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Title: Ideal multipartite secret sharing schemes
Authors: Farràs, Oriol
Martí-Farré, Jaume
Padró, Carles
Issue Date: 2011
Source: Farràs, O., Martí-Farré, J., & Padró, C. (2012). Ideal Multipartite Secret Sharing Schemes. Journal of Cryptology, 25(3), 434-463.
Series/Report no.: Journal of cryptology
Abstract: Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. In this work, the characterization of ideal multipartite access structures is studied with all generality. Our results are based on the well-known connections between ideal secret sharing schemes and matroids and on the introduction of a new combinatorial tool in secret sharing, integer polymatroids . Our results can be summarized as follows. First, we present a characterization of multipartite matroid ports in terms of integer polymatroids. As a consequence of this characterization, a necessary condition for a multipartite access structure to be ideal is obtained. Second, we use representations of integer polymatroids by collections of vector subspaces to characterize the representable multipartite matroids. In this way we obtain a sufficient condition for a multipartite access structure to be ideal, and also a unified framework to study the open problems about the efficiency of the constructions of ideal multipartite secret sharing schemes. Finally, we apply our general results to obtain a complete characterization of ideal tripartite access structures, which was until now an open problem.
ISSN: 0933-2790
DOI: 10.1007/s00145-011-9101-6
Rights: © 2011 International Association for Cryptologic Research.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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