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SECRET SHARING SCHEMES for PORTS of MATROIDS of RANK 3

  • Datos identificativos

    Identificador: imarina:9242146
    Autores:
    Farras O
    Resumen:
    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.
  • Otros:

    Autor según el artículo: Farras O
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Farràs Ventura, Oriol
    Palabras clave: Secret sharing schemes Matroids Matroid ports
    Resumen: 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.
    Áreas temáticas: Theoretical computer science Software Information systems Electrical and electronic engineering Control and systems engineering Computer science, cybernetics Ciência da computação Artificial intelligence
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: oriol.farras@urv.cat
    Identificador del autor: 0000-0002-7495-5980
    Fecha de alta del registro: 2023-08-05
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://www.kybernetika.cz/content/2020/5/903
    Referencia al articulo segun fuente origial: Kybernetika. 56 (5): 903-915
    Referencia de l'ítem segons les normes 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
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI del artículo: 10.14736/kyb-2020-5-0903
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2020
    Tipo de publicación: Journal Publications
  • Palabras clave:

    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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