Common information, matroid representation, and secret sharing for matroid ports

Michael Bamiloshin; Aner Ben-Efraim; Oriol Farràs; Carles Padró

doi:10.1007/s10623-020-00811-1

Common information, matroid representation, and secret sharing for matroid ports

Michael Bamiloshin, Aner Ben-Efraim, Oriol Farràs, Carles Padró

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this strategy to the classification of matroids according to their representations and to the search for bounds on secret sharing for matroid ports.

Original language	English
Pages (from-to)	143-166
Number of pages	24
Journal	Designs, Codes, and Cryptography
Volume	89
Issue number	1
DOIs	https://doi.org/10.1007/s10623-020-00811-1
State	Published - 1 Jan 2021
Externally published	Yes

Keywords

Common information
Information inequalities
Linear programming
Matroid representation
Secret sharing

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science Applications
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s10623-020-00811-1

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AU - Farràs, Oriol

AU - Padró, Carles

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N2 - Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this strategy to the classification of matroids according to their representations and to the search for bounds on secret sharing for matroid ports.

AB - Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this strategy to the classification of matroids according to their representations and to the search for bounds on secret sharing for matroid ports.

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KW - Information inequalities

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KW - Matroid representation

KW - Secret sharing

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Common information, matroid representation, and secret sharing for matroid ports

Abstract

Keywords

ASJC Scopus subject areas

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