The Secrecy Graph and Some of its Properties

Computer Science – Information Theory

Scientific paper

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5 pages. Accepted at 2008 IEEE Symposium on Information Theory (ISIT'08)

Scientific paper

A new random geometric graph model, the so-called secrecy graph, is introduced and studied. The graph represents a wireless network and includes only edges over which secure communication in the presence of eavesdroppers is possible. The underlying point process models considered are lattices and Poisson point processes. In the lattice case, analogies to standard bond and site percolation can be exploited to determine percolation thresholds. In the Poisson case, the node degrees are determined and percolation is studied using analytical bounds and simulations. It turns out that a small density of eavesdroppers already has a drastic impact on the connectivity of the secrecy graph.

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