Secure Communication in Stochastic Wireless Networks—Part II: Maximum Rate and Collusion

In Part I of this paper, we introduced the intrinsically secure communications graph (iS-graph)-a random graph which describes the connections that can be established with strong secrecy over a large-scale network, in the presence of eavesdroppers. We focused on the local connectivity of the iS-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 eavesdroppers are allowed to collude, i.e., exchange and combine information. We quantify exactly how eavesdropper collusion degrades the secrecy properties of the network, in comparison to a noncolluding scenario. Our analysis helps clarify how the presence of eavesdroppers can jeopardize the success of wireless physical-layer security.