The Secrecy Graph and Some of its Properties

TL;DR

This paper introduces the secrecy graph, a new model for secure wireless networks considering eavesdroppers, analyzing its properties through percolation theory and simulations, revealing eavesdropper density significantly affects network connectivity.

Contribution

The paper presents the secrecy graph model, analyzing its percolation thresholds and connectivity properties for lattice and Poisson point processes, with new insights into eavesdropper impact.

Findings

Small eavesdropper density drastically reduces connectivity.

Percolation thresholds can be determined via analogies to standard models.

Analytical bounds and simulations provide insights into network robustness.

Abstract

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.