Introduction to algorithms
Elements of information theory
Elements of information theory
Journal of Combinatorial Theory Series B
An explication of secret sharing schemes
Designs, Codes and Cryptography
On the information rate of perfect secret sharing schemes
Designs, Codes and Cryptography
On the information rate of secret sharing schemes
Theoretical Computer Science
Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
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
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
Secret sharing schemes on access structures with intersection number equal to one
Discrete Applied Mathematics
IEEE Transactions on Information Theory
Decomposition constructions for secret-sharing schemes
IEEE Transactions on Information Theory
SIAM Journal on Discrete Mathematics
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A secret sharing scheme is a protocol by which a dealer distributes a secret among a set of participants in such a way that only qualified sets of them can reconstruct the value of the secret whereas any non-qualified subset of participants obtain no information at all about the value of the secret. Secret sharing schemes have always played a very important role for cryptographic applications and in the construction of higher level cryptographic primitives and protocols. In this paper we investigate the construction of efficient secret sharing schemes by using a technique called hypergraph decomposition, extending in a non-trivial way the previously studied graph decomposition techniques. A major advantage of hypergraph decomposition is that it applies to any access structure, rather than only structures representable as graphs. As a consequence, the application of this technique allows us to obtain secret sharing schemes for several classes of access structures (such as hyperpaths, hypercycles, hyperstars and acyclic hypergraphs) with improved efficiency over previous results. Specifically, for these access structures, we present secret sharing schemes that achieve optimal information rate. Moreover, with respect to the average information rate, our schemes improve on previously known ones. In the course of the formulation of the hypergraph decomposition technique, we also obtain an elementary characterization of the ideal access structures among the hyperstars, which is of independent interest.