q-复合随机密钥图的迁移行为及其在网络控制中的应用
Transitional Behavior of q-Composite Random Key Graphs with Applications to Networked Control
摘要：
随机密钥图已经得到了相当大的关注，并被用于各种应用，包括安全传感器网络，社交网络，流行病的研究，密码分析，和推荐系统。本文研究了一个$q$ -复合随机密钥图，它在$n$节点上的构造如下：每个节点独立地从同一个$P_n$不同密钥池中均匀随机地选择一组$K_n$不同密钥，并且两个节点之间建立无向边当且仅当它们至少共享$q$密钥.这种图表示为$G_q(n,K_n,P_n)$模型的安全传感器网络采用众所周知的$q$ -复合密钥预分配。对于$G_q(n,K_n,P_n)$，我们分别分析了$G_q(n,K_n,P_n)$具有$k$ -连通性、$k$ -鲁棒性、Hamilton环和完美匹配的概率.我们研究这四个属性的动机是详细讨论它们在网络控制中的应用。我们的研究结果表明，$G_q(n,K_n,P_n)$表现出一个急剧的转变为每一个属性：随着$K_n$的增加，$G_q(n,K_n,P_n)$的属性急剧增加的概率从$0$到$1$。这些结果提供了基本的指导方针，设计安全的传感器网络为不同的控制相关的应用：分布式网络参数估计，容错共识，和弹性数据备份。
英文摘要：
Random key graphs have received considerable attention and been used in various applications including secure sensor networks, social networks, the study of epidemics, cryptanalysis, and recommender systems. In this paper, we investigate a $q$-composite random key graph, whose construction on $n$ nodes is as follows: each node independently selects a set of $K_n$ different keys uniformly at random from the same pool of $P_n$ distinct keys, and two nodes establish an undirected edge in between if and only if they share at least $q$ key(s). Such graph denoted by $G_q(n,K_n,P_n)$ models a secure sensor network employing the well-known $q$-composite key predistribution. For $G_q(n,K_n,P_n)$, we analyze the probabilities of $G_q(n,K_n,P_n)$ having $k$-connectivity, $k$-robustness, a Hamilton cycle and a perfect matching, respectively. Our studies of these four properties are motivated by a detailed discussion of their applications to networked control. Our results reveal that $G_q(n,K_n,P_n)$ exhibits a sharp transition for each property: as $K_n$ increases, the probability that $G_q(n,K_n,P_n)$ has the property sharply increases from $0$ to $1$. These results provide fundamental guidelines to design secure sensor networks for different control-related applications: distributed in-network parameter estimation, fault-tolerant consensus, and resilient data backup.
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。
