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

  • Klara Stokes
  • Oriol Farràs


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.


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

Mathematics Subject Classification (2000)

94C30 05B05 05B25 05B30 


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© 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

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