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

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 statisticallysecure asynchronous MPC (AMPC) with t < n/3 requires a communication of Ω(n) 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 requiresO(n) 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.