Practical Approaches to Varying Network Size in Combinatorial Key Predistribution Schemes

Combinatorial key predistribution schemes can provide a practical solution to the problem of distributing symmetric keys to the nodes of a wireless sensor network. Such schemes often inherently suit networks in which the number of nodes belongs to some restricted set of values (such as powers of primes). In a recent paper, Bose, Dey and Mukerjee have suggested that this might pose a problem, since discarding keyrings to suit a smaller network might adversely affect the properties of the scheme. In this paper we explore this issue, with specific reference to classes of key predistribution schemes based on transversal designs. We demonstrate through experiments that, for a wide range of parameters, randomly removing keyrings in fact has a negligible and largely predictable effect on the parameters of the scheme. In order to facilitate these computations, we provide a new, efficient, generally applicable approach to computing important properties of combinatorial key predistribution schemes. We also show that the structure of a resolvable transversal design can be exploited to give a deterministic method of removing keyrings to adjust the network size, in such a way that the properties of the resulting scheme are easy to analyse. We show that these schemes have the same asymptotic properties as the transversal design schemes on which they are based, and that for most parameter choices their behaviour is very similar.