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dc.contributor.authorFarràs Ventura, Oriol
dc.contributor.authorKaced, Tarik
dc.contributor.authorMartín Mollevi, Sebastià
dc.contributor.authorPadró Laimon, Carles
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationFarràs Ventura, O. [et al.]. Improving the linear programming technique in the search for lower bounds in secret sharing. "IEEE transactions on information theory", Novembre 2020, vol. 66, núm. 11, p. 7088-7100.
dc.description.abstractWe present a new improvement in the linear programming technique to derive lower bounds on the information ratio of secret sharing schemes. We obtain non-Shannon-type bounds without using information inequalities explicitly. Our new technique makes it possible to determine the optimal information ratio of linear secret sharing schemes for all access structures on $5$ participants and all graph-based access structures on $6$ participants. In addition, new lower bounds are presented also for some small matroid ports and, in particular, the optimal information ratios of the linear secret sharing schemes for the ports of the Vamos matroid are determined.
dc.description.sponsorshipOriol Farr`as is supported by the Spanish Government through TIN2014-57364-C2-1-R and by the Catalan government through 2017SGR-705. Tarik Kaced acknowledges the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-16-CE23-0016-01 (project PAMELA). Sebasti`a Mart´ın and Carles Padr´o are supported by Spanish Government through MTM2016-77213-R.
dc.format.extent13 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
dc.subject.lcshProgramming (Mathematics)
dc.subject.otherSecret sharing
dc.subject.otherInformation inequalities
dc.subject.otherRank inequalities
dc.subject.otherCommon information
dc.subject.otherLinear Programming
dc.titleImproving the linear programming technique in the search for lower bounds in secret sharing
dc.subject.lemacProgramació (Matemàtica)
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorFarràs Ventura, O.; Kaced, T.; Martin, S.; Padro, C.
local.citation.publicationNameIEEE transactions on information theory

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