Analyzing connectivity of heterogeneous secure sensor networks

TL;DR

This paper studies the connectivity of a heterogeneous secure sensor network using key predistribution, providing critical conditions for ensuring network connectivity and offering design guidelines.

Contribution

It extends and improves upon previous work by establishing new conditions for connectivity in heterogeneous sensor networks with multiple groups and key distributions.

Findings

Derived critical connectivity conditions for heterogeneous networks

Provided guidelines for secure sensor network design

Enhanced theoretical understanding of key predistribution effects

Abstract

We analyze connectivity of a heterogeneous secure sensor network that uses key predistribution to protect communications between sensors. For this network on a set $\mathcal{V}_n$ of $n$ sensors, suppose there is a pool $\mathcal{P}_n$ consisting of $P_n$ distinct keys. The $n$ sensors in $\mathcal{V}_n$ are divided into $m$ groups $\mathcal{A}_1, \mathcal{A}_2, \ldots, \mathcal{A}_m$. Each sensor $v$ is independently assigned to exactly a group according to the probability distribution with $\mathbb{P}[v \in \mathcal{A}_i]= a_i$ for $i=1,2,\ldots,m$, where $\sum_{i=1}^{m}a_i = 1$. Afterwards, each sensor in group $\mathcal{A}_i$ independently chooses $K_{i,n}$ keys uniformly at random from the key pool $\mathcal{P}_n$, where $K_{1,n} \leq K_{2,n}\leq \ldots \leq K_{m,n}$. Finally, any two sensors in $\mathcal{V}_n$ establish a secure link in between if and only if they have at least one key in common. We present critical conditions for connectivity of this heterogeneous secure sensor network. The result provides useful guidelines for the design of secure sensor networks. This paper improves the seminal work [1] (IEEE Transactions on Information Theory 2016) of Ya{\u{g}}an on connectivity in several aspects (omitted due to arxiv abstract's character limitation; see the paper for details).