I am working on an efficient mental poker framework. I have implemented a functional and secure commutative encryption scheme based on ElGamal as described in:
However, shuffling and dealing an entire deck is causing slowdown as the number of players involved in the game increases (more players means more commutative encryptions and decryptions). Even in initial, idealized tests things are pretty slow.
The system parameters currently used are an advisable 2048-bit safe prime (from RFC 5114) but I'm wondering if these key sizes are overkill in the case of something like mental poker where decryptions of relevant cards will happen within a few minutes and after the hand the security of the previous deck is irrelevant? This got me wondering in general if key sizes are flexible depending on "how long the encryption needs to last" - are there any guidelines here? Any pitfalls I'm not considering?