Date of Original Version



Technical Report

Abstract or Description

In wireless sensor networks (WSNs), the Eschenauer–Gligor (EG) key pre-distribution scheme is a widely recognized way to secure communications. Although the connectivity properties of secure WSNs with the EG scheme have been extensively investigated, few results address physical transmission constraints. These constraints reflect real–world implementations of WSNs in which two sensors have to be within a certain distance from each other to communicate. In this paper, we present zero–one laws for connectivity in WSNs employing the EG scheme under transmission constraints. These laws improve recent results [1], [2] significantly and help specify the critical transmission ranges for connectivity. Our analytical findings, which are also confirmed via numerical experiments, provide precise guidelines for the design of secure WSNs in practice. In addition to secure WSNs, our theoretical results are also applied to frequency hopping of wireless networks, as discussed in detail..


[1] B. Krishnan, A. Ganesh, and D. Manjunath. On connectivity thresholds in superposition of random key graphs on random geometric graphs. In Proc. IEEE ISIT, pages 2389–2393, 2013.

[2] K. Krzywdzinski and K. Rybarczyk. Geometric graphs with randomly deleted edges — connectivity and routing protocols. Mathematical Foundations of Computer Science, 6907:544–555, 2011.