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

  • Identification data

    Identifier:  imarina:9138837
    Handle:  https://hdl.handle.net/20.500.11797/imarina9138837
    Authors:  Farras, Oriol; Kaced, Tarik; Martin, Sebastia; Padro, Carles
    Abstract:
    © 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.

  • Others:

    Author, as appears in the article.: Farras, Oriol; Kaced, Tarik; Martin, Sebastia; Padro, Carles
    Department: Enginyeria Informàtica i Matemàtiques
    e-ISSN: 1557-9654
    URV's Author/s: Farràs Ventura, Oriol
    Keywords: Secret sharing schemes; Rank inequalities; Linear programming; Information inequalities; Common information
    Abstract: © 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.
    Thematic Areas: 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
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0018-9448
    Author's mail: oriol.farras@urv.cat
    Record's date: 2025-02-19
    Paper version: info:eu-repo/semantics/acceptedVersion
    Link to the original source: https://ieeexplore.ieee.org/document/9127978
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Paper original source: Ieee Transactions On Information Theory. 66 (11): 7088-7100
    APA: Farras, Oriol; Kaced, Tarik; Martin, Sebastia; Padro, Carles (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
    Article's DOI: 10.1109/TIT.2020.3005706
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2020
    Publication Type: Journal Publications

  • Keywords:

    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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