Advertisement

A Storage-Efficient and Robust Private Information Retrieval Scheme Allowing Few Servers

  • Daniel Augot
  • Françoise Levy-dit-Vehel
  • Abdullatif Shikfa
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8813)

Abstract

Since the concept of locally decodable codes was introduced by Katz and Trevisan in 2000 [11], it is well-known that information theoretically secure private information retrieval schemes can be built using locally decodable codes [15]. In this paper, we construct a Byzantine robust PIR scheme using the multiplicity codes introduced by Kopparty et al. [12]. Our main contributions are on the one hand to avoid full replication of the database on each server; this significantly reduces the global redundancy. On the other hand, to have a much lower locality in the PIR context than in the LDC context. This shows that there exists two different notions: LDC-locality and PIR-locality. This is made possible by exploiting geometric properties of multiplicity codes.

Keywords

Communication Complexity Query Complexity Storage Overhead Hash Family Private Information Retrieval 
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. 1.
    Beimel, A., Ishai, Y., Kushilevitz, E., Raymond, J.-F.: Breaking the n 1/(2k − 1) barrier for information-theoretic private information retrieval. In: Chazelle, B. (ed.) The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings, vol. 59, pp. 261–270 (2002)Google Scholar
  2. 2.
    Beimel, A., Stahl, Y.: Robust Information-Theoretic Private Information Retrieval. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 326–341. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  3. 3.
    Beimel, A., Stahl, Y.: Robust information-theoretic private information retrieval. J. Cryptology 20(3), 295–321 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Chor, B., Goldreich, O., Kushilevitz, E., Sudan, M.: Private information retrieval. Journal of the ACM 45(6), 965–981 (1998); Earlier version in FOCS 1995Google Scholar
  5. 5.
    Devet, C., Goldberg, I., Heninger, N.: Optimally robust private information retrieval. In: 21st USENIX Security Symposium, Security 2012, pp. 269–283. USENIX Association, Berkeley (2012)Google Scholar
  6. 6.
    Efremenko, K.: 3-query locally decodable codes of subexponential length. In: STOC 2009. Proceedings of the Forty-first Annual ACM Symposium on Theory of Computing, pp. 39–44. ACM (2009)Google Scholar
  7. 7.
    Gemmell, P., Sudan, M.: Highly resilient correctors for polynomials. Information Processing Letters 43(4), 169–174 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Guo, A., Kopparty, S., Sudan, M.: New affine-invariant codes from lifting. In: Proceedings of the 4th Conference on Innovations in Theoretical Computer Science, ITCS 2013, pp. 529–540. ACM, New York (2013)Google Scholar
  9. 9.
    Guruswami, V., Wang, C.: Linear-algebraic list decoding for variants of Reed–Solomon codes. IEEE Transactions on Information Theory 59(6), 3257–3268 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Hemenway, B., Ostrovsky, R., Wootters, M.: Local correctability of expander codes. CoRR, abs/1304.8129 (2013)Google Scholar
  11. 11.
    Katz, J., Trevisan, L.: On the efficiency of local decoding procedures for error-correcting codes. In: Yao, F., Luks, E. (eds.) Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, STOC 2000, pp. 80–86. ACM (2000)Google Scholar
  12. 12.
    Kopparty, S., Saraf, S., Yekhanin, S.: High-rate codes with sublinear-time decoding. In: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, STOC 2011, pp. 167–176. ACM, New York (2011)Google Scholar
  13. 13.
    Kushilevitz, E., Ostrovsky, R.: Replication is not needed: single database, computationally-private information retrieval. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science 1997, pp. 364–373 (October 1997)Google Scholar
  14. 14.
    Yekhanin, S.: Towards 3-query locally decodable codes of subexponential length. J. ACM 1, 1:1–1:16 (2008)Google Scholar
  15. 15.
    Yekhanin, S.: Locally Decodable Codes and Private Information Retrieval Schemes. In: Information Security and Cryptography. Springer (2010)Google Scholar
  16. 16.
    Yekhanin, S.: Locally Decodable Codes. Foundations and Trends in Theoretical Computer Science, vol. 6. NOW Publisher (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daniel Augot
    • 1
    • 2
  • Françoise Levy-dit-Vehel
    • 1
    • 2
    • 3
  • Abdullatif Shikfa
    • 4
  1. 1.INRIAFrance
  2. 2.Laboratoire d’informatique de l’École polytechniqueFrance
  3. 3.ENSTA ParisTech/U2ISFrance
  4. 4.Alcatel-LucentFrance

Personalised recommendations