Exact analysis of k-connectivity in secure sensor networks with unreliable links

The Eschenauer-Gligor (EG) random key predistri-bution scheme has been widely recognized as a typical approach to secure communications in wireless sensor networks (WSNs). However, there is a lack of precise probability analysis on the reliable connectivity of WSNs under the EG scheme. To address this, we rigorously derive the asymptotically exact probability of k-connectivity in WSNs employing the EG scheme with unreliable links represented by independent on/off channels, where k-connectivity ensures that the network remains connected despite the failure of any (k-1) sensors or links. Our analytical results are confirmed via numerical experiments, and they provide precise guidelines for the design of secure WSNs that exhibit a desired level of reliability against node and link failures.