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We investigate the secure connectivity of wireless sensor networks under the random pairwise key predistribution scheme of Chan, Perrig, and Song. Unlike recent work carried out under the assumption of full visibility, here we assume a (simplified) communication model where unreliable wireless links are represented as independent on/off channels. We present conditions on how to scale the model parameters so that the network 1) has no secure node that is isolated and 2) is securely connected, both with high probability, when the number of sensor nodes becomes large. The results are given in the form of zero-one laws, and exhibit significant differences with corresponding results in the full-visibility case. Through simulations, these zero-one laws are shown to also hold under a more realistic communication model, namely the disk model.