Round-Optimal Secure Multiparty Computation with Honest Majority.

We study the exact round complexity of secure multiparty computation (MPC) in the honest majority setting. We construct several round-optimal n-party protocols, tolerating any t < n/2 corruptions. 1. Security with abort: We give the first construction of two round MPC for general functions that achieves security with abort against malicious adversaries in the plain model. The security of our protocol only relies on one-way functions. 2. Guaranteed output delivery: We also construct protocols that achieve security with guaranteed output delivery: (i) Against fail-stop adversaries, we construct two round MPC either in the (bare) public-key infrastructure model with no additional assumptions, or in the plain model assuming two-round semi-honest oblivious transfer. In three rounds, however, we can achieve security assuming only one-way functions. (ii) Against malicious adversaries, we construct three round MPC in the plain model, assuming public-key encryption and Zaps. Previously, such protocols were only known based on specific learning assumptions and required the use of common reference strings. All of our results are obtained via general compilers that may be of independent interest.