Experimenting with Fast Private Set Intersection

  • Emiliano De Cristofaro
  • Gene Tsudik
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7344)

Abstract

Private Set Intersection (PSI) is a useful cryptographic primitive that allows two parties (client and server) to interact based on their respective (private) input sets, in such a way that client obtains nothing other than the set intersection, while server learns nothing beyond client set size. This paper considers one PSI construct from [DT10] and reports on its optimized implementation and performance evaluation. Several key implementation choices that significantly impact real-life performance are identified and a comprehensive experimental analysis (including micro-benchmarking, with various input sizes) is presented. Finally, it is shown that our optimized implementation of this RSA-OPRF-based PSI protocol markedly outperforms the one presented in [HEK12].

Keywords

Chinese Remainder Theorem Random Oracle Model Oblivious Transfer Modular Exponentiation Malicious Adversary 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [ADT11]
    Ateniese, G., De Cristofaro, E., Tsudik, G. (If) Size Matters: Size-Hiding Private Set Intersection. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol. 6571, pp. 156–173. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  2. [AL07]
    Aumann, Y., Lindell, Y.: Security Against Covert Adversaries: Efficient Protocols for Realistic Adversaries. In: Vadhan, S.P. (ed.) TCC 2007. LNCS, vol. 4392, pp. 137–156. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. [BBD+11]
    Baldi, P., Baronio, R., De Cristofaro, E., Gasti, P., Tsudik, G.: Countering gattaca: efficient and secure testing of fully-sequenced human genomes. In: CCS (2011), http://arxiv.org/abs/1110.2478
  4. [BCC+09]
    Belenkiy, M., Camenisch, J., Chase, M., Kohlweiss, M., Lysyanskaya, A., Shacham, H.: Randomizable Proofs and Delegatable Anonymous Credentials. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 108–125. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. [BLHB11]
    Bursztein, E., Lagarenne, J., Hamburg, M., Boneh, D.: OpenConflict: Preventing Real Time Map Hacks in Online Games. In: IEEE Security and Privacy (2011)Google Scholar
  6. [BNPS03]
    Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The one-more-RSA-inversion problems and the security of Chaum’s blind signature scheme. Journal of Cryptology 16(3) (2003)Google Scholar
  7. [Bon98]
    Boneh, D.: Twenty years of attacks on the RSA cryptosystem. Notices of the AMS 46(2) (1998)Google Scholar
  8. [CM99]
    Camenisch, J.L., Michels, M.: Proving in Zero-Knowledge that a Number Is the Product of Two Safe Primes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 107–122. Springer, Heidelberg (1999)Google Scholar
  9. [CS03]
    Camenisch, J.L., Shoup, V.: Practical Verifiable Encryption and Decryption of Discrete Logarithms. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 126–144. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. [DJL+10]
    De Cristofaro, E., Jarecki, S., Liu, X., Lu, Y., Tsudik, G.: Automatic Privacy Protection Program – UC Irvine Team Web Site (2010), http://sprout.ics.uci.edu/projects/iarpa-app
  11. [DKT10]
    De Cristofaro, E., Kim, J., Tsudik, G.: Linear-Complexity Private Set Intersection Protocols Secure in Malicious Model. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 213–231. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. [DSMRY09]
    Dachman-Soled, D., Malkin, T., Raykova, M., Yung, M.: Efficient Robust Private Set Intersection. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 125–142. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  13. [DT10]
    De Cristofaro, E., Tsudik, G.: Practical Private Set Intersection Protocols with Linear Complexity. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 143–159. Springer, Heidelberg (2010), http://eprint.iacr.org/2009/491 CrossRefGoogle Scholar
  14. [DT12]
    De Cristofaro, E., Tsudik, G.: On the Performance of certain Private Set Intersection Protocols. Cryptology ePrint Archive (2012), http://eprint.iacr.org/2012/054
  15. [ElG85]
    ElGamal, T.: A public key cryptosystem and a signature scheme based on discrete logarithms. IEEE Transactions on Information Theory 31(4) (1985)Google Scholar
  16. [FIPR05]
    Freedman, M.J., Ishai, Y., Pinkas, B., Reingold, O.: Keyword Search and Oblivious Pseudorandom Functions. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 303–324. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  17. [FKJM+06]
    Fouque, P.-A., Kunz-Jacques, S., Martinet, G., Muller, F., Valette, F.: Power Attack on Small RSA Public Exponent. In: Goubin, L., Matsui, M. (eds.) CHES 2006. LNCS, vol. 4249, pp. 339–353. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. [FNP04]
    Freedman, M.J., Nissim, K., Pinkas, B.: Efficient Private Matching and Set Intersection. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 1–19. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  19. [GGM86]
    Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. Journal of the ACM 33(4) (1986)Google Scholar
  20. [HEK12]
    Huang, Y., Evans, D., Katz, J.: Private Set Intersection: Are Garbled Circuits Better than Custom Protocols. In: NDSS (2012)Google Scholar
  21. [HL08]
    Hazay, C., Lindell, Y.: Efficient Protocols for Set Intersection and Pattern Matching with Security Against Malicious and Covert Adversaries. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 155–175. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. [HMRT11]
    Hazay, C., Mikkelsen, G.L., Rabin, T., Toft, T.: Efficient rsa key generation and threshold paillier in the two-party setting. Cryptology ePrint Archive (2011), http://eprint.iacr.org/2011/494
  23. [HN10]
    Hazay, C., Nissim, K.: Efficient Set Operations in the Presence of Malicious Adversaries. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 312–331. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  24. [IKNP03]
    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
  25. [JL09]
    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
  26. [JL10]
    Jarecki, S., Liu, X.: Fast Secure Computation of Set Intersection. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 418–435. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  27. [KL08]
    Katz, J., Lindell, Y.: Introduction to modern cryptography. Chapman & Hall/CRC (2008)Google Scholar
  28. [KS05]
    Kissner, L., Song, D.: Privacy-Preserving Set Operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)Google Scholar
  29. [MVOV97]
    Menezes, A., Oorschot, P.V., Vanstone, S.: Handbook of Applied Cryptography. CRC (1997)Google Scholar
  30. [NMH+10]
    Nagaraja, S., Mittal, P., Hong, C.Y., Caesar, M., Borisov, N.: BotGrep: Finding Bots with Structured Graph Analysis. In: Usenix Security (2010)Google Scholar
  31. [NP06]
    Naor, M., Pinkas, B.: Oblivious polynomial evaluation. SIAM Journal on Computing, 1–35(5) (2006)Google Scholar
  32. [NTL+11]
    Narayanan, A., Thiagarajan, N., Lakhani, M., Hamburg, M., Boneh, D.: Location Privacy via Private Proximity Testing. In: NDSS (2011)Google Scholar
  33. [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
  34. [RS60]
    Reed, S., Solomon, G.: Polynomial codes over certain finite fields. Journal of the Society for Industrial and Applied Mathematics 8(2) (1960)Google Scholar
  35. [Sha79]
    Shamir, A.: How to Share a Secret. Communications of ACM 22(11) (1979)Google Scholar
  36. [Yao82]
    Yao, A.C.: Protocols for secure computations. In: FOCS (1982)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Emiliano De Cristofaro
    • 1
  • Gene Tsudik
    • 2
  1. 1.PARCUSA
  2. 2.UCIrvineUSA

Personalised recommendations