传感器网络中的多跳路径和密钥预分配
Distinct Difference Configurations: Multihop Paths and Key Predistribution in Sensor Networks
摘要：
相异配置是$\mathbb{Z}^2$中的一组点，具有连接任意两个点的向量（\emph{difference vectors}）都相异的属性。这些配置的许多具体示例之前已经研究过：例如，截然不同的配置类别包括Costas阵列和声纳序列。出于这些结构在无线传感器网络的密钥预分配的应用，我们定义的$k$跳覆盖的不同的差异配置的不同的向量，可以表示为$k$或更少的差异向量的总和。当在无线传感器应用中使用不同的差异配置时，这是一个重要的参数，因为该参数描述了网络中短安全路径可以到达的节点密度。我们提供了一个不同的配置与$m$点的$k$跳覆盖的上限和下界，并利用连接与$B_{h}$序列构建配置与最大$k$跳覆盖。我们还构建了不同的差异配置，使所有的小向量被表示为两个配置的差异向量的总和，本地安全连接的应用程序中的一个重要任务。
英文摘要：
A distinct difference configuration is a set of points in $\mathbb{Z}^2$ with the property that the vectors (\emph{difference vectors}) connecting any two of the points are all distinct. Many specific examples of these configurations have been previously studied: the class of distinct difference configurations includes both Costas arrays and sonar sequences, for example. Motivated by an application of these structures in key predistribution for wireless sensor networks, we define the $k$-hop coverage of a distinct difference configuration to be the number of distinct vectors that can be expressed as the sum of $k$ or fewer difference vectors. This is an important parameter when distinct difference configurations are used in the wireless sensor application, as this parameter describes the density of nodes that can be reached by a short secure path in the network. We provide upper and lower bounds for the $k$-hop coverage of a distinct difference configuration with $m$ points, and exploit a connection with $B_{h}$ sequences to construct configurations with maximal $k$-hop coverage. We also construct distinct difference configurations that enable all small vectors to be expressed as the sum of two of the difference vectors of the configuration, an important task for local secure connectivity in the application.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
