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
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
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
Characterizing ideal weighted threshold secret sharing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
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
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th 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. 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. We study this open problem for access structures with rank three, that is, structures whose minimal qualified subsets have at most three participants. We prove that all access structures with rank three that are related to matroids with rank greater than three 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 matroids with rank three that can be represented by an ideal secret sharing scheme.