In this paper, we design unconditionally secure multi-party computation (MPC) protocols in the asynchronous communication setting with optimal resilience. Our protocols are secure against a computationally unbounded malicious adversary characterized by an adversary structure Z, which enumerates all possible subsets of potentially corrupt parties. We present protocols with both perfect-security, as well as with statistical-security. While the protocols in the former class achieve all the security properties in an error-free fashion, the protocols belonging to the latter category achieve all the security properties except with a negligible error. Our perfectly secure protocol incurs an amortized communication of |Z|^2 bits per multiplication. This improves upon the protocol of Choudhury and Pappu (INDOCRYPT 2020) with the least known amortized communication complexity of |Z|^3 bits per multiplication. On the other hand, our statistically secure protocol incurs an amortized communication of |Z| bits per multiplication. This is the first statistically secure asynchronous MPC protocol against general adversaries. Previously, perfectly secure and statistically secure MPC with an amortized communication cost of |Z|^2 and |Z| bits, respectively, per multiplication was known only in the relatively simpler synchronous communication setting (Hirt and Tschudi in ASIACRYPT, Springer, 2013).

Publication Information: published in Journal of Cryptology. Joint work with Ananya Appan and Anirudh Chandramouli.