Optimal Reductions Between Oblivious Transfers Using Interactive Hashing

  • Claude Crépeau
  • George Savvides
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4004)

Abstract

We present an asymptotically optimal reduction of one-out-of-two String Oblivious Transfer to one-out-of-two Bit Oblivious Transfer using Interactive Hashing in conjunction with Privacy Amplification. Interactive Hashing is used in an innovative way to test the receiver’s adherence to the protocol. We show that (1 + ε)k uses of Bit OT suffice to implement String OT for k-bit strings. Our protocol represents a two-fold improvement over the best constructions in the literature and is asymptotically optimal. We then show that our construction can also accommodate weaker versions of Bit OT, thereby obtaining a significantly lower expansion factor compared to previous constructions. Besides increasing efficiency, our constructions allow the use of any 2-universal family of Hash Functions for performing Privacy Amplification. Of independent interest, our reduction illustrates the power of Interactive Hashing as an ingredient in the design of cryptographic protocols.

Keywords

interactive hashing oblivious transfer privacy amplification 

References

  1. 1.
    Bennett, C.H., Brassard, G., Crépeau, C., Maurer, U.: Generalized privacy amplification. IEEE Trans. on Info. Theory 41(6), 1915–1923 (1995)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bennett, C.H., Brassard, G., Robert, J.-M.: Privacy amplification by public discussion. SIAM J. Comput. 17(2), 210–229 (1988)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Brassard, G., Crépeau, C., Wolf, S.: Oblivious transfers and privacy amplification. IEEE Transaction on Information Theory 16(4), 219–237 (2003)MathSciNetMATHGoogle Scholar
  4. 4.
    Brassard, G., Crépeau, C., Santha, M.: Oblivious transfers and intersecting codes. IEEETIT: IEEE Transactions on Information Theory 42 (1996)Google Scholar
  5. 5.
    Cachin, C., Crépeau, C., Marcil, J.: Oblivious transfer with a memory-bounded receiver. In: IEEE Symposium on Foundations of Computer Science (1998)Google Scholar
  6. 6.
    Zong Ding, Y., Harnik, D., Rosen, A., Shaltiel, R.: Constant-round oblivious transfer in the bounded storage model. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 446–472. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Dodis, Y., Micali, S.: Lower bounds for oblivious transfer reductions. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, p. 42. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Even, S., Goldreich, O., Lempel, A.: A randomized protocol for signing contracts. Commun. ACM 28(6), 637–647 (1985)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Kilian, J.: Founding crytpography on oblivious transfer. In: STOC 1988: Proceedings of the twentieth annual ACM symposium on Theory of computing, pp. 20–31. ACM Press, New York (1988)CrossRefGoogle Scholar
  10. 10.
    Naor, M., Ostrovsky, R., Venkatesan, R., Yung, M.: Perfect zero-knowledge arguments for NP using any one-way permutation. Journal of Cryptology 11(2) (1998)Google Scholar
  11. 11.
    Ostrovsky, R., Venkatesan, R., Yung, M.: Fair games against an all-powerful adversary. AMS DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 13 (1993)Google Scholar
  12. 12.
    Rabin, M.O.: How to exchange secrets by oblivious transfer. Technical Memo TR–81, Aiken Computation Laboratory. Harvard University (1981)Google Scholar
  13. 13.
    Stinson, D.R.: Some results on nonlinear zigzag functions. Journal of Combinatorial Mathematics and Combinatorial Computing 29, 127–138 (1999)MathSciNetMATHGoogle Scholar
  14. 14.
    Wiesner, S.: Conjugate coding. SIGACT News 15(1), 78–88 (1983)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Claude Crépeau
    • 1
  • George Savvides
    • 1
  1. 1.McGill UniversityMontéralCanada

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