We investigate the security of wireless sensor networks under the pairwise key distribution scheme of Chan et al. [2]. We present conditions on how to scale the model parameters so that the network is i) unassailable, and ii) unsplittable, both with high probability, as the number of sensor nodes becomes large. We show that the required number of secure keys to be stored in the memory of each sensors is order of magnitude smaller than what is required for the Eschenauer-Gligor scheme [5].