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The Eschenauer--Gligor (EG) random key predistribution scheme has been widelyrecognized as a typical approach to secure communications in wireless sensornetworks (WSNs). However, there is a lack of precise probability analysis onthe reliable connectivity of WSNs under the EG scheme. To address this, werigorously derive the asymptotically exact probability of $k$-connectivity inWSNs employing the EG scheme with unreliable links represented by independenton/off channels, where $k$-connectivity ensures that the network remainsconnected despite the failure of any $(k-1)$ sensors or links. Our analyticalresults are confirmed via numerical experiments, and they provide preciseguidelines for the design of secure WSNs that exhibit a desired level ofreliability against node and link failures.

Exact Analysis of k-Connectivity in Secure Sensor Networks with Unreliable Links