Skip to main content
SpringerLink
Log in

Robust Information-Theoretic Private Information Retrieval

  • Conference paper
  • First Online:
Security in Communication Networks (SCN 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2576))

Included in the following conference series:

Abstract

A Private Information Retrieval (PIR) protocol allows a user to retrieve a data item of its choice from a database, such that the servers storing the database do not gain information on the identity of the item being retrieved. PIR protocols were studied in depth since the subject was introduced in Chor, Goldreich, Kushilevitz, and Sudan 1995. The standard definition of PIR protocols raises a simple question - what happens if some of the servers crash during the operation? How can we devise a protocol which still works in the presence of crashing servers? Current systems do not guarantee availability of servers at all times for many reasons, e.g., crash of server or communication problems. Our purpose is to design robust PIR protocols, i.e., protocols which still work correctly even if only k out of l servers are available during the protocols’ operation (the user does not know in advance which servers are available). We present various robust PIR protocols giving different tradeofis between the different parameters. These protocols are incomparable, i.e., for different values of n and k we will get better results using different protocols. We first present a generic transformation from regular PIR protocols to robust PIR protocols, this transformation is important since any improvement in the communication complexity of regular PIR protocol will immediately implicate improvement in the robust PIR protocol communication. We also present two specific robust PIR protocols. Finally, we present robust PIR protocols which can tolerate Byzantine servers, i.e., robust PIR protocols which still work in the presence of malicious servers or servers with corrupted or obsolete databases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Chor, B., Goldreich, O., Kushilevitz, E., Sudan, M.: Private information retrieval. In: 36th FOCS. (1995) 41–51. J. version: JACM, 45:965-981, 1998.

    MathSciNet  MATH  Google Scholar 

  2. Ishai, Y., Kushilevitz, E.: Improved upper bounds on information theoretic private information retrieval. In: 31st STOC. (1999) 79–88

    Google Scholar 

  3. Ambainis, A.: Upper bound on the communication complexity of private information retrieval. In: 24th ICALP. Vol. 1256 of LNCS. (1997) 401–407

    MATH  Google Scholar 

  4. Itoh, T.: Efficient private information retrieval. IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences E82-A (1999) 11–20

    Google Scholar 

  5. Beimel, A., Ishai, Y.: Information-theoretic private information retrieval: A unified construction. In: 28th ICALP. Vol. 2076 of LNCS. (2001) 912–926

    MATH  Google Scholar 

  6. Beimel, A., Ishai, Y., Kushilevitz, E., Raymond, J.F.: Breaking the O(n1/2k-1 ) barrier for inforamtion-theoretic private information retrieval. In: 43rd FOCS. (2002) To Appear.

    Google Scholar 

  7. Beaver, D., Feigenbaum, J.: Hiding instances in multioracle queries. In: STACS’ 90. Vol. 415 of LNCS. (1990) 37–48

    Chapter  Google Scholar 

  8. Beaver, D., Feigenbaum, J., Kilian, J., Rogaway, P.: Locally random reductions: Improvements and applications. J. of Cryptology 10 (1997) 17–36

    Article  MathSciNet  Google Scholar 

  9. Stahl, Y.: Robust information-theoretic private information retrieval. Master’s thesis, Ben-Gurion University, Beer-Sheva (2002)

    Google Scholar 

  10. Mehlhorn, K.: Data structures and Algorithms. Volume 1. Sorting and Searching. Springer-Verlag (1984)

    Google Scholar 

  11. Newman, I., Wigderson, A.: Lower bounds on formula size of Boolean functions using hypergraph entropy. SIAM J. on Discrete Mathematics 8 (1995) 536–542

    Article  MathSciNet  Google Scholar 

  12. Alon, N., Naor, M.: Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions. Algorithmica 16 (1996) 434–449

    Article  MathSciNet  Google Scholar 

  13. Blackburn, S.R.: Combinatorial designs and their applications. Research Notes in Mathematics 403 (1999) 44–70

    MathSciNet  Google Scholar 

  14. Blackburn, S.R., Burmester, M., Desmedt, Y., Wild, P.R.: Efficient multiplicative sharing schemes. In EUROCRYPT’ 96. Volume 1070 of LNCS. (1996) 107–118

