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SECRET SHARING SCHEMES for PORTS of MATROIDS of RANK 3

  • Identification data

    Identifier: imarina:9242146
    Authors:
    Farras O
    Abstract:
    A secret sharing scheme is ideal if the size of each share is equal to the size of the secret. Brickell and Davenport showed that the access structure of an ideal secret sharing scheme is determined by a matroid. Namely, the minimal authorized subsets of an ideal secret sharing scheme are in correspondence with the circuits of a matroid containing a fixed point. In this case, we say that the access structure is a matroid port. It is known that, for an access structure, being a matroid port is not a suficient condition to admit an ideal secret sharing scheme. In this work we present a linear secret sharing scheme construction for ports of matroids of rank 3 in which the size of each share is at most n times the size of the secret. Using the previously known secret sharing constructions, the size of each share was O(n2= log n) the size of the secret. Our construction is extended to ports of matroids of any rank k 2, obtaining secret sharing schemes in which the size of each share is at most nk-2 times the size of the secret. This work is complemented by presenting lower bounds: There exist matroid ports that require (Fq; )-linear secret schemes with total information ratio (2n=2=n3=4p log q). © 2020 Institute of Information Theory and Automation of The Czech Academy of Sciences. All rights reserved.
  • Others:

    Author, as appears in the article.: Farras O
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Farràs Ventura, Oriol
    Keywords: Secret sharing schemes Matroids Matroid ports
    Abstract: A secret sharing scheme is ideal if the size of each share is equal to the size of the secret. Brickell and Davenport showed that the access structure of an ideal secret sharing scheme is determined by a matroid. Namely, the minimal authorized subsets of an ideal secret sharing scheme are in correspondence with the circuits of a matroid containing a fixed point. In this case, we say that the access structure is a matroid port. It is known that, for an access structure, being a matroid port is not a suficient condition to admit an ideal secret sharing scheme. In this work we present a linear secret sharing scheme construction for ports of matroids of rank 3 in which the size of each share is at most n times the size of the secret. Using the previously known secret sharing constructions, the size of each share was O(n2= log n) the size of the secret. Our construction is extended to ports of matroids of any rank k 2, obtaining secret sharing schemes in which the size of each share is at most nk-2 times the size of the secret. This work is complemented by presenting lower bounds: There exist matroid ports that require (Fq; )-linear secret schemes with total information ratio (2n=2=n3=4p log q). © 2020 Institute of Information Theory and Automation of The Czech Academy of Sciences. All rights reserved.
    Thematic Areas: Theoretical computer science Software Information systems Electrical and electronic engineering Control and systems engineering Computer science, cybernetics Ciência da computação Artificial intelligence
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: oriol.farras@urv.cat
    Author identifier: 0000-0002-7495-5980
    Record's date: 2023-08-05
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.kybernetika.cz/content/2020/5/903
    Papper original source: Kybernetika. 56 (5): 903-915
    APA: Farras O (2020). SECRET SHARING SCHEMES for PORTS of MATROIDS of RANK 3. Kybernetika, 56(5), 903-915. DOI: 10.14736/kyb-2020-5-0903
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.14736/kyb-2020-5-0903
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2020
    Publication Type: Journal Publications
  • Keywords:

    Artificial Intelligence,Computer Science, Cybernetics,Control and Systems Engineering,Electrical and Electronic Engineering,Information Systems,Software,Theoretical Computer Science
    Secret sharing schemes
    Matroids
    Matroid ports
    Theoretical computer science
    Software
    Information systems
    Electrical and electronic engineering
    Control and systems engineering
    Computer science, cybernetics
    Ciência da computação
    Artificial intelligence
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