Renaming in Message Passing Systems with Byzantine Failures

  • Michael Okun
  • Amnon Barak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4167)

Abstract

We study the renaming problem in a fully connected synchronous network with Byzantine failures. We show that when faulty processors are able to cheat about their original identities, this problem cannot be solved in an a priori bounded number of rounds for \(t\geq(n+n\textrm{ mod }3)/3\), where n is the size of the network and t is the number of failures. This result also implies a \(t\geq(n+n\textrm{ mod }4)/2\) bound for the case of faulty processors that are not able to falsify their original identities. In addition, we present several Byzantine renaming algorithms based on distinct approaches, each providing a different tradeoff between its running time and the solution quality.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Afek, Y., Attiya, H., Fouren, A., Stupp, G., Touitou, D.: Long-lived renaming made adaptive. In: PODC, pp. 91–103 (1999)Google Scholar
  2. 2.
    Afek, Y., Merritt, M.: Fast, wait-free (2k − 1)-renaming. In: PODC, pp. 105–112 (1999)Google Scholar
  3. 3.
    Attiya, H., Bar-Noy, A., Dolev, D., Peleg, D., Reischuk, R.: Renaming in an asynchronous environment. J. ACM 37(3), 524–548 (1990)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Attiya, H., Fouren, A.: Polynomial and adaptive long-lived (2k - 1)-renaming. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 149–163. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Attiya, H., Fouren, A.: Adaptive and efficient algorithms for lattice agreement and renaming. SIAM J. Comput. 31(2), 642–664 (2001)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Attiya, H., Welch, J.L.: Distributed Computing: Fundamentals, Simulations and Advanced Topics. McGraw-Hill, New York (1998)Google Scholar
  7. 7.
    Bar-Noy, A., Dolev, D.: A partial equivalence between shared-memory and message-passing in an asynchronous fail-stop distributed environment. Mathematical Systems Theory 26(1), 21–39 (1993)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Borowsky, E., Gafni, E.: Immediate atomic snapshots and fast renaming (extended abstract). In: PODC, pp. 41–51 (1993)Google Scholar
  9. 9.
    Chaudhuri, S., Herlihy, M., Tuttle, M.R.: Wait-free implementations in message-passing systems. Theor. Comput. Sci. 220(1), 211–245 (1999)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dijkstra, E.W.: On weak and strong termination. In: Dijkstra, E.W. (ed.) Selected Writings on Computing: A Personal Perspective, pp. 355–357. Springer, Heidelberg (1982)Google Scholar
  11. 11.
    Douceur, J.R.: The sybil attack. In: Druschel, P., Kaashoek, M.F., Rowstron, A. (eds.) IPTPS 2002. LNCS, vol. 2429, pp. 251–260. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  12. 12.
    Herlihy, M., Shavit, N.: The topological structure of asynchronous computability. J. ACM 46(6), 858–923 (1999)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Lamport, L., Shostak, R.E., Pease, M.C.: The Byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)MATHCrossRefGoogle Scholar
  14. 14.
    Lynch, N.A.: Distributed Algorithms. Morgan Kaufmann, San Francisco (1996)MATHGoogle Scholar
  15. 15.
    Moir, M., Anderson, J.H.: Wait-free algorithms for fast, long-lived renaming. Sci. Comput. Program. 25(1), 1–39 (1995)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Okun, M.: Agreement among unacquainted Byzantine generals. In: Fraigniaud, P. (ed.) DISC 2005. LNCS, vol. 3724, pp. 499–500. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. 17.
    Okun, M., Barak, A.: Efficient algorithms for anonymous Byzantine agreement. Theory Comput. Syst. (to appear)Google Scholar
  18. 18.
    Okun, M., Barak, A.: On anonymous Byzantine agreement. Leibniz Center TR 2004-2, The Hebrew University (2004)Google Scholar
  19. 19.
    Pease, M.C., Shostak, R.E., Lamport, L.: Reaching agreement in the presence of faults. J. ACM 27(2), 228–234 (1980)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Raynal, M.: An introduction to the renaming problem. In: PRDC, pp. 121–124 (2002)Google Scholar
  21. 21.
    Srikanth, T.K., Toueg, S.: Simulating authenticated broadcasts to derive simple fault-tolerant algorithms. Distributed Computing 2(2), 80–94 (1987)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Michael Okun
    • 1
  • Amnon Barak
    • 1
  1. 1.Department of Computer ScienceThe Hebrew University of Jerusalem 

Personalised recommendations