Título:
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Secret sharing, rank inequalities, and information inequalities
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Autor/a:
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Martín Mollevi, Sebastià; Padró Laimon, Carles; Yang, An
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Otros autores:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MAK - Matemàtica Aplicada a la Criptografia |
Abstract:
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Abstract:
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Beimel and Orlov proved that all information
inequalities on four or five variables, together with all information
inequalities on more than five variables that are known to date,
provide lower bounds on the size of the shares in secret sharing
schemes that are at most linear on the number of participants.
We present here another two negative results about the power of
information inequalities in the search for lower bounds in secret
sharing. First, we prove that all information inequalities on a
bounded number of variables can only provide lower bounds that
are polynomial on the number of participants. Second, we prove
that the rank inequalities that are derived from the existence of
two common informations can provide only lower bounds that
are at most cubic in the number of participants. |
Materia(s):
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-Àrees temàtiques de la UPC::Enginyeria de la telecomunicació -Information theory -cryptography -secret sharing -rank inequalities -information inequalities -polymatroids -Matemàtica aplicada |
Derechos:
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http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
Tipo de documento:
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Artículo - Versión presentada Artículo |
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