论文标题

由均匀多膜体确定的接入结构

Access Structures Determined by Uniform Polymatroids

论文作者

Kawa, Renata, Kula, Mieczyslaw

论文摘要

如果将参与者划分为几个部分,并且同一部分的所有参与者都起着同等的作用,则据说访问结构是多方的。许多作者已经为一些特殊有趣的多部分访问结构的特殊家庭家庭寻找理想的秘密共享方案。在本文中,提出了一个新的理想访问结构研究概念。我们不考虑通过施加某些规定的假设来定义的特殊类别的访问结构,而是使用Farràs,Martí-Farré和Padró开发的方法研究了从统一的多层化的统一聚合物获得的所有访问结构。他们满足必要的条件,即理想,即它们是矩阵端口。此外,这个家庭中的某些对象对于秘密共享的应用可能很有用。每个这样的多层化学定义理想的访问结构的事实,均匀的多符合性的聚合物的选择是动机。本文介绍的方法是通用的,可以在进一步的类似研究中继续与其他类别的多肌瘤一起继续进行。在这里,我们对由访问结构确定的参与者的层次结构特别感兴趣,我们区分了两个主要类别:它们是隔间和分层访问结构。讨论层次访问结构的绝大多数论文都考虑了隔室或完全分层的访问结构。主要结果总结在第4节中,其中列出了可能出现部分层次结构属性的情况。特别是,描述了所获得的结构的层次结构顺序。令人惊讶的是,从均匀多功能体获得的访问结构的分层顺序是平坦的,即每个链最多都有2个元素。第5节证明了一些分层访问结构的理想性。

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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