Sublinear Scaling for Multi-Client Private Information Retrieval

  • Wouter Lueks
  • Ian GoldbergEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8975)


Private information retrieval (PIR) allows clients to retrieve records from online database servers without revealing to the servers any information about what records are being retrieved. To achieve this, the servers must typically do a computation involving the entire database for each query. Previous work by Ishai et al. has suggested using batch codes to allow a single client (or collaborating clients) to retrieve multiple records simultaneously while allowing the server computation to scale sublinearly with the number of records fetched.

In this work, we observe a useful mathematical relationship between batch codes and efficient matrix multiplication algorithms, and use this to design a PIR server algorithm that achieves sublinear scaling in the number of records fetched, even when they are requested by distinct, non-collaborating clients; indeed, the clients can be completely unaware that the servers are implementing our optimization. Our multi-client server algorithm is several times faster, when enough records are fetched, than existing optimized PIR severs.

As an application of our work, we show how retrieving proofs of inclusion of certificates in a Certificate Transparency log server can be made privacy friendly using multi-client PIR.



We thank the anonymous reviewers and Ben Laurie for their helpful feedback. This research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and by the research program Sentinels as project ‘Revocable Privacy’ (10532). Wouter Lueks is a member of the Privacy and Identity Lab (PI.lab). Sentinels is being financed by Technology Foundation STW, the Netherlands Organization for Scientific Research (NWO), and the Dutch Ministry of Economic Affairs. The PI.lab is funded by ( This work benefitted from the use of the CrySP RIPPLE Facility at the University of Waterloo.


  1. 1.
    Aguilar Melchor, C., Gaborit, P.: A lattice-based computationally-efficient private information retrieval protocol. In: Western European Workshop on Research in Cryptology (2007)Google Scholar
  2. 2.
    Beimel, A., Stahl, Y.: Robust information-theoretic private information retrieval. J. Cryptology 20(3), 295–321 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chor, B., Goldreich, O., Kushilevitz, E., Sudan, M.: Private information retrieval. In: 36th Annual IEEE Symposium on Foundations of Computer Science, pp. 41–50 (1995)Google Scholar
  4. 4.
    Chor, B., Gilboa, N., Naor, M.: Private Information Retrieval by Keywords. Technical report TR CS0917, Department of Computer Science, Technion, Israel (1997)Google Scholar
  5. 5.
    Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. J. Symbolic Comput. 9(3), 251–280 (1990)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Devet, C., Goldberg, I.: The best of both worlds: combining information-theoretic and computational PIR for communication efficiency. In: De Cristofaro, E., Murdoch, S.J. (eds.) PETS 2014. LNCS, vol. 8555, pp. 63–82. Springer, Heidelberg (2014) Google Scholar
  7. 7.
    Devet, C., Goldberg, I., Heninger, N.: Optimally robust private information retrieval. In: 21st USENIX Security Symposium (2012)Google Scholar
  8. 8.
    Fox-IT BV: Black Tulip: Report of the investigation into the DigiNotar Certificate Authority breach, August 2012Google Scholar
  9. 9.
    Goldberg, I.: Improving the robustness of private information retrieval. In: 28th IEEE Symposium on Security and Privacy, pp. 131–148 (2007)Google Scholar
  10. 10.
    Goldberg, I., Devet, C., Hendry, P., Henry, R.: Percy++ project on SourceForge, version 0.9.0 (2013). Accessed September 2014
  11. 11.
    Goldberg, I., Devet, C., Lueks, W., Yang, A., Hendry, P., Henry, R.: Percy++ project on SourceForge, version 1.0 (2014). Accessed November 2014
  12. 12.
    Henry, R., Huang, Y., Goldberg, I.: One (block) size fits all: PIR and SPIR with variable-length records via multi-block queries. In: 20th Annual Network and Distributed System Security Symposium (2013)Google Scholar
  13. 13.
    Ishai, Y., Kushilevitz, E., Ostrovsky, R., Sahai, A.: Batch codes and their applications. In: 36th ACM Symposium on Theory of Computing, pp. 262–271 (2004)Google Scholar
  14. 14.
    Kushilevitz, E., Ostrovsky, R.: Replication is not needed: single database, computationally-private information retrieval. In: 38th Annual IEEE Symposium on Foundations of Computer Science, pp. 364–373 (1997)Google Scholar
  15. 15.
    Laurie, B., Langley, A., Kasper, E.: Certificate Transparency. RFC 6962 (Experimental), June 2013.
  16. 16.
    Olumofin, F., Goldberg, I.: Privacy-preserving queries over relational databases. In: Atallah, M.J., Hopper, N.J. (eds.) PETS 2010. LNCS, vol. 6205, pp. 75–92. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  17. 17.
    Olumofin, Femi, Goldberg, Ian: Revisiting the Computational Practicality of Private Information Retrieval. In: Danezis, George (ed.) FC 2011. LNCS, vol. 7035, pp. 158–172. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  18. 18.
    Olumofin, F., Tysowski, P.K., Goldberg, I., Hengartner, U.: Achieving efficient query privacy for location based services. In: Atallah, M.J., Hopper, N.J. (eds.) PETS 2010. LNCS, vol. 6205, pp. 93–110. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  19. 19.
    Shamir, A.: How to share a secret. Commun. ACM 22(11), 612–613 (1979)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Sion, R., Carbunar, B.: On the computational practicality of private information retrieval. In: 14th Network and Distributed Systems Security Symposium (2007)Google Scholar
  21. 21.
    Strassen, V.: Gaussian elimination is not optimal. Numer. Math. 13(4), 354–356 (1969)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute for Computing and Information Sciences (iCIS)Radboud University NijmegenNijmegenThe Netherlands
  2. 2.Cheriton School of Computer ScienceUniversity of WaterlooWaterlooCanada

Personalised recommendations