On the optimization of bipartite secret sharing schemes

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.contributor.author	Farràs Ventura, Oriol
dc.contributor.author	Metcalf-Burton, Jessica Ruth
dc.contributor.author	Padró Laimon, Carles
dc.contributor.author	Vázquez González, Leonor
dc.date	2012-05-01
dc.identifier.citation	Farràs Ventura, O., Metcalf-Burton, J., Padro, C., Vázquez, L. On the optimization of bipartite secret sharing schemes. "Designs codes and cryptography", 1 Maig 2012, vol. 63, núm. 2, p. 255-271.
dc.identifier.citation	0925-1022
dc.identifier.citation	10.1007/s10623-011-9552-7
dc.identifier.uri	http://hdl.handle.net/2117/105969
dc.language.iso	eng
dc.relation	https://link.springer.com/article/10.1007%2Fs10623-011-9552-7
dc.rights	info:eu-repo/semantics/openAccess
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Probabilitat
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Optimització
dc.subject	Coding theory
dc.subject	Programming (Mathematics)
dc.subject	Numerical analysis
dc.subject	Cryptography
dc.subject	Secret sharing
dc.subject	Multipartite secret sharing
dc.subject	Polymatroids
dc.subject	Linear programming
dc.subject	Codificació, Teoria de la
dc.subject	Programació (Matemàtica)
dc.subject	Anàlisi numèrica
dc.subject	Classificació AMS::94 Information And Communication, Circuits::94A Communication, information
dc.subject	90C Mathematical programming
dc.subject	Classificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques
dc.title	On the optimization of bipartite secret sharing schemes
dc.type	info:eu-repo/semantics/submittedVersion
dc.type	info:eu-repo/semantics/article
dc.description.abstract	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.
dc.description.abstract	Peer Reviewed

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