Paper 2024/990

Perfectly-secure Network-agnostic MPC with Optimal Resiliency

Abstract

We study network-agnostic secure multiparty computation with perfect security. Traditionally MPC is studied assuming the underlying network is either synchronous or asynchronous. In a network-agnostic setting, the parties are unaware of whether the underlying network is synchronous or asynchronous. The feasibility of perfectly-secure MPC in synchronous and asynchronous networks has been settled a long ago. The landmark work of [Ben-Or, Goldwasser, and Wigderson, STOC'88] shows that $n > 3t_s$ is necessary and sufficient for any MPC protocol with $n$-parties over synchronous network tolerating $t_s$ active corruptions. In yet another foundational work, [Ben-Or, Canetti, and Goldreich, STOC'93] show that the bound for asynchronous network is $n > 4t_a$, where $t_a$ denotes the number of active corruptions. However, the same question remains unresolved for network-agnostic setting till date. In this work, we resolve this long-standing question. We show that perfectly-secure network-agnostic $n$-party MPC tolerating $t_s$ active corruptions when the network is synchronous and $t_a$ active corruptions when the network is asynchronous is possible if and only if $n > 2 \max(t_s,t_a) + \max(2t_a,t_s)$. When $t_a \geq t_s$, our bound reduces to $n > 4t_a$, whose tightness follows from the known feasibility results for asynchronous MPC. When $t_s > t_a$, our result gives rise to a new bound of $n > 2t_s + \max(2t_a,t_s)$. Notably, the previous network-agnostic MPC in this setting [Appan, Chandramouli, and Choudhury, PODC'22] only shows sufficiency for a loose bound of $n > 3t_s + t_a$. When $t_s > 2t_a$, our result shows tightness of $ n > 3t_s$, whereas the existing work shows sufficiency for $n > 3t_s+t_a$.