Multi-Server PIR with Full Error Detection and Limited Error Correction

Authors Reo Eriguchi , Kaoru Kurosawa, Koji Nuida



PDF
Thumbnail PDF

File

LIPIcs.ITC.2022.1.pdf
  • Filesize: 0.86 MB
  • 20 pages

Document Identifiers

Author Details

Reo Eriguchi
  • Graduate School of Information Science and Technology, The University of Tokyo, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Kaoru Kurosawa
  • Research and Development Initiative, Chuo University, Tokyo, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan
Koji Nuida
  • Institute of Mathematics for Industry, Kyushu University, Japan
  • National Institute of Advanced Industrial Science and Technology, Tokyo, Japan

Cite AsGet BibTex

Reo Eriguchi, Kaoru Kurosawa, and Koji Nuida. Multi-Server PIR with Full Error Detection and Limited Error Correction. In 3rd Conference on Information-Theoretic Cryptography (ITC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 230, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum fΓΌr Informatik (2022)
https://doi.org/10.4230/LIPIcs.ITC.2022.1

Abstract

An 𝓁-server Private Information Retrieval (PIR) scheme allows a client to retrieve the Ο„-th element a_Ο„ from a database a = (a₁,…,a_n) which is replicated among 𝓁 servers. It is called t-private if any coalition of t servers learns no information on Ο„, and b-error correcting if a client can correctly compute a_Ο„ from 𝓁 answers containing b errors. This paper concerns the following problems: Is there a t-private 𝓁-server PIR scheme with communication complexity o(n) such that a client can detect errors with probability 1-Ξ΅ even if 𝓁-1 servers return false answers? Is it possible to add error correction capability to it? We first formalize a notion of (1-Ξ΅)-fully error detecting PIR in such a way that an answer returned by any malicious server depends on at most t queries, which reflects t-privacy. We then prove an impossibility result that there exists no 1-fully error detecting (i.e., Ξ΅ = 0) PIR scheme with o(n) communication. Next, for Ξ΅ > 0, we construct 1-private (1-Ξ΅)-fully error detecting and (𝓁/2-O(1))-error correcting PIR schemes which have n^{o(1)} communication, and a t-private one which has O(n^{c}) communication for any t β‰₯ 2 and some constant c < 1. Technically, we show generic transformation methods to add error correction capability to a basic fully error detecting PIR scheme. We also construct such basic schemes by modifying certain existing PIR schemes which have no error detection capability.

Subject Classification

ACM Subject Classification
  • Security and privacy β†’ Information-theoretic techniques
Keywords
  • Private Information Retrieval
  • Error Detection
  • Error Correction

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. A. Ambainis. Upper bound on the communication complexity of private information retrieval. In Automata, Languages and Programming, pages 401-407, 1997. Google Scholar
  2. K. Banawan and S. Ulukus. The capacity of private information retrieval from byzantine and colluding databases. IEEE Transactions on Information Theory, 65(2):1206-1219, 2019. Google Scholar
  3. A. Beimel and Y. Ishai. Information-theoretic private information retrieval: A unified construction. In Automata, Languages and Programming, pages 912-926, 2001. Google Scholar
  4. A. Beimel, Y. Ishai, E. Kushilevitz, and J.-F. Raymond. Breaking the o(n/sup 1/(2k-1)/) barrier for information-theoretic private information retrieval. In The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings., pages 261-270, 2002. Google Scholar
  5. A. Beimel and Y. Stahl. Robust information-theoretic private information retrieval. Journal of Cryptology, 20(3):295-321, 2007. Google Scholar
  6. Y.M. Chee, T. Feng, S. Ling, H. Wang, and L.F. Zhang. Query-efficient locally decodable codes of subexponential length. computational complexity, 22(1):159-189, 2013. Google Scholar
  7. B. Chor, O. Goldreich, E. Kushilevitz, and M. Sudan. Private information retrieval. Journal of the ACM, 45(6):965-982, 1998. Google Scholar
  8. C. Devet, I. Goldberg, and N. Heninger. Optimally robust private information retrieval. In 21st USENIX Security Symposium (USENIX Security 12), pages 269-283, 2012. Google Scholar
  9. Z. Dvir, P. Gopalan, and S. Yekhanin. Matching vector codes. In 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pages 705-714, 2010. Google Scholar
  10. Z. Dvir and S. Gopi. 2-server pir with subpolynomial communication. Journal of the ACM, 63(4):1-15, 2016. Google Scholar
  11. K. Efremenko. 3-query locally decodable codes of subexponential length. SIAM Journal on Computing, 41(6):1694-1703, 2012. Google Scholar
  12. I. Goldberg. Improving the robustness of private information retrieval. In 2007 IEEE Symposium on Security and Privacy (SP'07), pages 131-148, 2007. Google Scholar
  13. Vince Grolmusz. Superpolynomial size set-systems with restricted intersections mod 6 and explicit ramsey graphs. Combinatorica, 20(1):71-86, 2000. Google Scholar
  14. T. Itoh and Y. Suzuki. Improved constructions for query-efficient locally decodable codes of subexponential length. IEICE Transactions on Information and Systems, E93.D(2):263-270, 2010. Google Scholar
  15. K. Kurosawa. How to correct errors in multi-server pir. In Advances in Cryptology - ASIACRYPT 2019, pages 564-574, 2019. Google Scholar
  16. UV Linnik. On the least prime in an arithmetic progression. II. The Deuring-Heilbronn phenomenon. Rec. Math. [Mat. Sbornik] N.S., 15(3):347-368, 1944. Google Scholar
  17. A. Spitzbart. A generalization of Hermite’s interpolation formula. The American Mathematical Monthly, 67(1):42-46, 1960. Google Scholar
  18. H. Sun and S.A. Jafar. The capacity of private information retrieval. IEEE Transactions on Information Theory, 63(7):4075-4088, 2017. Google Scholar
  19. H. Sun and S.A. Jafar. The capacity of robust private information retrieval with colluding databases. IEEE Transactions on Information Theory, 64(4):2361-2370, 2018. Google Scholar
  20. D. Woodruff and S. Yekhanin. A geometric approach to information-theoretic private information retrieval. In 20th Annual IEEE Conference on Computational Complexity (CCC'05), pages 275-284, 2005. Google Scholar
  21. E.Y. Yang, Jie Xu, and K.H. Bennett. Private information retrieval in the presence of malicious failures. In Proceedings 26th Annual International Computer Software and Applications, pages 805-810, 2002. Google Scholar
  22. S. Yekhanin. Towards 3-query locally decodable codes of subexponential length. Journal of the ACM (JACM), 55(1):1-16, 2008. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail