We also show a simple technique for the sequential composition of protocols without simultaneous cessation (something that is inherent in bizantine protocols with o(n) turns in the case of t<n/2. In a revolutionary document, Feldman and Micali (STOC `88) present a Byzantine N-Party agreement that tolerates t < n/3 of the malicious parts that take place in expected constant cycles. Here we present a constant cycle protocol expected for authenticated Byzantine agreements, which are based on an honest majority (i.e. t < n/2) and rely only on the existence of a secure signature scheme and a public key infrastructure (PKI). In combination with the existing results, this gives the first expected constant cycle protocol for safe calculations to an honest majority in a point-to-point network that only accepts disposable functions and a PKI. Our most important technical tool – a new primitive that we are introducing as a moderate VSS – also provides simpler proof of the Feldman-Micali result. CRYPTO 2006 : Advances in Cryptology – CRYPTO 2006 pp 445-462 | Cite as. . . . .