Continuum Percolation in the Intrinsically Secure Communications Graph

TL;DR

This paper analyzes the global connectivity of the intrinsically secure communications graph (iS-graph) in large-scale networks, demonstrating a phase transition where secure long-range communication becomes feasible as node density increases.

Contribution

It characterizes the percolation properties of the iS-graph and proves the existence of a phase transition in secure connectivity in the presence of eavesdroppers.

Findings

Existence of a phase transition in the Poisson iS-graph.

Unbounded secure component emerges at critical node density.

Long-range secure communication is possible despite secrecy constraints.

Abstract

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, we are interested in characterizing the global properties of the iS-graph in terms of percolation on the infinite plane. We prove the existence of a phase transition in the Poisson iS-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.