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Practical Fully Simulatable Oblivious Transfer with Sublinear Communication

  • Bingsheng Zhang
  • Helger Lipmaa
  • Cong Wang
  • Kui Ren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7859)

Abstract

During an adaptive k-out-of-N oblivious transfer (OT), a sender has N private documents, and a receiver wants to adaptively fetch k documents from them such that the sender learns nothing about the receiver’s selection and the receiver learns nothing more than those chosen documents. Many fully simulatable and universally composable adaptive OT schemes have been proposed, but those schemes typically require \(\mathcal{O}(N)\) communication in the initialization phase, which yields \(\mathcal{O}(N)\) overall communication. On the other hand, in some applications, the receiver just needs to fetch a small number of documents, so the initialization cost dominates in the entire protocol, especially for 1-out-of-N OT. We propose the first fully simulatable adaptive OT with sublinear communication under the DDH assumption in the plain model. Our scheme has \(\mathcal{O}(N^{1/2})\) communication in both the initialization phase and each transfer phase. It achieves better (amortized) overall communication complexity compared to existing schemes when \(k=\mathcal{O}(N^{1/2})\).

Keywords

Adaptive oblivious transfer fully simulatable security sublinear communication zero knowledge batch argument 

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References

  1. 1.
    Groth, J., Kiayias, A., Lipmaa, H.: Multi-query Computationally-Private Information Retrieval with Constant Communication Rate. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 107–123. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Bayer, S., Groth, J.: Efficient Zero-Knowledge Argument for Correctness of a Shuffle. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 263–280. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Bellare, M., Goldreich, O.: On Defining Proofs of Knowledge. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 390–420. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  4. 4.
    Ben-Sasson, E., Goldreich, O., Harsha, P., Sudan, M., Vadhan, S.P.: Short PCPs Verifiable in Polylogarithmic Time. In: CCC (2005)Google Scholar
  5. 5.
    Camenisch, J., Neven, G., Shelat, A.: Simulatable Adaptive Oblivious Transfer. In: Naor, M. (ed.) EUROCRYPT 2007. LNCS, vol. 4515, pp. 573–590. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  6. 6.
    Canetti, R., Fischlin, M.: Universally Composable Commitments. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 19–40. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Chaum, D.: Zero-Knowledge Undeniable Signatures (extended abstract). In: Damgård, I.B. (ed.) EUROCRYPT 1990. LNCS, vol. 473, pp. 458–464. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  8. 8.
    Damgård, I., Fujisaki, E.: A Statistically-Hiding Integer Commitment Scheme Based on Groups with Hidden Order. In: Zheng, Y. (ed.) ASIACRYPT 2002. LNCS, vol. 2501, pp. 125–142. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  9. 9.
    Damgård, I., Goldreich, O., Okamoto, T., Wigderson, A.: Honest Verifier vs Dishonest Verifier in Public Coin Zero-Knowledge Proofs. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 325–338. Springer, Heidelberg (1995)Google Scholar
  10. 10.
    Gentry, C., Ramzan, Z.: Single-Database Private Information Retrieval with Constant Communication Rate. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 803–815. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Gordon, S.D., Katz, J., Kolesnikov, V., Krell, F., Malkin, T., Raykova, M., Vahlis, Y.: Secure Two-party Computation in Sublinear (amortized) Time. In: CCS (2012)Google Scholar
  12. 12.
