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Minimal Connectivity for Unconditionally Secure Message Transmission in Synchronous Directed Networks

  • Manan Nayak
  • Shashank Agrawal
  • Kannan Srinathan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6673)

Abstract

In this paper we give the minimal connectivity required in a synchronous directed network, which is under the influence of a computationally unbounded Byzantine adversary that can corrupt a subset of nodes, so that Secure Message Transmission is possible between sender S and receiver R. We also show that secure communication between a pair of nodes in a given synchronous directed network is possible in both directions if and only if reliable communication is possible between them. We assume that in a network, every node is capable of computation and we model the network along the lines of [14].

Keywords

Directed networks Connectivity Information-theoretic security 

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References

  1. 1.
    Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non-cryptographic Fault-tolerant Distributed Computation. In: Proceedings of the 20th Symposium on Theory of Computing (STOC), pp. 1–10. ACM Press, New York (1988)Google Scholar
  2. 2.
    Chaum, D., Crepeau, C., Damgard, I.: Multi-party Unconditionally Secure Protocols. In: Proceedings of 20th Symposium on Theory of Computing (STOC), pp. 11–19. ACM Press, New York (1988)Google Scholar
  3. 3.
    Desmedt, Y.G., Wang, Y.: Perfectly secure message transmission revisited. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 502–517. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Franklin, M.K., Wright, R.N.: Secure communication in minimal connectivity models. J. Cryptology 13(1), 9–30 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game. In: Proceedings of the 19th Symposium on Theory of Computing (STOC), pp. 218–229. ACM Press, New York (1987)Google Scholar
  6. 6.
    Hirt, M., Maurer, U.: Complete Characterization of Adversaries Tolerable in Secure Multi-party Computation. In: Proceedings of the 16th Symposium on Principles of Distributed Computing (PODC), pp. 25–34. ACM Press, New York (1997)Google Scholar
  7. 7.
    Kumar, M.V.N.A., Goundan, P.R., Srinathan, K., Pandu Rangan, C.: On perfectly secure communication over arbitrary networks. In: Proceedings of the 21st Symposium on Principles of Distributed Computing (PODC), pp. 193–202. ACM Press, Monterey (2002)Google Scholar
  8. 8.
    Lamport, L., Shostak, R., Pease, M.: The byzantine generals problem. ACM Trans. Program. Lang. Syst. 4(3), 382–401 (1982)CrossRefzbMATHGoogle Scholar
  9. 9.
    Patra, A., Shankar, B., Choudhary, A., Srinathan, K., Rangan, C.P.: Perfectly secure message transmission in directed networks tolerating threshold and non threshold adversary. In: Bao, F., Ling, S., Okamoto, T., Wang, H., Xing, C. (eds.) CANS 2007. LNCS, vol. 4856, pp. 80–101. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Rabin, T., Ben-Or, M.: Verifiable Secret Sharing and Multiparty Protocols with Honest Majority. In: Proceedings of the 21st Symposium on Theory of Computing (STOC), pp. 73–85. ACM Press, New York (1989)Google Scholar
  11. 11.
    Rabin, T., Ben-Or, M.: Verifiable secret sharing and multiparty protocols with honest majority. In: STOC 1989: Proceedings of the Twenty-First Annual ACM Symposium on Theory of Computing, pp. 73–85. ACM, New York (1989)CrossRefGoogle Scholar
  12. 12.
    Shankar, B., Gopal, P., Srinathan, K., Pandu Rangan, C.: Unconditionally reliable message transmission in directed networks. In: SODA 2008: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 1048–1055. Society for Industrial and Applied Mathematics, Philadelphia (2008)Google Scholar
  13. 13.
    Srinathan, K., Patra, A., Choudhary, A., Pandu Rangan, C.: Unconditionally secure message transmission in arbitrary directed synchronous networks tolerating generalized mixed adversary. In: ASIACCS 2009: Proceedings of the 4th International Symposium on Information, Computer, and Communications Security, pp. 171–182. ACM, New York (2009)Google Scholar
  14. 14.
    Srinathan, K., Pandu Rangan, C.: Possibility and complexity of probabilistic reliable communications in directed networks. In: Proceedings of 25th ACM Symposium on Principles of Distributed Computing, PODC 2006 (2006)Google Scholar
  15. 15.
    Yang, Q., Desmedt, Y.: Cryptanalysis of secure message transmission protocols with feedback. In: Kurosawa, K. (ed.) Information Theoretic Security. LNCS, vol. 5973, pp. 159–176. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manan Nayak
    • 1
  • Shashank Agrawal
    • 1
  • Kannan Srinathan
    • 1
  1. 1.Center for Security, Theory and Algorithmic Research (C-STAR)International Institute of Information TechnologyHyderabadIndia

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