On the optimization of bipartite secret sharing schemes

Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participa...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2012-05, Vol.63 (2), p.255-271
Main Authors: Farràs, Oriol, Metcalf-Burton, Jessica Ruth, Padró, Carles, Vázquez, Leonor
Format: Article
Language:English
Subjects:
65 Numerical analysis
65K Mathematical programming, optimization and variational techniques
90C Mathematical programming
94 Information And Communication, Circuits
94A Communication, information
Anàlisi numèrica
Circuits
Classificació AMS
Codificació, Teoria de la
Coding and Information Theory
Coding theory
Computer Science
Cryptography
Cryptology
Data Structures and Information Theory
Discrete Mathematics in Computer Science
Information and Communication
Investigació operativa
Linear programming
Matemàtiques i estadística
Multipartite secret sharing
Numerical analysis
Optimització
Polymatroids
Probabilitat
Programació (Matemàtica)
Programming (Mathematics)
Secret sharing
Àrees temàtiques de la UPC
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Summary:Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-011-9552-7