随机密钥图的k-连通性
k-Connectivity of Random Key Graphs
摘要：
随机密钥图表示安全的无线传感器网络的拓扑结构，应用开创性的随机密钥预分配方案，以确保传感器之间的通信。这些图受到了广泛的关注，并且还被用于安全传感器网络之外的各种应用领域;例如，密码分析、社交网络和推荐系统。形式上，通过向每个节点分配从$Y_n$密钥池中均匀随机选择的$X_n$密钥，然后在共享至少一个密钥的任何两个节点之间放置无向边，来构造具有$n$节点的随机密钥图。在文献中已经取得了相当大的进展，分析连通性和$k$ -连通性的随机密钥图，其中$k$ -连通性的图，确保连通性，即使在删除$k$节点或$k$边缘。然而，它仍然是一个开放的问题，在随机密钥图$X_n \geq 2$和$X_n = o(\sqrt{\ln n})$（$X_n=1$的情况下是平凡的）的$k$ -连通性。在本文中，我们回答了上述问题，提供了一个精确的分析下的随机密钥图的$k$ -连通性$X_n \geq 2$。
英文摘要：
Random key graphs represent topologies of secure wireless sensor networks that apply the seminal Eschenauer-Gligor random key predistribution scheme to secure communication between sensors. These graphs have received much attention and also been used in diverse application areas beyond secure sensor networks; e.g., cryptanalysis, social networks, and recommender systems. Formally, a random key graph with $n$ nodes is constructed by assigning each node $X_n$ keys selected uniformly at random from a pool of $Y_n$ keys and then putting an undirected edge between any two nodes sharing at least one key. Considerable progress has been made in the literature to analyze connectivity and $k$-connectivity of random key graphs, where $k$-connectivity of a graph ensures connectivity even after the removal of $k$ nodes or $k$ edges. Yet, it still remains an open question for $k$-connectivity in random key graphs under $X_n \geq 2$ and $X_n = o(\sqrt{\ln n})$ (the case of $X_n=1$ is trivial). In this paper, we answer the above problem by providing an exact analysis of $k$-connectivity in random key graphs under $X_n \geq 2$.
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。
