Round efficient computationally secure multi-party computation revisited

In this work, we consider the problem of secure multi-party computation (MPC) with n parties where at most t are under the control of a computationally bounded adversary given the constraint t < n/2. We aim to design a round efficient protocol by minimizing the number of rounds in which the broadcast primitive is involved. In this setting, the previous best protocol can be attributed to Katz-Koo (EUROCRYPT 2007) which is set in the offline-online paradigm (where the parties generate preprocessing data during the offline phase to lighten the computation in the online phase). Their online phase is a constant round protocol with no invocations of broadcast, while the offline phase protocol needs total 29 rounds with a broadcast invocation in one round. Our work improves the round complexity of their offline phase protocol, by running in 4 rounds, with only a single broadcast round. Additionally, we also improve the communication complexity of the offline phase protocol by a factor of Ω(n3). As a technical contribution, we present the first two round computationally-secure verifiable secret-sharing (VSS) scheme that invokes broadcast in only one round.