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
On the information rate of perfect 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 Linear Construction of Secret Sharing Schemes
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
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
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
Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions
Information Processing Letters
Characterizing Ideal Weighted Threshold Secret Sharing
SIAM Journal on Discrete Mathematics
Ideal Multipartite Secret Sharing Schemes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
On an infinite family of graphs with information ratio 2 − 1/k
Computing - Special Issue on the occasion of the 8th Central European Conference on Cryptography
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
An impossibility result on graph secret sharing
Designs, Codes and Cryptography
Matroids can be far from ideal secret sharing
TCC'08 Proceedings of the 5th conference on Theory of cryptography
On the optimization of bipartite secret sharing schemes
ICITS'09 Proceedings of the 4th international conference on Information theoretic security
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
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
Complexity of universal access structures
Information Processing Letters
On the optimization of bipartite secret sharing schemes
Designs, Codes and Cryptography
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Discrete Applied Mathematics
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The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. This paper deals with the open problem of optimizing this parameter for secret sharing schemes with general access structures. Specifically, our objective is to determine the optimal complexity of the access structures with exactly four minimal qualified subsets. Lower bounds on the optimal complexity are obtained by using the known polymatroid technique in combination with linear programming. Upper bounds are derived from decomposition constructions of linear secret sharing schemes. In this way, the exact value of the optimal complexity is determined for several access structures in that family. For the other ones, we present the best known lower and upper bounds.