Oblivious Transfer from Weak Noisy Channels

  • Jürg Wullschleger
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5444)

Abstract

Various results show that oblivious transfer can be implemented using the assumption of noisy channels. Unfortunately, this assumption is not as weak as one might think, because in a cryptographic setting, these noisy channels must satisfy very strong security requirements.

Unfair noisy channels, introduced by Damgård, Kilian and Salvail [Eurocrypt ’99], reduce these limitations: They give the adversary an unfair advantage over the honest player, and therefore weaken the security requirements on the noisy channel. However, this model still has many shortcomings: For example, the adversary’s advantage is only allowed to have a very special form, and no error is allowed in the implementation.

In this paper we generalize the idea of unfair noisy channels. We introduce two new models of cryptographic noisy channels that we call the weak erasure channel and the weak binary symmetric channel, and show how they can be used to implement oblivious transfer. Our models are more general and use much weaker assumptions than unfair noisy channels, which makes implementation a more realistic prospect. For example, these are the first models that allow the parameters to come from experimental evidence.

References

  1. 1.
    Bennett, C.H., Brassard, G., Robert, J.-M.: Privacy amplification by public discussion. SIAM Journal on Computing 17(2), 210–229 (1988)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Cachin, C.: Smooth entropy and rényi entropy. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 193–208. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Crépeau, C.: Equivalence between two flavours of oblivious transfers. In: Price, W.L., Chaum, D. (eds.) EUROCRYPT 1987. LNCS, vol. 304, pp. 350–354. Springer, Heidelberg (1988)Google Scholar
  4. 4.
    Crépeau, C.: Efficient cryptographic protocols based on noisy channels. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 306–317. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Crépeau, C., Kilian, J.: Achieving oblivious transfer using weakened security assumptions (extended abstract). In: Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science (FOCS 1988), pp. 42–52 (1988)Google Scholar
  6. 6.
    Crépeau, C., Morozov, K., Wolf, S.: Efficient unconditional oblivious transfer from almost any noisy channel. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 47–59. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  7. 7.
    Damgård, I.B., Fehr, S., Morozov, K., Salvail, L.: Unfair noisy channels and oblivious transfer. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 355–373. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Kilian, J., Salvail, L.: On the (im)possibility of basing oblivious transfer and bit commitment on weakened security assumptions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 56–73. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC 1987), pp. 218–229. ACM Press, New York (1987)Google Scholar
  11. 11.
    Goldreich, O., Vainish, R.: How to solve any protocol probleman efficiency improvement. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 73–86. Springer, Heidelberg (1988)Google Scholar
  12. 12.
    Holenstein, T.: Strengthening key agreement using hard-core sets. PhD thesis, ETH Zurich, Switzerland, Reprint as vol. 7 of ETH Series in Information Security and Cryptography, Hartung-Gorre Verlag (2006)Google Scholar
  13. 13.
    Impagliazzo, R., Levin, L.A., Luby, M.: Pseudo-random generation from one-way functions. In: Proceedings of the 21st Annual ACM Symposium on Theory of Computing (STOC 1989), pp. 12–24. ACM Press, New York (1989)Google Scholar
  14. 14.
    Kilian, J.: Founding cryptography on oblivious transfer. In: Proceedings of the 20th Annual ACM Symposium on Theory of Computing (STOC 1988), pp. 20–31. ACM Press, New York (1988)Google Scholar
  15. 15.
    Maurer, U., Wolf, S.: Privacy amplification secure against active adversaries. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 307–321. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  16. 16.
    Nascimento, A., Winter, A.: On the oblivious transfer capacity of noisy correlations. IEEE Trans. on Information Theory 54(6) (2008)Google Scholar
  17. 17.
    Nascimento, A.C.A., Skludarek, S., Barros, J., Imai, H.: The commitment capacity of the gaussian channel is infinite. IEEE Trans. on Information Theory, Special Issue on Information Security (2007)Google Scholar
  18. 18.
    Oggier, F., Morozov, K.: A practical scheme for string commitment based on the gaussian channel. In: Proceedings of 2006 IEEE Information Theory Workshop (ITW 2008) (2008)Google Scholar
  19. 19.
    Rabin, M.O.: How to exchange secrets by oblivious transfer. Technical Report TR-81, Harvard Aiken Computation Laboratory (1981)Google Scholar
  20. 20.
    Renner, R., Wolf, S.: Simple and tight bounds for information reconciliation and privacy amplification. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 199–216. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Wiesner, S.: Conjugate coding. SIGACT News 15(1), 78–88 (1983)CrossRefMATHGoogle Scholar
  22. 22.
    Wullschleger, J.: Oblivious-transfer amplification. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 555–572. Springer, Heidelberg (2007); Full version (PhD Thesis, ETH Zurich), http://arxiv.org/abs/cs.CR/0608076 CrossRefGoogle Scholar
  23. 23.
    Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual IEEE Symposium on Foundations of Computer Science (FOCS 1982), pp. 160–164 (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jürg Wullschleger
    • 1
  1. 1.University of BristolUK

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