Improved Connectivity Condition for Byzantine Fault Tolerance

TL;DR

This paper introduces a new, tight connectivity condition for Byzantine fault tolerance that allows reliable message passing in networks with potentially colluding faulty nodes, without requiring nodes to know the network structure.

Contribution

It provides a novel characterization of solvable agreement conditions under Byzantine faults, expanding the known bounds and removing the need for nodes to know the network topology.

Findings

New tight bound for Byzantine agreement based on minimal vertex cuts.

Algorithm that does not require nodes to know the network graph.

Applicable in scenarios with trustworthy nodes or subgraphs.

Abstract

Given a network in which some pairs of nodes can communicate freely, and some subsets of the nodes could be faulty and colluding to disrupt communication, when can messages reliably be sent from one given node to another? We give a new characterization of when the agreement problem can be solved and provide an agreement algorithm which can reach agreement when the number of Byzantine nodes along each minimal vertex cut is bounded. Our new bound holds for a strict superset of cases than the previously known bound. We show that the new bound is tight. Furthermore, we show that this algorithm does not require the processes to know the graph structure, as the previously known algorithm did. Finally, we explore some of the situations in which we can reach agreement if we assume that individual nodes or entire subgraphs are trustworthy.