A new polynomial-time algorithm for linear programming
Combinatorica
An algorithm for linear programming which requires O(((m+n)n2+(m+n)1.5n)L) arithmetic operations
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
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
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 General Decomposition Construction for Incomplete SecretSharing Schemes
Designs, Codes and Cryptography
On sharing secrets and Reed-Solomon codes
Communications of the ACM
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
Threshold Schemes with Disenrollment
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
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
Hypergraph decomposition and secret sharing
Discrete Applied Mathematics
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 with bipartite access structure
IEEE Transactions on Information Theory
Secret sharing schemes from three classes of linear codes
IEEE Transactions on Information Theory
Disenrollment with perfect forward secrecy in threshold schemes
IEEE Transactions on Information Theory
Lattice-Based Threshold Changeability for Standard Shamir Secret-Sharing Schemes
IEEE Transactions on Information Theory
Multiplicative Linear Secret Sharing Schemes Based on Connectivity of Graphs
IEEE Transactions on Information Theory
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The purpose of this paper is to describe a new decomposition construction for perfect secret sharing schemes with graph access structures. The previous decomposition construction proposed by Stinson is a recursive method that uses small secret sharing schemes as building blocks in the construction of larger schemes. When the Stinson method is applied to the graph access structures, the number of such “small” schemes is typically exponential in the number of the participants, resulting in an exponential algorithm. Our method has the same flavor as the Stinson decomposition construction; however, the linear programming problem involved in the construction is formulated in such a way that the number of “small” schemes is polynomial in the size of the participants, which in turn gives rise to a polynomial time construction. We also show that if we apply the Stinson construction to the “small” schemes arising from our new construction, both have the same information rate.