🔥 Emulated pairings

This project expands upon Feltroid Prime's note 'Faster Extension Field multiplications for Emulated Pairing Circuits'. The note describes using Fiat-Shamir and Schwartz-Zippel to verify precomputed field multiplications. I have prepared a more efficient version in the notes to allow for much larger circuit verification.

As we try to prove larger computations the degree of one of the polynomials grows linearly with the computation. With a large degree comes increased calldata size and computation costs for hashing each coefficient for Fiat-Shamir. I have shared a more optimised version which uses modding by another polynomial to eliminated irrelevant degrees off the target polynomial.