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 and t is the number of parties that can be under the influence of a Byzantine (active) adversary At having unbounded computing power. Our protocol communicates O(n5κ) bits per multiplication and involves a negligible error probability of 2−O(κ), where κ is the error parameter. As far as our knowledge is concerned, the only known AMPC protocol with n = 3t+1 providing information theoretic security with negligible 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 to send the same information to all other parties identically. Thus our AMPC protocol shows significant improvement in communication complexity over the AMPC protocol of [9]. As a tool for our AMPC protocol, we introduce a new asynchronous primitive called Asynchronous Complete Verifiable Secret Sharing (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 known communication-efficient AVSS protocols with n = 3t + 1.