Continuum Percolation in the Intrinsically Secure Communications Graph

The intrinsically secure communications graph (-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 informationtheoretic security, widely accepted as the strictest notion of security. In this paper, we are interested in characterizing the global properties of the -graph in terms of percolation on the infinite plane. We prove the existence of a phase transition in the Poisson -graph, whereby an unbounded component of securely connected nodes suddenly arises as we increase the density of legitimate nodes. Our work shows that long-range communication in a wireless network is still possible when a secrecy constraint is present.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Pedro C. Pinto, Moe Z. Win
• Keywords: CORR 2010, Education, Random Graph, Secure Communications, Strictest Notion