Access Structures Determined by Uniform Polymatroids
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A secret sharing scheme is a method of sharing a secret key among a finite set of participants in such a way that only certain specified subsets of participants can compute the key. The access structure of a secret sharing scheme is the family of these subsets of participants which are able to recover the secret. In this paper a new concept of study of ideal access structures is proposed. Unlike the approach used by other authors, we do not consider new classes of access structures defined by imposing certain prescribed assumptions, but we investigate all access structures obtained from uniform polymatroids using the method developed by Farras, Marti-Farre and Padro in the paper: "Ideal Multipartite Secret Sharing Schemes," J. Cryptol. vol. 25, pp. 434-463, 2012. The access structures obtained from uniform polymatroids are known to satisfy necessary condition to be ideal, so it is enough to investigate their properties, especially the ones which are useful for applications. Here we are especially interested in hierarchy of participants determined by the access structure and we distinguish two main classes: they are compartmented and hierarchical access structures.
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