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
Communications of the ACM
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
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
On the Power of Nonlinear Secret-Sharing
SIAM Journal on Discrete Mathematics
Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions
Information Processing Letters
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
On secret sharing schemes, matroids and polymatroids
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Matroids can be far from ideal secret sharing
TCC'08 Proceedings of the 5th conference on Theory of cryptography
On matroids and non-ideal secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
Complexity of universal access structures
Information Processing Letters
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 the optimization of bipartite secret sharing schemes
Designs, Codes and Cryptography
Information Sciences: an International Journal
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A perfect secret sharing scheme based on a graph G is a randomized distribution of a secret among the vertices of the graph so that the secret can be recovered from the information assigned to vertices at the endpoints of any edge, while the total information assigned to an independent set of vertices is independent (in statistical sense) of the secret itself. The efficiency of a scheme is measured by the amount of information the most heavily loaded vertex receives divided by the amount of information in the secret itself. The (worst case) information ratio of G is the infimum of this number. We calculate the best lower bound on the information ratio for an infinite family of graphs the entropy method can give. We argue that almost all existing constructions for secret sharing schemes are special cases of the generalized vector space construction. We give direct constructions of this type for the first two members of the family, and show that for the other members no such construction exists which would match the bound yielded by the entropy method.