Paper 2020/1556 Original: eprint.iacr.org/2020/1556 ↗

Honest Majority MPC with Abort with Minimal Online Communication

Abstract

In this work we focus on improving the communication complexity of the \emph{online phase} of honest majority MPC protocols. To this end, we present a general and simple method to compile arbitrary secret-sharing-based passively secure protocols defined over an arbitrary ring that are secure up to additive attacks in a malicious setting, to actively secure protocols with abort. The resulting protocol has a total communication complexity in the online phase of $1.5(n-1)$ shares, which amounts to $1.5$ shares per party asymptotically. An important aspect of our techniques is that they can be seen as generalization of ideas that have been used in other works in a rather \emph{ad-hoc} manner for different secret-sharing protocols. Thus, our work serves as a way of unifying key ideas in recent honest majority protocols, to understand better the core techniques and similarities among these works. Furthermore, for $n=3$, when instantiated with replicated secret-sharing-based protocols (Araki et al.~CCS 2016), the communication complexity in the online phase amounts to only $1$ ring element per party, matching the communication complexity of the BLAZE protocol (Patra \& Suresh, NDSS 2020), while having a much simpler design.