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

Secure Beamforming for MIMO Two-Way Communications with an Untrusted Relay

This paper studies the secure beamforming design in a multiple-antenna three-node system where two source nodes exchange messages with the help of an untrusted relay node. The relay acts as both an essential signal forwarder and a potential eavesdropper. Both two-phase and three-phase two-way relay strategies are considered. Our goal is to jointly optimize the source and relay beamformers for maximizing the secrecy sum rate of the two-way communications. We first derive the optimal relay beamformer structures. Then, iterative algorithms are proposed to find source and relay beamformers jointly based on alternating optimization. Furthermore, we conduct asymptotic analysis on the maximum secrecy sum-rate. Our analysis shows that when all transmit powers approach infinity, the two-phase two-way relay scheme achieves the maximum secrecy sum rate if the source beamformers are designed such that the received signals at the relay align in the same direction. This reveals an important advantage of signal alignment technique in against eavesdropping. It is also shown that if the source powers approach zero the three-phase scheme performs the best while the two-phase scheme is even worse than direct transmission. Simulation results have verified the efficiency of the secure beamforming algorithms as well as the analytical findings.Comment: 10 figures, Submitted to IEEE Transactions on Signal Processin

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