An Efficient Construction of Non-Interactive Secure Multiparty Computation

Abstract

An important issue of secure multi-party computation (MPC) is to improve the efficiency of communication. Non-interactive MPC (NIMPC) introduced by Beimel et al. in Crypto 2014 completely avoids interaction in the information theoretical setting by allowing a correlated randomness setup where the parties get correlated random strings beforehand and locally compute their messages sent to an external output server. The goal of this paper is to reduce the communication complexity in terms of the size of random strings and messages. In this paper, we present an efficient construction of NIMPC, which is designed for arbitrary functions. In contrast to the previous NIMPC protocols, which separately compute each output bit, the proposed protocol simultaneously computes all output bits. As a result, the communication complexity of the proposed protocol is $\frac{\lceil \log d \rceil \cdot L}{\lceil \log d\rceil +L}$ times smaller than that of the best known protocol where d and L denote the size of input domain and the output length. Thus, the proposed protocol is the most efficient if both input and output lengths are larger than two.