Volume 14, Issue 2 (7-2014)                   2014, 14(2): 97-114 | Back to browse issues page

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Cheraghi A. Determining the Optimal Complexity of Bipartite Access Structures. Quarterly Journal of Science Kharazmi University. 2014; 14 (2) :97-114
URL: http://jsci.khu.ac.ir/article-1-1722-en.html
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Abstract:   (3599 Views)
Determining the Optimal Complexity of Bipartite Access Structures

Abbas Cneraghi

Abstract

Keywords: Complexity, Secret Sharing Scheme, Access structure.



In a bipartite secret sharing scheme, the set of participants is divided into two parts, and all participants in each part play an equivalent role. The ideal bipartite access structures were characterized by Padro and Saez, but it is not known which is the optimal information rate of non ideal bipartite access structures. Determining the optimal complexity of general access structures is one of the major problems in secret sharing. We study this open problem restricted to the bipartite access structures, obtaining a new method to compute bounds on the optimal complexity. Namely, by using the connection between secret sharing schemes and polymatroids, we show a linear programming problem that determines, for each access structure, a lower bound on the complexity. Moreover, we show new optimal constructions for certain bipartite access structures.
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Type of Study: S | Subject: Science
Published: 2014/07/15

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