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Improving the Linear Programming Technique in the Search for Lower Bounds in Secret Sharing

  • Dades identificatives

    Identificador: imarina:9138837
    Handle: https://hdl.handle.net/20.500.11797/imarina9138837
    Autors:
    Farràs OKaced TMartín SPadró C
    Resum:
    © 1963-2012 IEEE. 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.

  • Altres:

    Autor segons l'article: Farràs O; Kaced T; Martín S; Padró C
    Departament: Enginyeria Informàtica i Matemàtiques
    e-ISSN: 1557-9654
    Autor/s de la URV: Farràs Ventura, Oriol
    Paraules clau: Secret sharing schemes Rank inequalities Linear programming Information inequalities Common information
    Resum: © 1963-2012 IEEE. 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.
    Àrees temàtiques: Matemática / probabilidade e estatística Library and information sciences Information systems Engineering, electrical & electronic Engenharias iv Engenharias iii Computer science, information systems Computer science applications Ciencias sociales Ciência da computação Astronomia / física
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0018-9448
    Adreça de correu electrònic de l'autor: oriol.farras@urv.cat
    Identificador de l'autor: 0000-0002-7495-5980
    Data d'alta del registre: 2023-02-19
    Versió de l'article dipositat: info:eu-repo/semantics/acceptedVersion
    Enllaç font original: https://ieeexplore.ieee.org/document/9127978
    Referència a l'article segons font original: Ieee Transactions On Information Theory. 66 (11): 7088-7100
    Referència de l'ítem segons les normes APA: Farràs O; Kaced T; Martín S; Padró C (2020). Improving the Linear Programming Technique in the Search for Lower Bounds in Secret Sharing. Ieee Transactions On Information Theory, 66(11), 7088-7100. DOI: 10.1109/TIT.2020.3005706
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI de l'article: 10.1109/TIT.2020.3005706
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2020
    Tipus de publicació: Journal Publications

  • Paraules clau:

    Computer Science Applications,Computer Science, Information Systems,Engineering, Electrical & Electronic,Information Systems,Library and Information Sciences
    Secret sharing schemes
    Rank inequalities
    Linear programming
    Information inequalities
    Common information
    Matemática / probabilidade e estatística
    Library and information sciences
    Information systems
    Engineering, electrical & electronic
    Engenharias iv
    Engenharias iii
    Computer science, information systems
    Computer science applications
    Ciencias sociales
    Ciência da computação
    Astronomia / física

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