Paper 2026/2393

Round Optimal MPC With Provable Cheater Identification

Abstract

Secure multiparty computation with provable identifiable selective abort (PISA), introduced by Kondi and Ravi (CCS 2025), guarantees that every honest party either obtains the computation output or a certificate that convinces any external auditor that a specific party cheated. Crucially, honest parties need not agree: some may get output while others receive evidence of cheating. In contrast, secure computation with identifiable abort (IA) requires just such unanimity; however, in the event that an honest party doesn't get output, it need merely be able to point to a cheater - not to prove their guilt. Secure computation with IA classically requires broadcast. Kondi and Ravi demonstrated that secure computation with PISA, on the other hand, can be built over point-to-point channels alone. While PISA is feasible exactly when guaranteed output delivery is, i.e. for $t < n / 2$, the best known construction over point-to-point channels requires six rounds. We settle the round complexity of PISA for all but a narrow band of thresholds. We prove that two rounds are impossible for $t \geq n /3$, even with arbitrary setup and computational assumptions; we give a three-round protocol for any $t < n/2$, which is therefore round-optimal for $n / 3 \leq t < n/2$; and we give a two-round protocol for $t < n/4$. The two-round protocol introduces a new primitive called one-or-nothing secret sharing with omissions.