Secure multiparty computation with minimal interaction

Abstract

We revisit the question of secure multiparty computation (MPC) with two rounds of interaction. It was previously shown by Gennaro et al. (Crypto 2002) that 3 or more communication rounds are necessary for general MPC protocols with guaranteed output delivery, assuming that there may be t ≥ 2 corrupted parties. This negative result holds regardless of the total number of parties, even if broadcast is allowed in each round, and even if only fairness is required. We complement this negative result by presenting matching positive results. Our first main result is that if only one party may be corrupted, then n ≥ 5 parties can securely compute any function of their inputs using only two rounds of interaction over secure point-to-point channels (without broadcast or any additional setup). The protocol makes a black-box use of a pseudorandom generator, or alternatively can offer unconditional security for functionalities in NC1. We also prove a similar result in a client-server setting, where there are m ≥ 2 clients who hold inputs and should receive outputs, and n additional servers with no inputs and outputs. For this setting, we obtain a general MPC protocol which requires a single message from each client to each server, followed by a single message from each server to each client. The protocol is secure against a single corrupted client and against coalitions of t