Optimal time Byzantine agreement for t < n/8 with linear messages

Abstract

The Byzantine Agreement problem provides an abstract setting in which methods for tolerating faults in distributed systems may be explored and perhaps influence practical designs. A Byzantine Agreement protocol is a distributed protocol in which one distinguished processor called the source broadcasts some initial value to all other processors. The protocol is designed to tolerate up to t faulty processors. The receiving processors should agree on some common output value. In case the source is correct the output value should be equal to the source's initial value. The quality of a Byzantine agreement protocol is measured by the following parameters: the ratio between the total number of processors n and the number of faulty processors t, the number of rounds of message exchange needed to reach an agreement, and the communication complexity, given by the size m of the maximal message. This paper presents a Byzantine Agreement protocol with n=8·t+1, optimal number of rounds (namely minf + 2, t + 1 where f is number of actual faults), and messages of linear size (namely m≤n+O(log n)). This is the first protocol that reaches Byzantine Agreement in optimal time, tolerates t=O(n) faults and uses messages of linear size. All previous protocols that stop in optimal time and tolerate t=O(n) faults require messages of size at least O(n ²). The new protocol uses a novel technique called Reconstructed Traversal which is based on the Reconstruction Principle and on the Coordinated Traversal protocol.