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A Representation of a Family of Secret Sharing Matroids

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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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Authors and Affiliations

  1. Information Security Group, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, U.K.

    Siaw-Lynn Ng

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  1. Siaw-Lynn Ng
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Ng, SL. A Representation of a Family of Secret Sharing Matroids. Designs, Codes and Cryptography 30, 5–19 (2003). https://doi.org/10.1023/A:1024741108241

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  • DOI: https://doi.org/10.1023/A:1024741108241

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