Paper 2026/1277

On the Round Complexity of Dishonest-Majority MPC

Abstract

What is the round complexity of $n$-party secure multiparty computation (MPC) over point-to-point networks in the dishonest-majority setting with unanimous or identifiable abort? Despite decades of research, this foundational question remains open. While two-round MPC is achievable given a broadcast channel, and broadcast protocols with expected-constant rounds exist tolerating any constant fraction of corruptions, a naive combination of the two yields MPC with expected $O(\log n)$ rounds. The core obstacle lies in maintaining round efficiency under parallel composition without an honest majority. Moreover, existing lower bounds for standard broadcast do not apply to broadcast with abort, leaving the exact round complexity of this setting unknown. In this work, we systematically investigate the round complexity of MPC over point-to-point networks, providing positive and negative results: - We show that any broadcast protocol (and thus generic MPC) with unanimous abort tolerating super-constant corruptions requires super-constant rounds, ruling out strict-constant-round protocols. - We construct a round-preserving, black-box parallel composition compiler for broadcast with unanimous abort. This yields our main result: Expected-constant-round MPC with unanimous abort in the PKI model against any constant fraction of corruptions, assuming oblivious transfer (OT) and verifiable random functions (VRFs). - Finally, we prove that expected-constant round broadcast (and MPC) with identifiable abort is impossible against $n - o(n)$ corruptions.