    Green, M., Hohenberger, S.: Blind Identity-Based Encryption and Simulatable Oblivious Transfer. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 265–282. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Green, M., Hohenberger, S.: Universally Composable Adaptive Oblivious Transfer. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 179–197. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Green, M., Hohenberger, S.: Practical Adaptive Oblivious Transfer from Simple Assumptions. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 347–363. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Groth, J.: Linear Algebra with Sub-linear Zero-knowledge Arguments. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 192–208. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Groth, J.: A Verifiable Secret Shuffle of Homomorphic Encryptions. Journal of Cryptology 23, 546–579 (2010)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Groth, J.: hort Pairing-Based Non-interactive Zero-Knowledge Arguments. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 321–340. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Ishai, Y., Paskin, A.: Evaluating Branching Programs on Encrypted Data. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 575–594. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Jarecki, S., Liu, X.: Efficient Oblivious Pseudorandom Function with Applications to Adaptive OT and Secure Computation of Set Intersection. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 577–594. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Kurosawa, K., Nojima, R.: Simple Adaptive Oblivious Transfer Without Random Oracle. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 334–346. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Kurosawa, K., Nojima, R., Phong, L.T.: Efficiency-improved fully simulatable adaptive OT under the DDH assumption. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 172–181. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  22. 22.
    Kurosawa, K., Nojima, R., Phong, L.T.: Generic Fully Simulatable Adaptive Oblivious Transfer. In: Lopez, J., Tsudik, G. (eds.) ACNS 2011. LNCS, vol. 6715, pp. 274–291. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Kushilevitz, E., Ostrovsky, R.: Replication is NOT Needed: Single Database, Computationally-Private Information Retrieval. In: FOCS (1997)Google Scholar
  24. 24.
    Laur, S., Lipmaa, H.: On the Feasibility of Consistent Computations. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 88–106. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Lim, C.H.: Efficient Multi-exponentiation and Application to Batch Verification of Digital Signatures (2000), online Tech. Report: http://dasan.sejong.ac.kr/~chlim/pub/multiexp.ps
  26. 26.
    Lipmaa, H.: An Oblivious Transfer Protocol with Log-Squared Communication. In: Zhou, J., López, J., Deng, R.H., Bao, F. (eds.) ISC 2005. LNCS, vol. 3650, pp. 314–328. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Lipmaa, H.: First CPIR Protocol with Data-Dependent Computation. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 193–210. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  28. 28.
    Lipmaa, H.: Progression-Free Sets and Sublinear Pairing-Based Non-Interactive Zero-Knowledge Arguments. In: Cramer, R. (ed.) TCC 2012. LNCS, vol. 7194, pp. 169–189. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  29. 29.
    Liskova, L., Stanek, M.: Efficient Simultaneous Contract Signing. In: Deswarte, Y., Cuppens, F., Jajodia, S., Wang, L. (eds.) Security and Protection in Information Processing Systems. IFIP, vol. 147, pp. 440–455. Springer, Boston (2004)CrossRefGoogle Scholar
  30. 30.
    Naor, M., Pinkas, B.: Oblivious Transfer with Adaptive Queries. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 573–590. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  31. 31.
    Naor, M., Pinkas, B.: Computationally Secure Oblivious Transfer. Journal of Cryptology 18, 1–35 (2005), http://dx.doi.org/10.1007/s00145-004-0102-6 MathSciNetMATHCrossRefGoogle Scholar
  32. 32.
    Pedersen, T.P.: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)Google Scholar
  33. 33.
    Rial, A., Kohlweiss, M., Preneel, B.: Universally Composable Adaptive Priced Oblivious Transfer. In: Shacham, H., Waters, B. (eds.) Pairing 2009. LNCS, vol. 5671, pp. 231–247. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  34. 34.
    Yao, A.: Protocols for Secure Computations (Extended Abstract). In: FOCS (1982)Google Scholar
  35. 35.
    Zhang, B.: Simulatable Adaptive Oblivious Transfer with Statistical Receiver’s Privacy. In: Boyen, X., Chen, X. (eds.) ProvSec 2011. LNCS, vol. 6980, pp. 52–67. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bingsheng Zhang
    • 1
  • Helger Lipmaa
    • 2
  • Cong Wang
    • 3
  • Kui Ren
    • 1
  1. 1.State University of New York at BuffaloUnited States
  2. 2.University of TartuEstonia
  3. 3.City University of Hong KongChina

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