A necessary and sufficient synchrony condition for solving Byzantine consensus in symmetric networks

  • Authors:

  • Olivier Baldellon;Achour Mostéfaoui;Michel Raynal

  • Affiliations:

  • LAAS, CNRS, Toulouse, France;IRISA, Université de Rennes 1, Rennes, France;IRISA, Université de Rennes 1, Rennes, France

  • Venue:
  • ICDCN'11 Proceedings of the 12th international conference on Distributed computing and networking
  • Year:
  • 2011

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Abstract

Solving the consensus problem requires in one way or another that the underlying system satisfies synchrony assumptions. Considering a system of n processes where up to t n/3 may commit Byzantine failures, this paper investigates the synchrony assumptions that are required to solve consensus. It presents a corresponding necessary and sufficient condition. Such a condition is formulated with the notions of a symmetric synchrony property and property ambiguity. A symmetric synchrony property is a set of graphs, where each graph corresponds to a set of bi-directional eventually synchronous links among correct processes. Intuitively, a property is ambiguous if it contains a graph whose connected components are such that it is impossible to distinguish a connected component that contains correct processes only from a connected component that contains faulty processes only. The paper connects then the notion of a symmetric synchrony property with the notion of eventual bi-source, and shows that the existence of a virtual ⋄[t + 1]bi-source is a necessary and sufficient condition to solve consensus in presence of up to t Byzantine processes in systems with bi-directional links and message authentication. Finding necessary and sufficient synchrony conditions when links are timely in one direction only, or when processes cannot sign messages, still remains open (and very challenging) problems.