Designs, Codes and Cryptography

, Volume 71, Issue 3, pp 503–524 | Cite as

Linear spaces and transversal designs: k-anonymous combinatorial configurations for anonymous database search notes

Article

Abstract

Anonymous database search protocols allow users to query a database anonymously. This can be achieved by letting the users form a peer-to-peer community and post queries on behalf of each other. In this article we discuss an application of combinatorial configurations (also known as regular and uniform partial linear spaces) to a protocol for anonymous database search, as defining the key-distribution within the user community that implements the protocol. The degree of anonymity that can be provided by the protocol is determined by properties of the neighborhoods and the closed neighborhoods of the points in the combinatorial configuration that is used. Combinatorial configurations with unique neighborhoods or unique closed neighborhoods are described and we show how to attack the protocol if such configurations are used. We apply k-anonymity arguments and present the combinatorial configurations with k-anonymous neighborhoods and with k-anonymous closed neighborhoods. The transversal designs and the linear spaces are presented as optimal configurations among the configurations with k-anonymous neighborhoods and k-anonymous closed neighborhoods, respectively.

Keywords

Anonymous database search Combinatorial configuration Partial linear space Neighborhood Linear space Transversal design k-Anonymity 

Mathematics Subject Classification (2000)

94C30 05B05 05B25 05B30 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abel R.J.R., Colbourn C.J., Dinitz J.H.: Mutually orthogonal Latin squares (MOLS). In: Colbourn C.J., Dinitz J.H. (eds.) The CRC Handbook Of Combinatorial Designs, 2nd edn. pp. 160–193. CRC Press, Boca Raton (2007).Google Scholar
  2. 2.
    Ball S., Bamberg J., Devillers A., Stokes K.: An alternative way to generalise the pentagon. J. Comb. Des. (2012). doi:10.1002/jcd.21325.
  3. 3.
    Bose R.C., Shrikhande S.S., Parker E.T.: Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture. Can. J. Math. 12, 189–203 (1960)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Dalenius T.: Finding a needle in a haystack or identifying anonymous census record. J. Off. Stat. 2(3), 329–336 (1986)Google Scholar
  5. 5.
    Dalenius T., Reiss S.P.: Data-swapping: a technique for disclosure control. J. Stat. Plan. Inference. 6(1), 73–85 (1982)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Domingo-Ferrer J.: A Three-Dimensional Conceptual Framework for Database Privacy. Secure Data Management, LNCS 4721/2007, pp. 193–202 (2007).Google Scholar
  7. 7.
    Domingo-Ferrer J., Bras-Amorós, M.: Peer-to-peer private information retrieval. Privacy in Statistical Databases, Lecture Notes in Computer Science. pp. 315–323 (2008).Google Scholar
  8. 8.
    Domingo-Ferrer J., Bras-Amorós M., Wu Q., Manjón J.: User-private information retrieval based on a peer-to-peer community. Data Knowl. Eng. 68(11), 1237–1252 (2009)CrossRefGoogle Scholar
  9. 9.
    Gropp H.: Configurations. In: Colbourn C.J., Dinitz J.H. (eds.) The CRC Handbook Of Combinatorial Designs, pp. 352–355. CRC Press, Boca Raton (2007).Google Scholar
  10. 10.
    Grünbaum B.: Configurations of Points and Lines. American Mathematical Society, Providence (2009)MATHGoogle Scholar
  11. 11.
    Hundepool A., Domingo-Ferrer J., Franconi L., Giessing S., Schulte Nordholt E., Spicer K., de Wolf P.-P.: Statistical Disclosure Control. Wiley, West Sussex (2012)CrossRefGoogle Scholar
  12. 12.
    Reiter M.K., Rubin A.D.: Crowds: anonymity for web transactions. ACM Trans. Inf. Syst. Secur. 1(1), 66–92 (1998)CrossRefGoogle Scholar
  13. 13.
    Samarati P., Sweeney L.: Protecting privacy when disclosing information: k-anonymity and its enforcement through generalization and suppression. SRI International Technical Report (1998).Google Scholar
  14. 14.
    Lee J., Stinson D.R.: A combinatorial approach to key predistribution for distributed sensor networks. IEEE Wireless Communications and Networking Conference, CD-ROM, paper PHY53-06, pp. 6 (2005).Google Scholar
  15. 15.
    Pfitzmann A., Khntopp M., Federrath H.: Anonymity, unobservability, and pseudonymity a proposal for terminology. In Designing Privacy Enhancing Technologies, Lecture Notes in Computer Science, Springer Berlin, pp. 1–9. (2009). An updated version of this document can be found at the following URL: “http://dud.inf.tu-dresden.de/literatur/Anon_Terminology_v0.34.pdf” (2001). Accessed Feb 2012.
  16. 16.
    Spink A., Wolfram D., Jansen M.B.J., Saracevic T.: Searching the web: the public and their queries. J. Am. Soc. Inf. Sci. Technol. 52(3), 226–234 (2001)CrossRefGoogle Scholar
  17. 17.
    Stokes K., Bras-Amorós M.: On query self-submission in peer-to-peer user-private information retrieval. Proceedings of the 4th International Workshop on Privacy and Anonymity in the Information Society (PAIS’11), ACM, New York, NY, USA. 978-1-4503-0611-9 (2011).Google Scholar
  18. 18.
    Stokes K., Bras-Amorós M.: Optimal configurations for peer-to-peer user-private information retrieval. Comput. Math. Appl. 59(4), 1568–1577 (2010)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Stokes K., Bras-Amorós M.: Combinatorial structures for an anonymous data search protocol. Proceedings of Workshop on Computational Security, CRM (UAB), Barcelona, November 28–December 2, (2011).Google Scholar
  20. 20.
    Swanson C.M., Stinson D.R.: Extended combinatorial constructions for peer-to-peer user-private information retrieval. CoRR abs/1112.2762 (2012).Google Scholar
  21. 21.
    Sweeney L.: k-anonymity: a model for protecting privacy. Int. J. Uncertain. Fuzziness Knowl. Syst. 10(5), 557–570 (2002)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Teevan J., Adar E., Jones R., Potts M.: History repeats itself: repeat queries in Yahoos query logs. In Proceedings of the 29th Annual ACM Conference on Research and Development in Information Retrieval, SIGIR 06. pp. 703–704 (2005).Google Scholar
  23. 23.
    Westin A.F.: Privacy and Freedom. Atheneum, New York (1967)Google Scholar
  24. 24.
    Willenborg L., DeWaal T.: Elements of Statistical Disclosure Control. Springer, New York (2001)CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Computer Engineering and MathematicsUniversitat Rovira i VirgiliTarragonaSpain
  2. 2.Estudis d’Informàtica, Multimedia i Telecommunicació, Internet Interdisciplinary Institute (IN3)Universitat Oberta de Catalunya, Edifici Media-TICBarcelonaSpain

Personalised recommendations