Optimally Resilient Asynchronous MPC with Linear Communication Complexity

We present a secure asynchronous multiparty computation (AMPC) protocol with optimal resilience, involving n = 3t + 1 parties and tolerating a computationally bounded static adversary, capable of corrupting upto t parties. For a security parameter k and for circuits of sufficiently large size, our protocol has an amortized communication complexity of O(cMnk) bits, where cM denotes the number of multiplication gates in the arithmetic circuit, representing the function to be computed. Prior to our work, the most efficient optimally resilient, computationally secure AMPC protocol was due to Hirt et al. (ICALP 2008). The protocol offers an amortized communication complexity of O(cMn2k) bits. Our protocol follows the standard offline-online paradigm. In the offline phase, the parties produce encryptions of random multiplication triples. These are used to securely evaluate the multiplication gates in the online phase, using Beaver's circuit-randomization technique (CRYPTO 1991). The offline protocol of earlier works deploy linearly homomorphic encryption schemes. Our offline phase is much simpler and more efficient than the existing protocols and uses linearly homomorphic encryption scheme with support for one homomorphic multiplication.