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Ideal Secret Sharing Schemes Whose Minimal Qualified Subsets Have at Most Three Participants

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Security and Cryptography for Networks (SCN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4116))

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Abstract

One of the main open problems in secret sharing is the characterization of the access structures of ideal secret sharing schemes. As a consequence of the results by Brickell and Davenport, every one of those access structures is related in a certain way to a unique matroid. We study this open problem for access structures with rank three, that is, structures whose minimal qualified subsets have at most three participants. We prove that all access structures with rank three that are related to matroids with rank greater than three are ideal. After the results in this paper, the only open problem in the characterization of the ideal access structures with rank three is to characterize the matroids with rank three that can be represented by an ideal secret sharing scheme.

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Author information

Authors and Affiliations

  1. Dept. of Applied Maths. IV, Technical University of Catalonia, Barcelona

    Jaume Martí-Farré & Carles Padró

Authors
  1. Jaume Martí-Farré
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  2. Carles Padró
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, via Ponte don Melillo, 84084, Fisciano (SA), Italy

    Roberto De Prisco

  2. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2006 Springer-Verlag Berlin Heidelberg

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Martí-Farré, J., Padró, C. (2006). Ideal Secret Sharing Schemes Whose Minimal Qualified Subsets Have at Most Three Participants. In: De Prisco, R., Yung, M. (eds) Security and Cryptography for Networks. SCN 2006. Lecture Notes in Computer Science, vol 4116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11832072_14

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  • DOI: https://doi.org/10.1007/11832072_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38080-1

  • Online ISBN: 978-3-540-38081-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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