Efficient Constructions of Non-interactive Secure Multiparty Computation from Pairwise Independent Hashing

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. Existing studies have been devoted to constructing NIMPC with small communication complexity, and many NIMPC have been presented so far. In this paper, we present a new generic construction of NIMPC for arbitrary functions from a class of functions called indicator functions. We employ pairwise independent hash functions to construct the proposed NIMPC, which results in smallest communication complexity compared to the existing generic constructions. We further present a concrete construction of NIMPC for the set of indicator functions with smallest communication complexity known so far. The construction also employs pairwise independent hash functions. It will be of independent interest to see how pairwise independent hash functions helps in constructing NIMPC.