Simple and Communication Complexity Efficient Almost Secure and Perfectly Secure Message Transmission Schemes

  • Yvo Desmedt
  • Stelios Erotokritou
  • Reihaneh Safavi-Naini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6055)


Recently Kurosawa and Suzuki considered almost secure (1-phase n-channel) message transmission when n = (2t + 1). The authors gave a lower bound on the communication complexity and presented an exponential time algorithm achieving this bound. In this paper we present a polynomial time protocol achieving the same security properties for the same network conditions.

Additionally, we introduce and formalize new security parameters to message transmission protocols which we feel are missing and necessary in the literature.

We also focus on 2-phase protocols. We present a protocol achieving perfectly secure message transmission of a single message with O(n 2) communication complexity in polynomial time. This is an improvement on previous protocols which achieve perfectly secure message transmission of a single message with a communication complexity of O(n 3).


Information-theoretic cryptography Perfectly secure message transmission Almost secure message transmission Cryptographic protocols Privacy Reliability Coding theory Secret sharing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Agarwal, S., Cramer, R., de Haan, R.: Asymptotically optimal two-round perfectly secure message transmission. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 394–408. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Dolev, D., Dwork, C., Waarts, O., Yung, M.: Perfectly secure message transmission. Journal of the ACM 40(1), 17–47 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Franklin, M., Galil, Z., Yung, M.: Eavesdropping games: A graph-theoretic approach to privacy in distributed systems. Journal of the ACM 47(2), 225–243 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Franklin, M.K., Wright, R.N.: Secure communication in minimal connectivity models. Journal of Cryptology 13(1), 9–30 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jaggi, S., Langberg, M., Katti, S., Ho, T., Katabi, D., Medard, M.: Resilient network coding in the presence of Byzantine adversaries. In: INFOCOM, pp. 616–624. IEEE, Los Alamitos (2007)Google Scholar
  6. 6.
    Kumar, M.V.N.A., Goundan, P.R., Srinathan, K., Rangan, C.P.: On perfectly secure communication over arbitrary networks. In: PODC 2002, pp. 193–202 (2002)Google Scholar
  7. 7.
    Kurosawa, K., Suzuki, K.: Truly efficient 2-round perfectly secure message transmission scheme. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 324–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  8. 8.
    Kurosawa, K., Suzuki, K.: Almost secure (1-round, n-channel) message transmission scheme. In: Desmedt, Y. (ed.) ICITS 2007. LNCS, vol. 4883, pp. 99–112. Springer, Heidelberg (2009)Google 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.
    Sayeed, H.M., Abu-Amara, H.: Efficient perfectly secure message transmission in synchronous networks. Inf. Comput. 126(1), 53–61 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Srinathan, K., Choudhary, A., Patra, A., Rangan, C.P.: Efficient single phase unconditionally secure message transmission with optimum communication complexity. In: PODC 2008, p. 457 (2008)Google Scholar
  13. 13.
    Srinathan, K., Kumar, M.V.N.A., Rangan, C.P.: Asynchronous secure communication tolerating mixed adversaries. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 224–242. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Srinathan, K., Narayanan, A., Rangan, C.P.: Optimal perfectly secure message transmission. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 545–561. Springer, Heidelberg (2004)Google Scholar
  15. 15.
    Wang, Y., Desmedt, Y.: Perfectly Secure Message Transmission Revisited. IEEE Transactions on Information Theory 54(6), 2582–2595 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Yvo Desmedt
    • 1
    • 2
  • Stelios Erotokritou
    • 1
  • Reihaneh Safavi-Naini
    • 3
  1. 1.Department of Computer ScienceUniversity College LondonUK
  2. 2.Research Center for Information Security (RCIS), AISTJapan
  3. 3.Department of Computer ScienceUniversity of CalgaryCanada

Personalised recommendations