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...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/105969 |
| Acceso en línea: | https://hdl.handle.net/2117/105969 https://dx.doi.org/10.1007/s10623-011-9552-7 |
| Access Level: | acceso abierto |
| Palabra clave: | Coding theory Programming (Mathematics) Numerical analysis Cryptography Secret sharing Multipartite secret sharing Polymatroids Linear programming Codificació, Teoria de la Programació (Matemàtica) Anàlisi numèrica Classificació AMS::94 Information And Communication, Circuits::94A Communication, information 90C Mathematical programming Classificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització |
| Sumario: | 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. |
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