Feistel Structures for MPC, and More

Efficient PRP/PRFs are instrumental to the design of cryptographic protocols. We investigate the design of dedicated PRP/PRFs for three application areas - secure multiparty computation (MPC), ZKSNARK and zero-knowledge (ZK) based PQ signature schemes. In particular, we explore a family of PRFs which are generalizations of the well-known Feistel design approach followed in a previously proposed application specific design - MiMC. Attributing to this approach we call our family of PRP/PRFs GMiMC.

In MPC applications, our construction shows improvements (over MiMC) in throughput by a factor of more than 4 and simultaneously a 5-fold reduction of preprocessing effort, albeit at the cost of a higher latency. Another use-case where MiMC outperforms other designs, in SNARK applications, our design GMiMCHash shows moderate improvement. Additionally, in this case our design benefits from the flexibility of using smaller (prime) fields. In the area of recently proposed ZK-based PQ signature schemes where MiMC was not competitive at all, our new design has 30 times smaller signature size than MiMC.