Some improved bounds on the information rate of perfect secret sharing schemes
Journal of Cryptology
An explication of secret sharing schemes
Designs, Codes and Cryptography
Geometric secret sharing schemes and their duals
Designs, Codes and Cryptography
Finite geometries
Perfect Secret Sharing Schemes on Five Participants
Designs, Codes and Cryptography
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Communications of the ACM
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 bipartite access structure
IEEE Transactions on Information Theory
A note on secret sharing schemes with three homogeneous access structure
Information Processing Letters
Characterizing ideal weighted threshold secret sharing
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
On codes, matroids and secure multi-party computation from linear secret sharing schemes
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
On matroids and non-ideal secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, access structures such that there is at most one participant in the intersection of any two minimal qualified subsets. Examples of such access structures are those defined by finite projective planes and those defined by graphs. In this work, ideal access structures with intersection number equal to one are completely characterized and bounds on the optimal information rate are provided for the non-ideal case.