Byzantine Consensus in Directed Graphs with Message Authentication

2026-05-11

AI Summary

This study addresses the solvability of Byzantine fault-tolerant consensus in directed communication networks, focusing on exact consensus in synchronous systems and approximate consensus in asynchronous ones. By integrating graph-theoretic analysis, message authentication mechanisms (such as digital signatures), and distributed consensus theory, the work establishes for the first time necessary and sufficient structural conditions on the underlying directed graphs under which consensus can be achieved in both system models. These conditions significantly relax the traditional assumptions requiring undirected or strongly connected topologies. The results precisely characterize the structural properties that directed graphs must satisfy to support consensus despite Byzantine failures, thereby providing a rigorous theoretical foundation for designing consensus protocols in real-world systems with weak connectivity.

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.

Problem

• Byzantine Consensus
• Directed Graphs
• Message Authentication
• Exact Consensus
• Approximate Consensus

Innovation

• Byzantine Consensus
• Directed Graphs
• Message Authentication
• Synchronous Systems
• Asynchronous Systems