Modeling Location Uncertainty for Eavesdroppers: A Secrecy Graph Approach

In this paper, we consider end-to-end secure communication in a large wireless network, where the locations of eavesdroppers are uncertain. Our framework attempts to bridge the gap between physical layer security under uncertain channel state information of the eavesdropper and network level connectivity under security constraints, by modeling location uncertainty directly at the network level as correlated node and link failures in a secrecy graph. Bounds on the percolation threshold are obtained for square and triangular lattices, and bounds on mean degree are obtained for Poisson secrecy graphs. Both analytic and simulation results show the dramatic effect of uncertainty in location of eavesdroppers on connectivity in a secrecy graph.