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 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
Communications of the ACM
How to (Really) Share a Secret
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
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
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions
Information Processing Letters
Hierarchical Threshold Secret Sharing
Journal of Cryptology
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
Multipartite Secret Sharing by Bivariate Interpolation
Journal of 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
Monotone circuits for monotone weighted threshold functions
Information Processing Letters
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
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
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
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
Two Constructions on Limits of Entropy Functions
IEEE Transactions on Information Theory
Finding lower bounds on the complexity of secret sharing schemes by linear programming
Discrete Applied Mathematics
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Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the tripartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.