Distributed Computing

, Volume 26, Issue 5–6, pp 321–340 | Cite as

Byzantine agreement with homonyms

  • Carole Delporte-GalletEmail author
  • Hugues Fauconnier
  • Rachid Guerraoui
  • Anne-Marie Kermarrec
  • Eric Ruppert
  • Hung Tran-The


So far, the distributed computing community has either assumed that all the processes of a distributed system have distinct identifiers or, more rarely, that the processes are anonymous and have no identifiers. These are two extremes of the same general model: namely, \(n\) processes use \(\ell \) different identifiers, where \(1 \le \ell \le n\). In this paper, we ask how many identifiers are actually needed to reach agreement in a distributed system with \(t\) Byzantine processes. We show that having \(3t+1\) identifiers is necessary and sufficient for agreement in the synchronous case but, more surprisingly, the number of identifiers must be greater than \(\frac{n+3t}{2}\) in the partially synchronous case. This demonstrates two differences from the classical model (which has \(\ell =n\)): there are situations where relaxing synchrony to partial synchrony renders agreement impossible; and, in the partially synchronous case, increasing the number of correct processes can actually make it harder to reach agreement. The impossibility proofs use the fact that a Byzantine process can send multiple messages to the same recipient in a round. We show that removing this ability makes agreement easier: then, \(t+1\) identifiers are sufficient for agreement, even in the partially synchronous model, assuming processes can count the number of messages with the same identifier they receive in a round.


Consensus Message passing  Process identifiers  Byzantine failures 



We are grateful to Christian Cachin for his useful comments on our model with homonyms. We thank the anonymous reviewers for all of their very helpful comments. An abbreviated version of this paper appeared in [8]. Eric Ruppert received funding from the Natural Sciences and Engineering Research Council of Canada. This work is supported by the ERC Starting Grant GOSSPLE number 204742 and the ANR VERSO SHAMAN.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Carole Delporte-Gallet
    • 1
    Email author
  • Hugues Fauconnier
    • 1
  • Rachid Guerraoui
    • 2
  • Anne-Marie Kermarrec
    • 3
  • Eric Ruppert
    • 4
  • Hung Tran-The
    • 1
  1. 1.University Paris DiderotParisFrance
  2. 2.Ecole Polytechnique Fédérale de LausanneLausanneSwitzerland
  3. 3.INRIA Rennes-Bretagne AtlantiqueRennesFrance
  4. 4.York UniversityTorontoCanada

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