Secret Keys from Channel Noise

  • Hadi Ahmadi
  • Reihaneh Safavi-Naini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6632)

Abstract

We study the problem of unconditionally secure Secret Key Establishment (SKE) when Alice and Bob are connected by two noisy channels that are eavesdropped by Eve. We consider the case that Alice and Bob do not have any sources of initial randomness at their disposal. We start by discussing special cases of interest where SKE is impossible and then provide a simple SKE construction over binary symmetric channels that achieves some rates of secret key. We next focus on the Secret Key (SK) capacity and provide lower and upper bounds on this capacity. We prove the lower bound by proposing a multi-round SKE protocol, called the main protocol. The main protocol consists of an initialization round and the repetition of a two-round SKE sub-protocol, called the basic protocol. We show that the two bounds coincide when channels do not leak information to the adversary. We apply the results to the case that communicants are connected by binary symmetric channels.

References

  1. 1.
    Ahlswede, R., Csiszár, I.: Common randomness in information theory and cryptography. Part I: secret sharing. IEEE Transaction Information Theory 39, 1121–1132 (1993)MATHCrossRefGoogle Scholar
  2. 2.
    Ahmadi, H., Safavi-Naini, R.: Secret key establishment over a pair of independent broadcast channels. In: International Symposium Information Theory and its Application (2010); Full version on the arXiv preprint server, arXiv:1001.3908Google Scholar
  3. 3.
    Ahmadi, H., Safavi-Naini, R.: Secret keys from channel noise. Technical Reports 2011/056, Cryptology ePrint archive, http://eprint.iacr.org/2011/056
  4. 4.
    Barros, J., Imai, H., Nascimento, A.C.A., Skludarek, S.: Bit commitment over Gaussian channels. In: IEEE International Symposium Information Theory, pp. 1437–1441 (2006)Google Scholar
  5. 5.
    Bloch, M., Barros, J., Rodrigues, M.R.D., McLaughlin, S.W.: Wireless information theoretic security. IEEE Transaction Information Theory 54, 2515–2534 (2008)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Carter, J.L., Wegman, M.N.: Universal Classes of Hash Functions. Journal of Computer and System Sciences 18, 143–154 (1979)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Crépeau, C., Kilian, J.: Weakening security assumptions and oblivious transfer. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 2–7. Springer, Heidelberg (1990)Google Scholar
  8. 8.
    Csiszár, I., Körner, J.: Broadcast channels with confidential messages. IEEE Transaction Information Theory 24, 339–348 (1978)MATHCrossRefGoogle Scholar
  9. 9.
    Csiszár, I., Narayan, P.: Common randomness and secret key generation with a helper. IEEE Transaction Information Theory 46, 344–366 (2000)MATHCrossRefGoogle Scholar
  10. 10.
    Dodis, Y., Spencer, J.: On the (non)universality of the one-time pad. In: IEEE Annual Symposium FOCS, pp. 376–388 (2002)Google Scholar
  11. 11.
    Khisti, A., Diggavi, S., Wornell, G.: Secret key generation with correlated sources and noisy channels. In: IEEE International Symposium Information Theory, pp. 1005–1009 (2008)Google Scholar
  12. 12.
    Maurer, U.: Secret key agreement by public discussion from common information. IEEE Transaction Information Theory 39, 733–742 (1993)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Prabhakaran, V., Eswaran, K., Ramchandran, K.: Secrecy via sources and channels - a secret key - secret message rate trade-off region. In: IEEE International Symposium Information Theory, pp. 1010–1014 (2008)Google Scholar
  14. 14.
    Shannon, C.E.: Communication theory of secrecy systems. Bell System Technical Journal 28, 656–715 (1948)MathSciNetGoogle Scholar
  15. 15.
    Venkatesan, S., Anantharam, V.: The common randomness capacity of a pair of independent discrete memoryless channels. IEEE Transaction Information Theory 44, 215–224 (1998)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    von Neumannm, J.: Various techniques used in connection with random digits. National Bureau of Standards Applied Math Series 12, 36–38 (1951)Google Scholar
  17. 17.
    Wegman, M.N., Carter, J.L.: New hash functions and their use in authentication and set equality. Journal of Computer and System Sciences 22, 265–279 (1981)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Wyner, A.D.: The wire-tap channel. Bell System Technical Journal 54, 1355–1367 (1975)MathSciNetGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Hadi Ahmadi
    • 1
  • Reihaneh Safavi-Naini
    • 1
  1. 1.Department of Computer ScienceUniversity of CalgaryCanada

Personalised recommendations