Should MPCProtocol be generic over a secret-shared number

[th4s]

Clarify whether having MPCProtocol be generic over a secret-shared number with an associated type makes sense for the kinds of MPC protocols we want to support.

[Mikerah]

The answer is no.
Protocols like HoneyBadgerMPC require a minimum field size of n where n is the number of parties that are a part of the shamir secret sharing scheme. Pretty sure this applies for all of the protocols that rely on stuff like shamir secret sharing.

So, we should explore the approach of having associated types for both secret shared numbers and public numbers.

[th4s]

Objection: https://play.rust-lang.org/?version=stable&mode=debug&edition=2021&gist=e97a4eb0852433e0bb8de71932fe7ed0

An associated type trait can only be implemented ONCE for some struct.

[Mikerah]

I don't think that's a problem.
We only need to design the higher-level APIs to be such that the developer can choose the ring/field they need.