Some improved bounds on the information rate of perfect secret sharing schemes
Journal of Cryptology
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
A characterization of span program size and improved lower bounds for monotone span programs
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Designs, Codes and Cryptography
Communications of the ACM
Lower bounds on the information rate of secret sharing schemes with homogeneous access structure
Information Processing Letters
On the Information Rate of Secret Sharing Schemes (Extended Abstract)
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
New General Lower Bounds on the Information Rate of Secret Sharing Schemes
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Secret sharing schemes with three or four minimal qualified subsets
Designs, Codes and Cryptography
Separating the Power of Monotone Span Programs over Different Fields
SIAM Journal on Computing
On the Power of Nonlinear Secret-Sharing
SIAM Journal on Discrete Mathematics
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
On the size of monotone span programs
SCN'04 Proceedings of the 4th international conference on Security in Communication Networks
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
Ideal Multipartite Secret Sharing Schemes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Ideal secret sharing schemes whose minimal qualified subsets have at most three participants
Designs, Codes and Cryptography
An impossibility result on graph secret sharing
Designs, Codes and Cryptography
On the optimization of bipartite secret sharing schemes
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
Secret-sharing schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Finding lower bounds on the complexity of secret sharing schemes by linear programming
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Designs, Codes and Cryptography
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One of the main open problems in secret sharing is the characterization of the access structures of ideal secret sharing schemes. As a consequence of the results by Brickell and Davenport, every one of those access structures is related in a certain way to a unique matroid. Matroid ports are combinatorial objects that are almost equivalent to matroid-related access structures. They were introduced by Lehman in 1964 and a forbidden minor characterization was given by Seymour in 1976. These and other subsequent works on that topic have not been noticed until now by the researchers interested on secret sharing. By combining those results with some techniques in secret sharing, we obtain new characterizations of matroid-related access structures. As a consequence, we generalize the result by Brickell and Davenport by proving that, if the information rate of a secret sharing scheme is greater than 2/3, then its access structure is matroid-related. This generalizes several results that were obtained for particular families of access structures. In addition, we study the use of polymatroids for obtaining upper bounds on the optimal information rate of access structures. We prove that every bound that is obtained by this technique for an access structure applies to its dual structure as well. Finally, we present lower bounds on the optimal information rate of the access structures that are related to two matroids that are not associated with any ideal secret sharing scheme: the Vamos matroid and the non-Desargues matroid.