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
Communications of the ACM
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
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
A note on secret sharing schemes with three homogeneous access structure
Information Processing Letters
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Characterizing ideal weighted threshold secret sharing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of 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. Brickell and Davenport proved that every one of these ideal access structures is related in a certain way to a unique matroid. Specifically, they are matroid ports. In addition to the search of general results, this difficult open problem has been studied in previous works for several families of access structures. In this paper we do the same for access structures with rank 3, that is, structures whose minimal qualified subsets have at most three participants. We completely characterize and classify the rank-3 access structures that are matroid ports. We prove that all access structures with rank three that are ports of matroids greater than 3 are ideal. After the results in this paper, the only open problem in the characterization of the ideal access structures with rank three is to characterize the rank-3 matroids that can be represented by an ideal secret sharing scheme.