1970-01-01

(2026-02) Statistically Secure Asynchronous MPC with Linear Communication and -mathcal{O}(n^5) Additive Overhead

[[Xiaoyu Ji]]
[[Yifan Song]]

2026-02-19

Abstract

Secure multiparty computation (MPC) allows distrusted parties to jointly evaluate a common function while keeping their inputs private. In this work, we focus on improving the communication complexity of information-theoretic asynchronous MPC with optimal resilience ( $t < n/3$ ). The current state-of-the-art work in this setting by Goyal, Liu-Zhang, and Song [Crypto’24] achieves amortized linear communication per gate with $\Omega(n^{14})$ additive overhead. In comparison, the best-known result in the synchronous setting by Goyal, Song, and Zhu [Crypto’20] achieves the amortized linear communication per gate with only $\mathcal{O}(n^{6})$ additive overhead, revealing a significant gap that we aim to close.

This work closes this gap and goes further. We present the first statistically secure asynchronous MPC protocol achieving amortized linear communication per gate with only $\mathcal{O}(n^{5})$ additive overhead assuming a functionality for Agreement on Common Set (ACS). With the best-known instantiation for ACS, we obtain an asynchronous MPC protocol in the plain model with additive overhead $\mathcal{O}((\kappa+n)n^4\log\kappa)$ in expectation, where $\kappa$ is the security parameter. In the setting of statistical security with optimal resilience, this even surpasses the best synchronous result when $n\geq\sqrt{\kappa\log\kappa}$ .

Technically, our contributions include (i) a new protocol for generating Beaver triples with linear communication per triple and $\mathcal{O}(n^3)$ additive overhead assuming functionalities for generating random degree- $t$ Shamir sharings and ACS, and (ii) a new protocol for generating random degree- $t$ Shamir sharings with linear communication per sharing and $\mathcal{O}(n^{5})$ additive overhead assuming a functionality for ACS.