Intrinsically secure communication in large-scale wireless networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 169-181).The ability to exchange secret information is critical to many commercial, governmental, and military networks. Information-theoretic security - widely accepted as the strictest notion of security - relies on channel coding techniques that exploit the inherent randomness of the propagation channels to significantly strengthen the security of digital communications systems. Motivated by recent developments in the field, this thesis aims at a characterization of the fundamental secrecy limits of large-scale wireless networks. We start by introducing an information-theoretic definition of the intrinsically secure communications graph (iS-graph), based on the notion of strong secrecy. The iS-graph is a random geometric graph which captures the connections that can be securely established over a large-scale network, in the presence of spatially scattered eavesdroppers. Using fundamental tools from stochastic geometry, we analyze how the spatial densities of legitimate and eavesdropper nodes influence various properties of the Poisson iS-graph, such as the distribution of node degrees, the node isolation probabilities, and the achievable secrecy rates. We study how the wireless propagation effects (e.g., fading and shadowing) and eavesdropper collusion affect the secrecy properties of the network. We also explore the potential of sectorized transmission and eavesdropper neutralization as two techniques for enhancing the secrecy of communications. We then shift our focus to the global properties of the iS-graph, which concern secure connectivity over multiple hops. We first characterize percolation of the Poisson iS-graph on the infinite plane. We show that each of the four components of the iS-graph (in, out, weak, and strong component) experiences a phase transition at some nontrivial critical density of legitimate nodes. Operationally, this is important because it implies that long-range communication over multiple hops is still feasible when a security constraint is present. We then consider full-connectivity on a finite region of the Poisson iS-graph. Specifically, we derive simple, explicit expressions that closely approximate the probability of a node being securely connected to all other nodes inside the region. We also show that the iS-graph is asymptotically fully out-connected with probability one, but full in-connectivity remains bounded away from one, no matter how large the density of legitimate nodes is made. Our results clarify how the spatial density of eavesdroppers can compromise the intrinsic security of wireless networks. We are hopeful that further efforts in combining stochastic geometry with information-theoretic principles will lead to a more comprehensive treatment of wireless security.by Pedro C. Pinto.Ph.D