TL;DR: It is proved 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.
Abstract: 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.
TL;DR: The authors describe a method of securing concurrence among asynchronous processors in the presence of undetected faults by transmitting a target message among the processors to secure agreement as to a value within the messages such that no more than two messages need be sent.
Abstract: The authors describe a method of securing concurrence among asynchronous processors in the presence of undetected faults, comprising the steps of (1) invoking an authentication protocol in order to ensure that received messages were faithfully relayed by intermediate processors whether faulty or not, and (2) transmitting a target message among the processors to secure agreement as to a value within the messages such that no more than two messages need be sent.