On the scalability of the random pairwise key predistribution scheme: Gradual deployment and key ring sizes

The pairwise key distribution scheme of Chan et al. is a randomized key predistribution scheme which enables cryptographic protection in wireless sensor networks (WSNs). Although this pairwise scheme has several advantages over other randomized key predistribution schemes, including the original scheme of Eschenauer and Gligor, it has been deemed non  -scalable for the following two reasons: (i) There are implementation difficulties when sensors need to be deployed in multiple stages; and (ii) the possibly large number of keys stored at each sensor node is random and may vary from sensor to sensor. Here, we explore these issues as follows: (i) We propose an implementation of the pairwise scheme that supports the gradual deployment of sensor nodes in several consecutive phases; (ii) We show how the scheme parameters should scale with the maximum number nn of sensor nodes in the network so that a.a.s. secure connectivity is maintained throughout every deployment phase of the network; (iii) We derive scaling conditions on the scheme parameters for all   the sensors in the network to have O(logn)O(logn) many keys with very high probability as nn grows large. This dimensioning of the key rings can be made to support a.a.s. secure connectivity at every step of deployment.