Secure Multi-Party Computation Using Pre-distributed Information from an Initializer

Secure Multi-Party Computation (MPC) is a concept that includes a system of n participants communicating each other securely such that the participants want to compute any given function using their private inputs without giving any information about their inputs. The matter of computing a multiplication gate has raised a security concern. That is, because the multiplication gate rises the degree of the resulted polynomial while there is a limited number of required participants to reconstruct and compute the outcome. In this study, we propose a MPC protocol using a server or a remote computer as an initializer, which has become popular these days to conduct a probabilistic functionality in the circuit. The initializer does not get involved in the actual online computation and it can just share some random pre-computed information at any time prior to it. Our protocol needs only one round of online secret sharing, and the online computation of both the inputs addition and multiplication gates can be executed in parallel. The extension of our protocol can be used for the multiplication gates with different multiplicative depths (intermediate levels). The proposed protocol is information-theoretic secure against a coalition of t passive adversaries with the presence of at least n≥ t+ 1 participants. The communication complexity of a multiplication gate is linear