Computational Irrelevancy: Bridging the Gap Between Pseudo- and Real Randomness in MPC Protocols

Due to the fact that classical computers cannot efficiently obtain random numbers, it is common practice to design cryptosystems in terms of real random numbers and then replace them with cryptographically secure pseudorandom ones for concrete implementations. However, as pointed out by the previous work (Nuida, PKC 2021), this technique may lead to compromise of security in secure multiparty computation (MPC) protocols, due to the property that a seed for a pseudorandom generator (PRG) is visible by an adversary in the context of MPC. Although this work suggested to use information-theoretically secure protocols (together with PRGs with high min-entropy) to alleviate the problem, yet it is preferable to base the security on computational assumptions rather than the stronger information-theoretic ones. By observing that the contrived constructions in the aforementioned work use MPC protocols and PRGs that are closely related to each other, we notice that it may help to alleviate the problem by using protocols and PRGs that are “unrelated” to each other. In this paper, we propose a notion called “computational irrelevancy” to formalise the term “unrelated” and under this condition provide a security guarantee under computational assumptions.