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In this paper, we design secure multi-party computation (MPC) protocols inthe asynchronous communication setting with optimal resilience. Our protocolsare secure against a computationally-unbounded malicious adversary,characterized by an adversary structure $\mathcal{Z}$, which enumerates allpossible subsets of potentially corrupt parties. Our protocols incur acommunication of $\mathcal{O}(|\mathcal{Z}|^2)$ and$\mathcal{O}(|\mathcal{Z}|)$ bits per multiplication for perfect andstatistical security respectively. These are the first protocols with thiscommunication complexity, as such protocols were known only in the synchronouscommunication setting (Hirt and Tschudi, ASIACRYPT 2013).

Revisiting the Efficiency of Asynchronous Multi Party Computation Against General Adversaries