Bee’s Strategy Against Byzantines Replacing Byzantine Participants

Abstract

Schemes for the identification and replacement of two-faced Byzantine processes are presented. The detection is based on the comparison of the (blackbox) decision result of a Byzantine consensus on input consisting of the inputs of each of the processes, in a system containing n processes $p_1,\dots , p_n$. Process $p_i$ that received a gossiped message from $p_j$ with the input of another process $p_k$, that differs from $p_k$’s input value as received from $p_k$ by $p_i$, reports on $p_k$ and $p_j$ being two-faced. If enough processes (where enough means at least $t+1$, $t<n$ is a threshold on the number of Byzantine participants) report on the same participant $p_j$ to be two-faced, participant $p_j$ is replaced. If less than the required $t+1$ processes threshold report on a participant $p_j$, both the reporting processes and the reported process are replaced. If one of them is not Byzantine, its replacement is the price to pay to cope with the uncertainty created by Byzantine processes. The scheme ensures that any two-faced Byzantine participant that prevents fast termination is eliminated and replaced. Such replacement may serve as a preparation for the next invocations of Byzantine agreement possibly used to implement a replicated state machine.

The research was partially supported by the Rita Altura Trust Chair in Computer Sciences; the Lynne and William Frankel Center for Computer Science; the Ministry of Foreign Affairs, Italy; the grant from the Ministry of Science, Technology and Space, Israel, and the National Science Council (NSC) of Taiwan; the Ministry of Science, Technology and Space, Infrastructure Research in the Field of Advanced Computing and Cyber Security; and the Israel National Cyber Bureau. Michel Raynal visited BGU with the support of the Dozor foundation. Contact author: Shlomi Dolev.