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dc.contributor.authorPadró Laimon, Carles
dc.contributor.authorVázquez González, Leonor
dc.contributor.authorYang, An
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2017-06-29T07:37:30Z
dc.date.available2017-06-29T07:37:30Z
dc.date.issued2013-05-01
dc.identifier.citationPadro, C., Vázquez, L., Yang, A. Finding lower bounds on the complexity of secret sharing schemes by linear programming. "Discrete applied mathematics", 1 Maig 2013, vol. 161, núm. 7-8, p. 1072-1084.
dc.identifier.issn0166-218X
dc.identifier.urihttp://hdl.handle.net/2117/105967
dc.description.abstractOptimizing the maximum, or average, length of the shares in relation to the length of the secret for every given access structure is a difficult and long-standing open problem in cryptology. Most of the known lower bounds on these parameters have been obtained by implicitly or explicitly using that every secret sharing scheme defines a polymatroid related to the access structure. The best bounds that can be obtained by this combinatorial method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants. By applying this linear programming approach, we improve some of the known lower bounds for the access structures on five participants and the graph access structures on six participants for which these parameters were still undetermined. Nevertheless, the lower bounds that are obtained by this combinatorial method are not tight in general. For some access structures, they can be improved by adding to the linear program non-Shannon information inequalities as new constraints. We obtain in this way new separation results for some graph access structures on eight participants and for some ports of non-representable matroids. Finally, we prove that, for two access structures on five participants, the combinatorial lower bound cannot be attained by any linear secret sharing scheme
dc.format.extent13 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Modelització matemàtica
dc.subject.lcshCombinatorial probabilities
dc.subject.lcshNumerical analysis
dc.subject.otherSecret sharing
dc.subject.otherlinear programming
dc.subject.otherpolymatroid
dc.subject.othernon-Shannon information inequalities
dc.titleFinding lower bounds on the complexity of secret sharing schemes by linear programming
dc.typeArticle
dc.subject.lemacCombinacions (Matemàtica)
dc.subject.lemacAnàlisi numèrica
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.identifier.doi10.1016/j.dam.2012.10.020
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::60 Probability theory and stochastic processes::60C05 Combinatorial probability
dc.subject.amsClassificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0166218X12004003?via%3Dihub
dc.rights.accessOpen Access
local.identifier.drac18547224
dc.description.versionPostprint (author's final draft)
local.citation.authorPadro, C.; Vázquez, L.; Yang, A.
local.citation.publicationNameDiscrete applied mathematics
local.citation.volume161
local.citation.number7-8
local.citation.startingPage1072
local.citation.endingPage1084


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