Towards Achieving Asynchronous MPC with Linear Communication and Optimal Resilience

Secure multi-party computation (MPC) allows a set of $n$ parties to jointly compute a function over their private inputs. The seminal works of Ben-Or, Canetti and Goldreich [STOC '93] and Ben-Or, Kelmer and Rabin [PODC '94] settled the feasibility of MPC over asynchronous networks. Despite the significant line of work devoted to improving the communication complexity, current protocols with information-theoretic security and optimal resilience $t<n/3$ communicate $\Omega(n^4C)$ field elements for a circuit with $C$ multiplication gates. In contrast, synchronous MPC protocols with $O(nC)$ communication have long been known.

In this work we make progress towards closing this gap. We provide a novel MPC protocol in the asynchronous setting with statistical security that makes black-box use of an asynchronous complete secret-sharing (ACSS) protocol. The cost per multiplication reduces to the cost of distributing a constant number of sharings via ACSS, improving a linear factor over the state of the art by Choudhury and Patra [IEEE Trans. Inf. Theory '17].

With a recent concurrent work achieving ACSS with linear cost per sharing, we achieve an MPC with ${O}(nC)$ communication and optimal resilience.