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

  • Jaume Martí-Farré
  • Carles Padró
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4116)

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.

Keywords

Secret sharing Ideal secret sharing schemes Ideal access structures Secret sharing representable matroids Information rate 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jaume Martí-Farré
    • 1
  • Carles Padró
    • 1
  1. 1.Dept. of Applied Maths. IVTechnical University of CataloniaBarcelona

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