Paper 2017/1006

Round and Communication Efficient Unconditionally-secure MPC with $t < n/3$ in Partially Synchronous Network

Ashish Choudhury, Arpita Patra, and Divya Ravi

Abstract

In this work, we study unconditionally-secure multi-party computation (MPC) tolerating $t < n/3$ corruptions, where $n$ is the total number of parties involved. In this setting, it is well known that if the underlying network is completely asynchronous, then one can achieve only statistical security; moreover it is impossible to ensure input provision and consider inputs of all the honest parties. The best known statistically-secure asynchronous MPC (AMPC) with $t<n/3$ requires a communication of $O(n^5)$ field elements per multiplication. We consider a partially synchronous setting, where the parties are assumed to be globally synchronized initially for few rounds and then the network becomes completely asynchronous. In such a setting, we present a MPC protocol, which requires $O(n^2)$ communication per multiplication while ensuring input provision. Our MPC protocol relies on a new four round, communication efficient statistical verifiable secret-sharing (VSS) protocol with broadcast communication complexity independent of the number of secret-shared values.