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Finding Lower Bounds on the Complexity of Secret Sharing Schemes by Linear Programming

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6034))

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Abstract

Determining the optimal complexity of secret sharing schemes for every given access structure is a difficult and long-standing open problem in cryptology. Lower bounds have been found by a combinatorial method that uses polymatroids. In this paper, we point out that the best lower bound that can be obtained by this method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants. By applying this linear programming approach, we present better lower bounds on the optimal complexity and the optimal average complexity of several access structures. Finally, by adding the Ingleton inequality to the previous linear programming approach, we find a few examples of access structures for which there is a gap between the optimal complexity of linear secret sharing schemes and the combinatorial lower bound.

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Author information

Authors and Affiliations

  1. Universitat Politècnica de Catalunya,  

    Carles Padró & Leonor Vázquez

Authors
  1. Carles Padró
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  2. Leonor Vázquez
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Editors and Affiliations

  1. Faculty of Mathematics, Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Alejandro López-Ortiz

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Padró, C., Vázquez, L. (2010). Finding Lower Bounds on the Complexity of Secret Sharing Schemes by Linear Programming. In: López-Ortiz, A. (eds) LATIN 2010: Theoretical Informatics. LATIN 2010. Lecture Notes in Computer Science, vol 6034. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12200-2_31

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  • DOI: https://doi.org/10.1007/978-3-642-12200-2_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-12199-9

  • Online ISBN: 978-3-642-12200-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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