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dc.contributor.authorFarràs Ventura, Oriol
dc.contributor.authorHansen, Torben
dc.contributor.authorKaced, Tarik
dc.contributor.authorPadró Laimon, Carles
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationFarràs Ventura, O., Hansen, T., Kaced, T., Padro, C. Optimal non-perfect uniform secret sharing schemes. A: Annual International Cryptology Conference. "Advances in Cryptology (CRYPTO 2014). 34th Annual Cryptology Conference: Santa Barbara, CA, USA: august 17-21, 2014: proceedings, part II". Santa Barbara, CA: Springer, 2014, p. 217-234.
dc.description.abstractA secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.
dc.format.extent18 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Anàlisi multivariant
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.lcshSequences (Mathematics)
dc.subject.lcshCoding theory
dc.subject.otherSecret sharing
dc.subject.otherNon-perfect secret sharing
dc.subject.otherInformation Ratio
dc.titleOptimal non-perfect uniform secret sharing schemes
dc.typeConference report
dc.subject.lemacSeqüències (Matemàtica)
dc.subject.lemacCodificació, Teoria de la
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::62 Statistics::62L Sequential methods
dc.subject.amsClassificació AMS::94 Information And Communication, Circuits::94A Communication, information
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
local.citation.authorFarràs Ventura, O.; Hansen, T.; Kaced, T.; Padro, C.
local.citation.contributorAnnual International Cryptology Conference
local.citation.pubplaceSanta Barbara, CA
local.citation.publicationNameAdvances in Cryptology (CRYPTO 2014). 34th Annual Cryptology Conference: Santa Barbara, CA, USA: august 17-21, 2014: proceedings, part II

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