Polynomial algorithms for multiple processor agreement

Reaching agreement in a distributed system while handling malfunctioning behavior is a central issue for reliable computer systems. All previous algorithms for reaching the agreement required an exponential number of messages to be sent, with or without authentication. We give polynomial algorithms for reaching (Byzantine) agreement, both with and without the use of authentication protocols. We also prove that no matter what kind of information is exchanged, there is no way to reach agreement with fewer than t+1 rounds of exchange, where t is the upper bound on the number of faults.