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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.date.accessioned2018-02-23T09:46:09Z
dc.date.available2018-12-01T01:31:02Z
dc.date.issued2017-12-01
dc.identifier.citationFarràs Ventura, O., Hansen, T., Kaced, T., Padro, C. On the information ratio of non-perfect secret sharing schemes. "Algorithmica", 1 Desembre 2017, vol. 79, núm. 4, p. 987-1013.
dc.identifier.issn0178-4617
dc.identifier.urihttp://hdl.handle.net/2117/114396
dc.descriptionThe final publication is available at Springer via http://dx.doi.org/10.1007/s00453-016-0217-9
dc.description.abstractA secret sharing scheme is non-perfect if some subsets of players 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 and the construction of efficient linear non-perfect secret sharing schemes. To this end, we extend the known connections between matroids, 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 on the secret value that is obtained by each subset of players. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, access functions whose values depend only on the number of players, generalize the threshold access structures. The optimal information ratio of the uniform access functions with rational values has been determined by Yoshida, Fujiwara and Fossorier. By using the tools that are described in our work, we provide a much simpler proof of that result and we extend it to access functions with real values.
dc.format.extent27 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshCoding theory
dc.subject.otherSecret sharing
dc.subject.otherNon-perfect secret sharing
dc.subject.otherAccess function
dc.subject.otherInformation ratio
dc.subject.otherPolymatroid
dc.titleOn the information ratio of non-perfect secret sharing schemes
dc.typeArticle
dc.subject.lemacCodificació, Teoria de la
dc.contributor.groupUniversitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia
dc.identifier.doi10.1007/s00453-016-0217-9
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::94 Information And Communication, Circuits::94A Communication, information
dc.relation.publisherversionhttps://link.springer.com/article/10.1007%2Fs00453-016-0217-9
dc.rights.accessOpen Access
local.identifier.drac21578575
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/644024/EU/A FRAMEWORK FOR USER CENTRED PRIVACY AND SECURITY IN THE CLOUD/CLARUS
local.citation.authorFarràs Ventura, O.; Hansen, T.; Kaced, T.; Padro, C.
local.citation.publicationNameAlgorithmica
local.citation.volume79
local.citation.number4
local.citation.startingPage987
local.citation.endingPage1013


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