In a seminal paper, Feldman and Micali (STOC '88) show an n-party Byzantine agreement protocol tolerating t < n/3 malicious parties that runs in expected constant rounds. Here, 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 a secure signature scheme and a public-key infrastructure (PKI). Combined with existing results, this gives the first expected constant-round protocol for secure computation with honest majority in a point-to-point network assuming only one-way functions and a PKI. Our key technical tool — a new primitive we introduce called moderated VSS — also yields a simpler proof of the Feldman-Micali result. We also show a simple technique for sequential composition of protocols without simultaneous termination (something that is inherent for Byzantine agreement protocols using o(n) rounds) for the case of t < n/2.
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