Byzantine Agreement By Distributed Randomization in 0log N Rounds

J H John H Reif

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In the beginning of the system's execution, another process Pq distinct from Pj P fl (the sender or "commander") sends a message M. To each P. . M^ is called the initial message, and its value, v e { 0, 1} . Let v be the complement of v. Each ?! is supplied with the same program, AP (called the Agreement Protocol ). As long as a P. Computes according to AP, it is called proper . Once a processor P. Deviates from AP it is faulty and is considered to remain faulty even if, later on, it reverts ba...ck to -4- following AP. We assume that the set of processors that eventually become faulty is independent of the random choices of our algorithm. Byzantine Agreement is achieved when (1) All proper processors agree on the same value, and (2) if the sender Pq sends the same value to everybody (operates correctly) then all proper processors agree on its value. Our analysis of the problem is based on the worst case assumption that faulty processors are not predictable and may be malicious. An algorithm should sustain any strange behavior of faulty processors, even a collusion to prevent the proper processors from reaching agreement.

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