On expected constant-round protocols for Byzantine agreement

In a seminal paper, Feldman and Micali show an n-party Byzantine agreement protocol in the plain model that tolerates $t<n/3$ malicious parties and runs in expected constant rounds. Here, resolving a question that had been open since their work, we show an expected constant-round protocol for authenticated Byzantine agreement assuming honest majority (i.e., $t<n/2$), and relying only on the existence of signature schemes and a public-key infrastructure. Combined with existing results, this gives the first expected constant-round protocol for secure computation with honest majority in a point-to-point network under the same assumptions. Our key technical tool — a new primitive we introduce called moderated VSS — also yields a simpler proof of the Feldman–Micali result.In addition, we show a simple technique for sequential composition of Byzantine agreement protocols that do not achieve simultaneous termination, something that is inherent for protocols using $o(t)$ rounds.