Designs, Codes and Cryptography

, Volume 74, Issue 2, pp 495–510 | Cite as

Extending Brickell–Davenport theorem to non-perfect secret sharing schemes



One important result in secret sharing is the Brickell–Davenport theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. We present a generalization of the Brickell–Davenport theorem to the general case, in which non-perfect schemes are also considered. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated with matroids. Some optimality properties of such schemes are discussed.


Secret sharing Non-perfect secret sharing scheme Matroid Polymatroid 

Mathematics Subject Classification

94A62 05B35 


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Universitat Rovira i VirgiliTarragonaSpain
  2. 2.Nanyang Technological UniversitySingaporeSingapore

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