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.issued
2012-05-01
dc.identifier
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
https://hdl.handle.net/2117/105969
dc.identifier
10.1007/s10623-011-9552-7
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
dc.description.abstract
Postprint (author's final draft)
dc.format
application/pdf
dc.relation
https://link.springer.com/article/10.1007%2Fs10623-011-9552-7
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
Programming (Mathematics)
dc.subject
Numerical analysis
dc.subject
Secret sharing
dc.subject
Multipartite secret sharing
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
