Non-representable multipartite secret sharing matroids

The characterization of the access structures of ideal secret-sharing schemes is one of the main open problems in secret-sharing and has important connections with matroid theory. Since every matroid is multipartite and has a corresponding discrete polymatroid, by dealing with the rank functions of discrete polymatroids, a new necessary condition for a multipartite matroid to be non-representable was obtained. Furthermore, this conclusion was applied to m-partite matroids with m2 and Vamos matroid respectively. The results give new contributions to the open problem (that is, which matroids induce ideal access structures) since an ideal secret-sharing scheme can be seen as a representation of the corresponding matroid.