A Representation of a Family of Secret Sharing Matroids |
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Authors: | Siaw-Lynn Ng |
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Institution: | (1) Information Security Group, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, U.K. |
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Abstract: | 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 |
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Keywords: | ideal secret sharing schemes matroids projective geometry |
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