Secure communication in stochastic wireless networks – Part II: Maximum rate and collusion

Abstract—In Part I of this paper, we introduced the intrinsically secure communications graph (-graph)—a random graph which describes the connections that can be established with strong se-crecy over a large-scale network, in the presence of eavesdroppers. We focused on the local connectivity of the-graph, and proposed techniques to improve it. In this second part, we characterize the maximum secrecy rate (MSR) that can be achieved between a node and its neighbors. We then consider the scenario where the eaves-droppers are allowed to collude, i.e., exchange and combine infor-mation. We quantify exactly how eavesdropper collusion degrades the secrecy properties of the network, in comparison to a noncol-luding scenario. Our analysis helps clarify how the presence of eavesdroppers can jeopardize the success of wireless physical-layer security. Index Terms—Colluding eavesdroppers, physical-layer security, secrecy capacity, stochastic geometry, wireless networks. I