Advertisement

On the Feasibility of Extending Oblivious Transfer

  • Yehuda Lindell
  • Hila Zarosim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)

Abstract

Oblivious transfer is one of the most basic and important building blocks in cryptography. As such, understanding its cost is of prime importance. Beaver (STOC 1996) showed that it is possible to obtain poly(n) oblivious transfers given only n actual oblivious transfer calls and using one-way functions, where n is the security parameter. In addition, he showed that it is impossible to extend oblivious transfer information theoretically. The notion of extending oblivious transfer is important theoretically (to understand the complexity of computing this primitive) and practically (since oblivious transfers can be expensive and thus extending them using only one-way functions is very attractive).

Despite its importance, very little is known about the feasibility of extending oblivious transfer, beyond the fact that it is impossible information theoretically. Specifically, it is not known whether or not one-way functions are actually necessary for extending oblivious transfer, whether or not it is possible to extend oblivious transfers with adaptive security, and whether or not it is possible to extend oblivious transfers when starting with O(logn) oblivious transfers. In this paper, we address these questions and provide almost complete answers to all of them. We show that the existence of any oblivious transfer extension protocol with security for static semi-honest adversaries implies one-way functions, that an oblivious transfer extension protocol with adaptive security implies oblivious transfer with static security, and that the existence of an oblivious transfer extension protocol from only O(logn) oblivious transfers implies oblivious transfer itself.

Keywords

Security Parameter Random String Oblivious Transfer Extended View Real Execution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Aiello, W., Ishai, Y., Reingold, O.: Priced Oblivious Transfer: How to Sell Digital Goods. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 119–135. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  2. 2.
    Beaver, D.: Precomputing Oblivious Transfer. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 97–109. Springer, Heidelberg (1995)Google Scholar
  3. 3.
    Beaver, D.: Correlated Pseudorandomness and the Complexity of Private Computations. In: The 28th STOC, pp. 479–488 (1996)Google Scholar
  4. 4.
    Canetti, R.: Security and Composition of Multiparty Cryptographic Protocols. Journal of Cryptology 13(1), 143–202 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Even, S., Goldreich, O., Lempel, A.: A Randomized Protocol for Signing Contracts. Communications of the ACM 28(6), 637–647 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Gertner, Y., Kannan, S., Malkin, T., Reingold, O., Viswanathan, M.: The Relationship Between Public Key Encryption and Oblivious Transfer. In: The 41st FOCS, pp. 325–335 (2000)Google Scholar
  7. 7.
    Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game – A Completeness Theorem for Protocols with Honest Majority. In: 19th STOC, pp. 218–229 (1987) (For details see [9])Google Scholar
  8. 8.
    Goldreich, O.: A Note on Computational Indistinguishability. Information Processing Letters 34(6), 277–281 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Goldreich, O.: Foundations of Cryptography. Basic Applications, vol. 2. Cambridge University Press (2004)Google Scholar
  10. 10.
    Haitner, I., Ishai, Y., Kushilevitz, E., Lindell, Y., Petrank, E.: Black-Box Constructions of Protocols for Secure Computation. SIAM Journal on Computing 40(2), 225–266 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Ishai, Y., Kilian, J., Nissim, K., Petrank, E.: Extending Oblivious Transfers Efficiently. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 145–161. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Impagliazzo, R., Zuckerman, D.: How to Recycle Random Bits. In: The 30th FOCS, pp. 248–253 (1989)Google Scholar
  13. 13.
    Kilian, J.: Founding Cryptography on Oblivious Transfer. In: The 20th STOC, pp. 20–31 (1988)Google Scholar
  14. 14.
    Lindell, A.Y.: Adaptively Secure Two-Party Computation with Erasures. In: Fischlin, M. (ed.) CT-RSA 2009. LNCS, vol. 5473, pp. 117–132. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Lindell, Y., Zarosim, H.: Adaptive Zero-Knowledge Proofs and Adaptively Secure Oblivious Transfer. The Journal of Cryptology 24(4), 761–799 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Lindell, Y., Zarosim, H.: On the Feasibility of Extending Oblivious Transfer. Cryptology ePrint Archive: Report 2012/333 (2012)Google Scholar
  17. 17.
    Rabin, M.: How to Exchange Secrets by Oblivious Transfer. Tech. Memo TR-81. Aiken Computation Laboratory, Harvard University (1981)Google Scholar
  18. 18.
    Winkler, S., Wullschleger, J.: On the Efficiency of Classical and Quantum Oblivious Transfer Reductions. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 707–723. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  19. 19.
    Wolf, S., Wullschleger, J.: Oblivious Transfer Is Symmetric. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 222–232. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Yao, A.: How to Generate and Exchange Secrets. In: The 27th FOCS, pp. 162–167 (1986)Google Scholar

Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Yehuda Lindell
    • 1
  • Hila Zarosim
    • 1
  1. 1.Dept.of Computer ScienceBar-Ilan UniversityIsrael

Personalised recommendations