Honest Majority MPC with Abort with Minimal Online Communication
Abstract: In this work we focus on improving the communication complexity of the 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 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.
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