Journal of Combinatorial Theory Series B
An explication of secret sharing schemes
Designs, Codes and Cryptography
Perfect Secret Sharing Schemes on Five Participants
Designs, Codes and Cryptography
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Weighted threshold secret sharing schemes
Information Processing Letters
Communications of the ACM
On the Composition of Matroids and Ideal Secret Sharing Schemes
Designs, Codes and Cryptography
Journal of Algebraic Combinatorics: An International Journal
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th Annual International Cryptology Conference on Advances in Cryptology
On the Information Rate of Secret Sharing Schemes (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
A Representation of a Family of Secret Sharing Matroids
Designs, Codes and Cryptography
Secret sharing schemes with three or four minimal qualified subsets
Designs, Codes and Cryptography
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Multipartite secret sharing by bivariate interpolation
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Characterizing ideal weighted threshold secret sharing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Ideal secret sharing schemes whose minimal qualified subsets have at most three participants
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
On matroids and non-ideal secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
On Non-representable Secret Sharing Matroids
ISPEC '09 Proceedings of the 5th International Conference on Information Security Practice and Experience
On the optimization of bipartite secret sharing schemes
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Ideal secret sharing schemes for useful multipartite access structures
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
On the optimization of bipartite secret sharing schemes
Designs, Codes and Cryptography
On partial anonymity in secret sharing
EuroPKI'07 Proceedings of the 4th European conference on Public Key Infrastructure: theory and practice
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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. Several particular families of multipartite schemes, such as the weighted threshold schemes, the hierarchical and the compartmented schemes, and the ones with bipartite or tripartite access structure have been considered in the literature. The characterization of the access structures of ideal secret sharing schemes is one of the main open problems in secret sharing. 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. One of the main contributions of this paper is the application of discrete polymatroids to secret sharing. They are proved to be a powerful tool to study the properties of multipartite matroids. In this way, we obtain some necessary conditions and some sufficient conditions for a multipartite access structure to be ideal.Our results can be summarized as follows. First, we present a characterization of matroid-related multipartite access structures in terms of discrete polymatroids. As a consequence of this characterization, a necessary condition for a multipartite access structure to be ideal is obtained. Second, we use linear representations of discrete polymatroids to characterize the linearly representable multipartite matroids. In this way we obtain a sufficient condition for a multipartite access structure to be ideal. Finally, we apply our general results to obtain a complete characterization of ideal tripartite access structures, which was until now an open problem.