Private Database Queries Using Somewhat Homomorphic Encryption

  • Dan Boneh
  • Craig Gentry
  • Shai Halevi
  • Frank Wang
  • David J. Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7954)

Abstract

In a private database query system, a client issues queries to a database and obtains the results without learning anything else about the database and without the server learning the query. While previous work has yielded systems that can efficiently support disjunction queries, performing conjunction queries privately remains an open problem. In this work, we show that using a polynomial encoding of the database enables efficient implementations of conjunction queries using somewhat homomorphic encryption. We describe a three-party protocol that supports efficient evaluation of conjunction queries. Then, we present two implementations of our protocol using Paillier’s additively homomorphic system as well as Brakerski’s somewhat homomorphic cryptosystem. Finally, we show that the additional homomorphic properties of the Brakerski cryptosystem allow us to handle queries involving several thousand elements over a million-record database in just a few minutes, far outperforming the implementation using the additively homomorphic system.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R. (ed.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Brakerski, Z., Gentry, C., Vaikuntanathan, V.: Fully homomorphic encryption without bootstrapping. In: Innovations in ITCS 2012 (2012)Google Scholar
  3. 3.
    Chor, B., Kushilevitz, E., Goldreich, O., Sudan, M.: Private information retrieval. J. ACM 45(6), 965–981 (1998)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    De Cristofaro, E., Lu, Y., Tsudik, G.: Efficient techniques for privacy-preserving sharing of sensitive information. In: McCune, J.M., Balacheff, B., Perrig, A., Sadeghi, A.-R., Sasse, A., Beres, Y. (eds.) Trust 2011. LNCS, vol. 6740, pp. 239–253. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  5. 5.
    Gentry, C.: A fully homomorphic encryption scheme. Ph.D. thesis, Stanford University (2009), http://crypto.stanford.edu/craig
  6. 6.
    Gentry, C., Halevi, S., Smart, N.P.: Fully homomorphic encryption with polylog overhead. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 465–482. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Gentry, C., Halevi, S., Vaikuntanathan, V.: A simple BGN-type cryptosystem from LWE. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 506–522. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Gertner, Y., Ishai, Y., Kushilevitz, E., Malkin, T.: Protecting data privacy in private information retrieval schemes. In: STOC 1998, pp. 151–160 (1998)Google Scholar
  9. 9.
    Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28(2), 270–299 (1984)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Ishai, Y., Prabhakaran, M., Sahai, A.: Founding cryptography on oblivious transfer – efficiently. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 572–591. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  11. 11.
    Kissner, L., Song, D.: Privacy-preserving set operations. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 241–257. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Raykova, M., Cui, A., Vo, B., Liu, B., Malkin, T., Bellovin, S.M., Stolfo, S.J.: Usable, Secure, Private Search. IEEE Security and Privacy, 53–60 (October 2012)Google Scholar
  14. 14.
    Smart, N.P., Vercauteren, F.: Fully homomorphic SIMD operations (2011), Manuscript at http://eprint.iacr.org/2011/133

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dan Boneh
    • 1
  • Craig Gentry
    • 2
  • Shai Halevi
    • 2
  • Frank Wang
    • 3
  • David J. Wu
    • 1
  1. 1.Stanford UniversityUSA
  2. 2.IBM ResearchUSA
  3. 3.MITUSA

Personalised recommendations