Continuum Percolation in the Intrinsically Secure Communications Graph

The intrinsically secure communications graph (iS-graph) is a random graph which captures the connections that can be securely established over a large-scale network, in the presence of eavesdroppers. It is based on principles of information-theoretic security, widely accepted as the strictest notion of security. In this paper, we are interested in characterizing the global properties of the iS-graph in terms of percolation on the infinite plane. We prove the existence of a phase transition in the Poisson iS-graph, whereby an unbounded component of securely connected nodes suddenly arises as we increase the density of legitimate nodes. Our work shows that long-range communication in a wireless network is still possible when a secrecy constraint is present.Comment: Accepted in the IEEE International Symposium on Information Theory and its Applications (ISITA'10), Taichung, Taiwan, Oct. 201

Wireless Secrecy in Large-Scale Networks

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper provides an overview of the main properties of this new class of random graphs. We first analyze the local properties of the iS-graph, namely the degree distributions and their dependence on fading, target secrecy rate, and eavesdropper collusion. To mitigate the effect of the eavesdroppers, we propose two techniques that improve secure connectivity. Then, we analyze the global properties of the iS-graph, namely percolation on the infinite plane, and full connectivity on a finite region. These results help clarify how the presence of eavesdroppers can compromise secure communication in a large-scale network.Comment: To appear: Proc. IEEE Information Theory and Applications Workshop (ITA'11), San Diego, CA, Feb. 2011, pp. 1-10, Invited Pape

Percolation and Connectivity in the Intrinsically Secure Communications Graph

The ability to exchange secret information is critical to many commercial, governmental, and military networks. The intrinsically secure communications graph (iS-graph) is a random graph which describes the connections that can be securely established over a large-scale network, by exploiting the physical properties of the wireless medium. This paper aims to characterize the global properties of the iS-graph in terms of: (i) percolation on the infinite plane, and (ii) full connectivity on a finite region. First, for the Poisson iS-graph defined on the infinite plane, the existence of a phase transition is proven, whereby an unbounded component of connected nodes suddenly arises as the density of legitimate nodes is increased. This shows that long-range secure communication is still possible in the presence of eavesdroppers. Second, full connectivity on a finite region of the Poisson iS-graph is considered. The exact asymptotic behavior of full connectivity in the limit of a large density of legitimate nodes is characterized. Then, simple, explicit expressions are derived in order to closely approximate the probability of full connectivity for a finite density of legitimate nodes. The results help clarify how the presence of eavesdroppers can compromise long-range secure communication.Comment: Submitted for journal publicatio

Techniques for Enhanced Physical-Layer Security

Information-theoretic security--widely accepted as the strictest notion of security--relies on channel coding techniques that exploit the inherent randomness of propagation channels to strengthen the security of communications systems. Within this paradigm, we explore strategies to improve secure connectivity in a wireless network. We first consider the intrinsically secure communications graph (iS-graph), a convenient representation of the links that can be established with information-theoretic security on a large-scale network. We then propose and characterize two techniques--sectorized transmission and eavesdropper neutralization--which are shown to dramatically enhance the connectivity of the iS-graph.Comment: Pre-print, IEEE Global Telecommunications Conference (GLOBECOM'10), Miami, FL, Dec. 201

Percolation in the Secrecy Graph

The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers, which, in the model, is determined solely by the locations of the nodes and eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the locations of the nodes and eavesdroppers are given by Poisson point processes, and present bounds for different types of percolation, including in-, out- and undirected percolation.Comment: 22 pages, 3 figure

Continuum AB percolation and AB random geometric graphs

Consider a bipartite random geometric graph on the union of two independent homogeneous Poisson point processes in $d$-space, with distance parameter $r$ and intensities $\lambda,\mu$. We show for $d \geq 2$ that if $\lambda$ is supercritical for the one-type random geometric graph with distance parameter $2r$, there exists $\mu$ such that $(\lambda,\mu)$ is supercritical (this was previously known for $d=2$). For $d=2$ we also consider the restriction of this graph to points in the unit square. Taking $\mu = \tau \lambda$ for fixed $\tau$, we give a strong law of large numbers as $\lambda \to \infty$, for the connectivity threshold of this graph

When Does Relay Transmission Give a More Secure Connection in Wireless Ad Hoc Networks?

Relay transmission can enhance coverage and throughput, while it can be vulnerable to eavesdropping attacks due to the additional transmission of the source message at the relay. Thus, whether or not one should use relay transmission for secure communication is an interesting and important problem. In this paper, we consider the transmission of a confidential message from a source to a destination in a decentralized wireless network in the presence of randomly distributed eavesdroppers. The source-destination pair can be potentially assisted by randomly distributed relays. For an arbitrary relay, we derive exact expressions of secure connection probability for both colluding and non-colluding eavesdroppers. We further obtain lower bound expressions on the secure connection probability, which are accurate when the eavesdropper density is small. By utilizing these lower bound expressions, we propose a relay selection strategy to improve the secure connection probability. By analytically comparing the secure connection probability for direct transmission and relay transmission, we address the important problem of whether or not to relay and discuss the condition for relay transmission in terms of the relay density and source-destination distance. These analytical results are accurate in the small eavesdropper density regime.Comment: Accepted for publication in IEEE Transactions On Information Forensics and Securit