dc.contributor.author Farràs Ventura, Oriol dc.contributor.author Kaced, Tarik dc.contributor.author Martín Mollevi, Sebastià dc.contributor.author Padró Laimon, Carles dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2021-02-10T09:06:37Z dc.date.available 2021-11-01T01:27:36Z dc.date.issued 2020-11 dc.identifier.citation Farràs 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.identifier.issn 0018-9448 dc.identifier.uri http://hdl.handle.net/2117/338198 dc.description.abstract We 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.sponsorship Oriol Farras 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). Sebastia Mart´ın and Carles Padr´o are supported by Spanish Government through MTM2016-77213-R. dc.format.extent 13 p. dc.language.iso eng dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica dc.subject.lcsh Programming (Mathematics) dc.subject.other Secret sharing dc.subject.other Information inequalities dc.subject.other Rank inequalities dc.subject.other Common information dc.subject.other Linear Programming dc.title Improving the linear programming technique in the search for lower bounds in secret sharing dc.type Article dc.subject.lemac Programació (Matemàtica) dc.contributor.group Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia dc.identifier.doi 10.1109/TIT.2020.3005706 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::65 Numerical analysis::65K Mathematical programming, optimization and variational techniques dc.relation.publisherversion https://ieeexplore.ieee.org/document/9127978 dc.rights.access Open Access local.identifier.drac 30264982 dc.description.version Postprint (author's final draft) dc.relation.projectid info:eu-repo/grantAgreement/MINECO/1PE/MTM2016-77213-R local.citation.author Farràs Ventura, O.; Kaced, T.; Martin, S.; Padro, C. local.citation.publicationName IEEE transactions on information theory local.citation.volume 66 local.citation.number 11 local.citation.startingPage 7088 local.citation.endingPage 7100
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