Percolation in the Secrecy Graph

TL;DR

This paper investigates the connectivity of wireless networks under secrecy constraints using the secrecy graph model, analyzing percolation thresholds based on Poisson point processes for nodes and eavesdroppers.

Contribution

It provides bounds for percolation thresholds in secrecy graphs with Poisson-distributed nodes and eavesdroppers, advancing understanding of secure network connectivity.

Findings

Bounds for in-, out-, and undirected percolation thresholds

Analysis of critical eavesdropper density for infinite network connectivity

Insights into secure communication in large-scale wireless networks

Abstract

The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the presence of eavesdroppers, which, in the model, is determined solely by the locations of the nodes and eavesdroppers. In the case of infinite networks, a critical parameter is the maximum density of eavesdroppers that can be accommodated while still guaranteeing an infinite component in the network, i.e., the percolation threshold. We focus on the case where the locations of the nodes and eavesdroppers are given by Poisson point processes, and present bounds for different types of percolation, including in-, out- and undirected percolation.