Efficient Asynchronous Multiparty Computation with Optimal Resilience

We propose an efficient information theoretic secure asynchronous multiparty computation (AMPC)protocol with optimal fault tolerance; i.e., with n = 3t + 1, where n is the total number of parties andt is the number of parties that can be under the influence of a Byzantine (active) adversaryAt havingunbounded computing power. Our protocol communicates O(n5κ) bits per multiplication and involvesa negligible error probability of 2−O(κ), where κ is the error parameter. As far as our knowledge isconcerned, the only known AMPC protocol with n = 3t+1 providing information theoretic security withnegligible error probability is due to [9], which communicates Ω(nκ) bits and A-Casts Ω(nκ log(n))bits per multiplication. Here A-Cast is an asynchronous broadcast primitive, which allows a party tosend the same information to all other parties identically. Thus our AMPC protocol shows significantimprovement in communication complexity over the AMPC protocol of [9]. As a tool for our AMPCprotocol, we introduce a new asynchronous primitive called Asynchronous Complete Verifiable SecretSharing (ACVSS), which is first of its kind and is of independent interest. For designing our ACVSS,we employ a new asynchronous verifiable secret sharing (AVSS) protocol which is better than all knowncommunication-efficient AVSS protocols with n = 3t + 1.