Designing secure networks with q-composite key predistribution under different link constraints

In many applications of wireless sensor networks (WSNs), sensors are deployed in hostile environments where an adversary can eavesdrop communications. To secure communications in WSNs, the q-composite key predistribution scheme has been widely recognized as a suitable approach. In this paper, we investigate connectivity in secure WSNs operating under the q-composite scheme, in consideration of different link constraints: the unreliability of wireless links and the requirement that two sensors have to be within certain distance to have a link. We formally derive conditions on how to scale the model parameters so that the network is securely connected with high probability when the number of sensors becomes large. The results are given in the form of zero-one laws and provide useful guidelines for designing securely and reliably connected sensor networks.