由一致多拟阵确定的存取结构
Access Structures Determined by Uniform Polymatroids
摘要：
如果参与者的集合被分成几个部分，并且同一部分中的所有参与者扮演相同的角色，则访问结构被称为多部分的。许多作者一直在寻找适合于某些特殊的多方接入结构族的理想秘密共享方案。本文提出了研究理想存取结构的新概念。我们不考虑特殊类的访问结构定义强加某些规定的假设，但我们调查所有的访问结构获得一致的polymatroids使用的方法开发的Farràs，马蒂-Farré和Padró。它们满足理想的必要条件，即，它们是拟阵端口。此外，这个家族中的一些对象可以用于秘密共享的应用。一致多拟阵的选择是由这样一个事实，即每个这样的多拟阵定义理想的访问结构的动机。本文提出的方法是通用的，并可以继续与其他类的多拟阵在进一步的类似研究。在这里，我们对由访问结构确定的参与者层次结构特别感兴趣，并且我们区分了两个主要类别：它们是分区的和分层的访问结构。绝大多数讨论分层访问结构的论文都考虑了分区或完全分层的访问结构。第4节总结了主要结果，其中介绍了可能出现部分层次属性的情况。特别地，描述了所获得的结构的分层顺序。令人惊讶的是，从均匀多拟阵获得的访问结构的层次顺序是平坦的，即，每条链最多有两个元素。在第5节中证明了一些分层存取结构族的理想性。
英文摘要：
An access structure is said to be multipartite, if the set of participants is divided into several parts and all participants in the same part play an equivalent role. The search for ideal secret sharing schemes for some special interesting families of multipartite access structures, has been carried out by many authors. In this paper a new concept of study of ideal access structures is proposed. We do not consider special 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 Farràs, Martí-Farré and Padró. They satisfy necessary condition to be ideal, i.e., they are matroid ports. Moreover some objects in this family can be useful for the applications of secret sharing. The choice of uniform polymatroids is motivated by the fact that each such polymatroid defines ideal access structures. The method presented in this article is universal and can be continued with other classes of polymatroids in further similar studies. 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. The vast majority of papers discussing hierarchical access structures consider access structures which are compartment or totally hierarchical. The main results are summarized in Section 4, which presents situations where partial hierarchy properties may arise. In particular, hierarchical orders of obtained structures are described. It is surprising, that the hierarchical orders of access structures obtained from uniform polymatroids are flat, i.e., every chain has at most 2 elements. The ideality of some families of hierarchical access structures is proved in Section 5.
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