Byzantine Consensus in Directed Graphs with Message Authentication

TL;DR

This paper investigates the conditions under which Byzantine consensus can be achieved in directed graphs with message authentication, providing necessary and sufficient criteria for both synchronous and asynchronous systems.

Contribution

It establishes the exact graph conditions needed for Byzantine consensus with message authentication in both synchronous and asynchronous networks.

Findings

Identifies necessary and sufficient conditions on directed graphs for exact consensus in synchronous systems.

Determines the conditions for approximate consensus in asynchronous systems.

Shows that message authentication enables Byzantine consensus under specific graph topologies.

Abstract

We consider the problem of reaching consensus in communication networks that are modeled by directed graphs. We assume the existence of a message authentication mechanism (such as digital signatures) to verify the integrity of messages. We identify the necessary and sufficient conditions on the directed communication graph for the following problems to be solvable: (i) exact consensus in synchronous systems; and (ii) approximate consensus in asynchronous systems.