Communication Efficient Semi-Honest Three-Party Secure Multiparty Computation with an Honest Majority

In this work, we propose a novel protocol for secure three-party computation with an honest majority. For each AND gate, our protocol requires only two bits of communication in the online phase and two bits of communication in the offline phase. Also, only P2 and P3 are involved in the online phase. Our protocol is simulation-based secure in the presence of semi-honest adversaries, and achieves privacy but not correctness in the presence of malicious adversaries. The best previously known construction in this setting requires three bits of communication per AND gate in the online phase and does not achieve constant communication rounds for P1. This makes our protocol especially interesting for cases where P1 can only communicate to the other parties with high latency. Additionally, our protocol can achieve circuit privacy against P3 if P1 and P2 also send bits for every XOR gate to P3. This property may be interesting to achieve a two-party computation where P3 only acts as an auxiliary party with no input and should not learn the computed function. Our protocol also supports the client-server model and works for both arithmetic and boolean circuits.