Linear programming and network flows (2nd ed.)
Linear programming and network flows (2nd ed.)
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
More information theoretical inequalities to be used in secret sharing?
Information Processing Letters
Communications of the ACM
Linear VSS and Distributed Commitments Based on Secret Sharing and Pairwise Checks
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Generalized Secret Sharing and Monotone Functions
CRYPTO '88 Proceedings of the 8th 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
Improved constructions of secret sharing schemes by applying (λ, ω)-decompositions
Information Processing Letters
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
A First Course in Information Theory (Information Technology: Transmission, Processing and Storage)
Secret Sharing and Non-Shannon Information Inequalities
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
An impossibility result on graph secret sharing
Designs, Codes and 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
Piecewise linear conditional information inequality
IEEE Transactions on Information Theory
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
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
The complexity of the graph access structures on six participants
Designs, Codes and Cryptography
| Hi-index | 0.00 |
Determining the optimal complexity of secret sharing schemes for every given access structure is a difficult and long-standing open problem in cryptology. Lower bounds have been found by a combinatorial method that uses polymatroids. In this paper, we point out that the best lower bound that can be obtained by this method can be determined by using linear programming, and this can be effectively done for access structures on a small number of participants. By applying this linear programming approach, we present better lower bounds on the optimal complexity and the optimal average complexity of several access structures. Finally, by adding the Ingleton inequality to the previous linear programming approach, we find a few examples of access structures for which there is a gap between the optimal complexity of linear secret sharing schemes and the combinatorial lower bound.