Journal of Combinatorial Theory Series B
An explication of secret sharing schemes
Designs, Codes and Cryptography
Designs, Codes and Cryptography
Regular Article: Weak Maps and Stabilizers of Classes of Matroids
Advances in Applied Mathematics
On the Composition of Matroids and Ideal Secret Sharing Schemes
Designs, Codes and Cryptography
Ideal Multipartite Secret Sharing Schemes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Ideal hierarchical secret sharing schemes
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
On codes, matroids and secure multi-party computation from linear secret sharing schemes
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
On matroids and non-ideal secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
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Deciding whether a matroid is secret sharing or not is a well-known open problem. In Ng and Walker [6] it was shown that a matroid decomposes into uniform matroids under strong connectivity. The question then becomes as follows: when is a matroid m with N uniform components secret sharing? When N = 1, m corresponds to a uniform matroid and hence is secret sharing. In this paper we show, by constructing a representation using projective geometry, that all connected matroids with two uniform components are secret sharing