Communication Efficient Statistical Asynchronous Multiparty Computation with Optimal Resilience

We propose an efficient statistically secure asynchronous multiparty computation (AMPC) protocol with optimal fault tolerance; i.e., with n = 3t + 1, where n is the total number of parties and t is the number of parties that can be under the influence of a Byzantine (active) adversary A(t) having unbounded computing power. Our protocol privately communicates O(n(5) kappa) bits per multiplication gate and involves a negligible error probability of 2(-Omega(kappa)), where kappa, is the error parameter. As far as our knowledge is concerned, the only known statistically secure AMPC protocol with n = 3t + is due to [7], which privately communicates Omega(n(11) kappa(4)) bits and A-casts Omega(n(11) kappa(2) log(n)) bits per multiplication gate. Here A-cast is an asynchronous broadcast primitive, which allows a party to send some information to all other parties identically. Thus our AMPC protocol shows significant improvement in communication complexity over the AMPC protocol of [7].