    Google Scholar 

  15. Fiat, A., Naor, M.: Broadcast encryption. In CRYPTO’ 93. Volume 773 of LNCS. (1994) 480–491

    Chapter  Google Scholar 

  16. Stinson, D., van Trung, T., Wei, R.: Secure frameproof codes, key distribution patterns, group testing algorithms and related structures. J. of Statistical Planning and Inference 86(2) (2000) 595–617

    Article  MathSciNet  Google Scholar 

  17. Alon, N.: Explicit construction of exponential sized families of k-independent sets. Discrete Math. 58 (1986) 191–193

    Article  MathSciNet  Google Scholar 

  18. Atici, M., Magliveras, S.S., Stinson, D.R., Wei, W.D.: Some recursive constructions for perfect hash families. J. Combin. Des. 4 (1996) 353–363

    Article  MathSciNet  Google Scholar 

  19. Blackburn, S.R.: Perfect hash families: Probabilistic methods and explicit constructions. J. of Combin. Theory-Series A 92 (2000) 54–60

    Article  MathSciNet  Google Scholar 

  20. Blackburn, S.R., Wild, P.R.: Optimal linear perfect hash families. J. Combinatorial Theory 83 (1998) 233–250

    Article  MathSciNet  Google Scholar 

  21. Fredman, M.L., Komlos, J.: On the size of separating systems and families of perfect hash functions. SIAM J. Alg. Discrete Methods 5 (1984) 61–68

    Article  MathSciNet  Google Scholar 

  22. Korner, J., Marton: New bounds for perfect hashing via information theory. European J. Combin. 9 (1988) 523–530

    Article  MathSciNet  Google Scholar 

  23. Stinson, D.R., Wei, R., Zhu, L.: New constructions for perfect hash families and related structures using combinatorial designs and codes. J. of Combinatorial Designs 8 (2000) 189–200

    Article  MathSciNet  Google Scholar 

  24. Czech, Z.J., Havas, G., Majewski, B.S.: Perfect hashing. Theoretical Computer Science 182 (1997) 1–143

    Article  MathSciNet  Google Scholar 

  25. Shamir, A.: How to share a secret. CACM 22 (1979) 612–613

    Article  MathSciNet  Google Scholar 

  26. Slot, C., van Emde Boas, P.: On tape versus core; an application of space efficient perfect hash functions to the invariance of space. In: 16thSTOC. (1984) 391–400

    Google Scholar 

  27. Motwani, R., Raghavan, P.: Randomized Algorithms. Cambridge University Press (1995)

    Google Scholar 

  28. Reed, I.S., Solomon, G.: Polynomial codes over certain finite fields. J. SIAM 8 (1960) 300–304

    MathSciNet  MATH  Google Scholar 

  29. Macwilliams, F.R., Sloane, N.J.A.: The Theory of Error-Correcting Codes. Mathematical library. North-Holland (1978)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Dept., Ben-Gurion University, 84105, Beer-Sheva, Israel

    Amos Beimel & Yoav Stahl

Authors
  1. Amos Beimel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yoav Stahl
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, UniversitĂ  di Salerno, Via S. Allende, 84081, Baronissi (SA), Italy

    Stelvio Cimato  & Giuseppe Persiano  & 

  2. Dept. of Computer Engineering and Informatics, Computer Technology Institute and University of Patras, 26500, Rio, Greece

    Clemente Galdi

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Beimel, A., Stahl, Y. (2003). Robust Information-Theoretic Private Information Retrieval. In: Cimato, S., Persiano, G., Galdi, C. (eds) Security in Communication Networks. SCN 2002. Lecture Notes in Computer Science, vol 2576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36413-7_24

Download citation

  • DOI: https://doi.org/10.1007/3-540-36413-7_24

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00420-2

  • Online ISBN: 978-3-540-36413-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation