Transitional Behavior of q-Composite Random Key Graphs with Applications to Networked Control [article]

Jun Zhao
2017 arXiv   pre-print
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
more » ... y 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.
arXiv:1708.08313v1 fatcat:5hxmiewadzeafia4vna7mpwkay