Adaptive Byzantine Agreement in O(t) Phases

Abstract

In order to achieve consistency on a value among m nodes involved in a distributed system, and thereby dealing with up to t faulty nodes, t<m, authenticated Byzantine agreement protocols (BAPs) are employed. The best of all authenticated BAPs, with respect to the worst case number of messages, needs O(t) phases and O(m+t ²) messages. As a disadvantage, this high number of messages is needed even in the faultless case. Adaptive Byzantine agreement protocols (ABAPs), a subclass of BAPs, minimize the number of messages for the faultless case (O(m)), at the expense of the fault cases, in order to reduce the expected communication overhead if faults occur rarely: If no faults occur, ABAPs do not need more messages than protocols not tolerating any faults. In contrast with usual BAPs, ABAPs are far from being studied exhaustively up to now.

In this paper, an ABAP is given which needs O(m ² t) messages and up to 2t+3 phases for distributing one value consistently. In the faultless case, exactly m−1 messages and t+1 phases are needed. This is the first ABAP with a linear worst case number of phases.

It is sketched how to extend this protocol into one which achieves consistency on values of all m nodes, using O(m2t) messages and 2t+4 phases, and 2(m−l) messages and t+2 phases in the faultless case.