On the Optimization of Bipartite Secret Sharing Schemes

  • Oriol Farràs
  • Jessica Ruth Metcalf-Burton
  • Carles Padró
  • Leonor Vázquez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5973)

Abstract

Bipartite secret sharing schemes are those having a bipartite access structure, that is, the set of participants is divided into two parts, and all participants in each part play an equivalent role. The bipartite access structures that admit an ideal secret sharing scheme have been characterized, but it is not known which is the optimal complexity of non-ideal bipartite access structures. By using the connection between secret sharing schemes and polymatroids, we find new bounds on the optimal complexity of these acess structures and, for some of them, we find the exact value of this parameter. Some of these bounds are obtained by using a method based on linear programming.

Keywords

Cryptography secret sharing multipartite secret sharing polymatroids linear programming 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Oriol Farràs
    • 1
  • Jessica Ruth Metcalf-Burton
    • 2
  • Carles Padró
    • 1
  • Leonor Vázquez
    • 1
  1. 1.Dep. de Matemàtica Aplicada 4Universitat Politècnica de CatalunyaBarcelonaSpain
  2. 2.Mathematics DepartmentUniversity of MichiganAnn ArborU.S.A.

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