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, the authors are interested in characterizing the global properties of the iS-graph in terms of percolation on the infinite plane. They prove the existence of a phase transition in the Poisson iS-graph, whereby an unbounded component of securely connected nodes suddenly arises as they increase the density of legitimate nodes. Their paper shows that long-range communication in a wireless network is still possible when a secrecy constraint is present.