_final_exponent() {
     let final_exp = (BN254_MODULUS.pow(12) - BigUint::one()) / BN254_ORDER.clone();
     assert_eq!(Bn254::FINAL_EXPONENT.to_vec(), final_exp.to_bytes_be());
 }
+
+#[test]
+fn test_bn254_frobenius_coeffs_fq6() {
+    #[allow(clippy::needless_range_loop)]
+    for i in 0..3 {
+        assert_eq!(
+            Bn254::FROBENIUS_COEFF_FQ6_C1[i],
+            convert_bn254_halo2_fq2_to_fp2(FROBENIUS_COEFF_FQ6_C1[i]),
+            "FROBENIUS_COEFFS_FQ6_C1[{}] failed",
+            i,
+        )
+    }
+}