Ideal Hierarchical Secret Sharing Schemes

Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 58; no. 5; pp. 3273 - 3286
Main Authors: Farras, O., Padro, C.
Format: Journal Article Publication
Language:English
Published: New York, NY IEEE 01.05.2012
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
90 Operations research, mathematical programming
90B Operations research and management science
90C Mathematical programming
Applied sciences
Bismuth
Boolean polymatroids
Classificació AMS
Code Division Multiple Access
Construction
Cryptography
Electronic mail
Exact sciences and technology
Government
hierarchical secret sharing
ideal secret sharing schemes
Information sharing
Information theory
Information, signal and communications theory
integer polymatroids
Integers
Inventions
Investigació operativa
Joints
Matemàtiques i estadística
Mathematical analysis
multi partite secret sharing
multipartite secret sharing
Operations research
Periodic structures
Ports
Programació (Matemàtica)
Programming (Mathematics)
secret sharing
Telecommunications and information theory
Thresholds
Vectors
weighted secret sharing schemes
weighted threshold secret sharing
Àrees temàtiques de la UPC
Finite field
integer polymatroids
hierarchical secret sharing
weighted threshold secret sharing
Matroid
multipartite secret sharing
ideal secret sharing schemes
Secret sharing
Hierarchized structure
Boolean polymatroids
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well-known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2011.2182034