Generalized linear threshold scheme
Proceedings of CRYPTO 84 on Advances in cryptology
Designs, Codes and Cryptography
Communications of the ACM
Journal of Algebraic Combinatorics: An International Journal
How to (Really) Share a Secret
CRYPTO '88 Proceedings of the 8th 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
Hierarchical Threshold Secret Sharing
Journal of Cryptology
Characterizing Ideal Weighted Threshold Secret Sharing
SIAM Journal on Discrete Mathematics
Multipartite Secret Sharing by Bivariate Interpolation
Journal of Cryptology
On the Complexity of Matroid Isomorphism Problems
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Secret-sharing schemes: a survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Secret sharing schemes with bipartite access structure
IEEE Transactions on Information Theory
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We present new families of access structures that, similarly to the multilevel and compartmented access structures introduced in previous works, are natural generalizations of threshold secret sharing. Namely, they admit an ideal linear secret sharing schemes over every large enough finite field, they can be described by a small number of parameters, and they have useful properties for the applications of secret sharing. The use of integer polymatroids makes it possible to find many new such families and it simplifies in great measure the proofs for the existence of ideal secret sharing schemes for them.