Round-Optimal Black-Box Multiparty Computation from Polynomial-Time Assumptions

A central direction of research in secure multiparty computation with dishonest majority has been to achieve three main goals:

1. reduce the total number of rounds of communication (to four, which is optimal);
2. use only polynomial-time hardness assumptions, and
3. rely solely on cryptographic assumptions in a black-box manner.

This is especially challenging when we do not allow a trusted setup assumption of any kind. While protocols achieving two out of three goals in this setting have been designed in recent literature, achieving all three simultaneously remained an elusive open question. Specifically, it was answered positively only for a restricted class of functionalities. In this paper, we completely resolve this long-standing open question. Specifically, we present a protocol for all polynomial-time computable functions that does not require any trusted setup assumptions and achieves all three of the above goals simultaneously.