MESSAGE-OPTIMAL PROTOCOLS FOR BYZANTINE AGREEMENT

It is often important for the correct processes in a distributed system to reach agreement, despite the presence of some faulty processes. Byzantine Agreement (BA) is a paradigm problem that attempts to isolate the key features of reaching agreement. We focus here on the number of messages required to reach BA, with particular emphasis on the number of messages required in the failure-free runs, since these are the ones that occur most often in practice. The number of messages required is sensitive to the types of failures considered. In earlier work, Amdur et al. (1992) established tight upper and lower bounds on the worst- and average-case number of messages required in failure-free runs for crash failures. We provide tight upper and lower bounds for all remaining types of failures that have been considered in the literature on the BA problem: receiving omission, sending omission, and general omission failures, as well as arbitrary failures with or without message authentication. We also establish a tradeoff between number of rounds and number of messages in the failure-free runs required to reach agreement in the case of crash, sending, and general omission failures.