std::math::Fp2 implementation for BN254 is not correct due to choice of quadratic non residue

[onurinanc]

In the std::math::Fp2 line 8. It is specified that /// the Goldilocks or the BN254 field) relative to the irreducible polynomial X^2 - 7.

X^2 - 7 is an irreducible polynomial over the Goldilocks field.

However, X^2 - 7 is not an irreducible polynomial over the BN254 field. It means that the Fp2 implementation of the BN254 is not proper, and might have issues since "not every element has an inverse in the extension field"

So, we need to separate the fp2 implementations of Goldilocks and BN254

For, BN254 Fp2 implementation, we can choose the irreducible polynomial X^2 + 1

[onurinanc]

I double-checked this and realized I made the irreducibility test with the bn254 base field, which is wrong. I made the test with the bn254 scalar field right now and x^2 - 7 is irreducible.

We can close this issue.

[chriseth]

Still, the implementation does not assert anything about the field.