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A fundamental problem of distributed computing is that of simulating a (secure) broadcast channel, within the setting of a point-to-point network. This problem is known as Byzantine Agreement and has been the focus of much research. Lamport et al. showed that in order to achieve Byzantine Agreement in the standard model, more than 2/3 of the participating parties must be honest. They further showed that by augmenting the network with a public-key infrastructure, it is possible to obtain secure protocols for any number of faulty parties. This augmented problem is called "authenticated Byzantine Agreement".In this paper we consider the question of concurrent, parallel and sequential composition of authenticated Byzantine Agreement protocols. We present surprising impossibility results showing that:Authenticated Byzantine Agreement cannot be composed in parallel or concurrently (even twice), if 1/3 or more of the parties are faulty. Deterministic authenticated Byzantine Agreement protocols that run for r rounds and tolerate 1/3 or more faulty parties, can only be composed sequentially less than 2r times. In contrast, we present randomized protocols for authenticated Byzantine Agreement that compose sequentially for any polynomial number of times. We exhibit two such protocols: The first protocol tolerates corruptions of up to 1/2 of themparties, while In the first protocol, the number of faulty parties may be any number less than 1/2. On the other hand, the second protocol can tolerate any number of faulty parties, but is limited to the case that the overall number of parties is O(log k), where k is a security parameter. Finally, we show that when the model is further augmented so that unique and common session identifiers are assigned to each concurrent session, then any polynomial number of authenticated Byzantine agreement protocols can be concurrently executed, while tolerating any number of faulty parties.