Secure communication in minimal connectivity models

  • Matthew Franklin
  • Rebecca N. Wright
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1403)

Abstract

Problems of secure communication and computation have been studied extensively in network models. In this work, we ask what is possible in the information-theoretic setting when the adversary is very strong (Byzantine) and the network connectivity is very low (minimum needed for crash-tolerance). For some natural models, our results imply a sizable gap between the connectivity required for perfect security and for probabilistic security. Our results also have implications to the commonly studied simple channel model and to general secure multiparty computation.

References

  1. [ABLP89]
    N. Alon, A. Bar-Noy, N. Linial, and D. Peleg, “On the complexity of radio communication,” ACM STOC, 1989, 274–285.Google Scholar
  2. [Bea89]
    D. Beaver, “Multiparty protocols tolerating half faulty processors,” Proc. Crypto '89, 560–572.Google Scholar
  3. [BF97]
    A. Beimel and M. Franklin, “Reliable communication over partially authenticated networks,” Proc. Workshop on Distributed Algorithms (WDAG), Springer-Verlag LNCS 1320, 1997, 245–259.Google Scholar
  4. [BCG93]
    M. Ben-Or, R. Canetti, and O. Goldreich, “Asynchronous secure computation,” ACM STOC, 1993, 52–61.Google Scholar
  5. [BGW88]
    M. Ben-Or, S. Goldwasser, and A. Wigderson, “Completeness theorems for non-cryptographic fault-tolerant distributed computing,” ACM STOC, 1988, 1–10.Google Scholar
  6. [BT85]
    G. Bracha and S. Toueg, “Asynchronous consensus and broadcast protocols”, JACM 32(4): 824–840 (1985).MathSciNetCrossRefGoogle Scholar
  7. [BDK97]
    M. Burmester, Y. Desmedt, and G. Kabatianski, “Trust and Security: A New Look at the Byzantine Generals Problem”, Network Threats, DI-MACS Series in Discrete Mathematics and Theoretical Computer Science, American Mathematical Society, (to appear).Google Scholar
  8. [CCD88]
    D. Chaum, C. Crepeau, and I. Damgard, “Multiparty unconditional secure protocols,” ACM STOC, 1988, 11–19.Google Scholar
  9. [Ch85]
    D. Cheriton and W. Zwaenepoel, “Distributed process group in the V kernel” ACM Trans. on Computer Systems 3, (1985), 77–107.CrossRefGoogle Scholar
  10. [Dol82]
    D. Dolev, “The Byzantine Generals strike again,” J. Algorithms 3:14–30, 1982.MATHMathSciNetCrossRefGoogle Scholar
  11. [DDWY93]
    D. Dolev, C. Dwork, O. Waarts, and M. Yung, “Perfectly secure message transmission,” JACM 40(1): 17–47, 1993.MATHMathSciNetCrossRefGoogle Scholar
  12. [FY95]
    M. Franklin and M. Yung, “Secure hypergraphs: privacy from partial broadcast,” ACM STOC, 1995, 36–44.Google Scholar
  13. [GGL91]
    O. Goldreich, S. Goldwasser, and N. Linial, “Fault-tolerant computation in the full information model,” IEEE FOCS, 1991, 447–457.Google Scholar
  14. [PSL80]
    M. Pease, R. Shostak, and L. Lamport, “Reaching Agreement in the Presence of Faults”, JACM 27(2): 228–234, 1980.MATHMathSciNetCrossRefGoogle Scholar
  15. [PG89]
    F. M. Pittelli and H. Garcia-Molina, “Reliable Scheduling in a TMR Database System”, ACM Transactions on Computer Systems 7(1): 25–60, 1989.CrossRefGoogle Scholar
  16. [Rab94]
    T. Rabin, “Robust sharing of secrets when the dealer is honest or faulty,” JACM 41(6):1089–1109, 1994.CrossRefGoogle Scholar
  17. [RB89]
    T. Rabin and M. Ben-Or, “Verifiable secret sharing and multiparty protocols with honest majority,” ACM STOC, 1989, 73–85.Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Matthew Franklin
    • 1
  • Rebecca N. Wright
    • 1
  1. 1.AT&T Labs ResearchFlorham ParkUSA

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