An Oblivious Transfer Protocol with Log-Squared Communication

  • Helger Lipmaa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3650)


We propose a one-round 1-out-of-n computationally-private information retrieval protocol for ℓ-bit strings with low-degree polylogarithmic receiver-computation, linear sender-computation and communication Θ(k Open image in new window log2 n+ℓ Open image in new window logn), where k is a possibly non-constant security parameter. The new protocol is receiver-private if the underlying length-flexible additively homomorphic public-key cryptosystem is IND-CPA secure. It can be transformed to a one-round computationally receiver-private and information-theoretically sender-private 1-out-of-n oblivious-transfer protocol for ℓ-bit strings, that has the same asymptotic communication and is private in the standard complexity-theoretic model.


Computationally-private information retrieval length-flexible additively homomorphic public-key cryptosystem oblivious transfer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AIR01]
    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. [Cha04]
    Chang, Y.-C.: Single Database Private Information Retrieval with Logarithmic Communication. In: Wang, H., Pieprzyk, J., Varadharajan, V. (eds.) ACISP 2004. LNCS, vol. 3108, pp. 50–61. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. [CMS99]
    Cachin, C., Micali, S., Stadler, M.: Computational Private Information Retrieval with Polylogarithmic Communication. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 402–414. Springer, Heidelberg (1999)Google Scholar
  4. [DJ01]
    Damgård, I., Jurik, M.: A Generalisation, a Simplification and Some Applications of Paillier’s Probabilistic Public-Key System. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  5. [DJ03]
    Damgård, I., Jurik, M.: A Length-Flexible Threshold Cryptosystem with Applications. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 350–364. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. [KO97]
    Kushilevitz, E., Ostrovsky, R.: Replication is Not Needed: Single Database, Computationally-Private Information Retrieval. In: 38th Annual Symposium on Foundations of Computer Science, Miami Beach, Florida, October 20-22, pp. 364–373. IEEE Computer Society, Los Alamitos (1997)CrossRefGoogle Scholar
  7. [LAN02]
    Lipmaa, H., Asokan, N., Niemi, V.: Secure Vickrey Auctions without Threshold Trust. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357, pp. 87–101. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. [Lip04]
    Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Total Communication. Technical Report 2004/063, International Association for Cryptologic Research (February 25, 2004)Google Scholar
  9. [NP99]
    Naor, M., Pinkas, B.: Oblivious Transfer and Polynomial Evaluation. In: Proceedings of the Thirty-First Annual ACMSymposium on the Theory of Computing, Atlanta, Georgia, USA, May 1-4, pp. 245–254. ACM Press, New York (1999)Google Scholar
  10. [NP01]
    Naor, M., Pinkas, B.: Efficient Oblivious Transfer Protocols. In: Proceedings of the Twelfth Annual ACM-SIAM Symposium on Discrete Algorithms, Washington, DC, USA, January 7-9, pp. 448–457. ACM Press, New York (2001)Google Scholar
  11. [Pai99]
    Paillier, P.: Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)Google Scholar
  12. [Ste98]
    Stern, J.P.: A New and Efficient All or Nothing Disclosure of Secrets Protocol. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 357–371. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Helger Lipmaa
    • 1
    • 2
  1. 1.Cybernetica ASTartuEstonia
  2. 2.Institute of Computer ScienceUniversity of TartuTartuEstonia

Personalised recommendations