Parameter control in predistribution schemes of cryptographic keys

Predistribution schemes of cryptographic keys are recognized as appropriate solutions to secure communication in large-scale wireless sensor networks. Among various schemes, the seminal scheme proposed by Eschenauer and Gligor, and its extension introduced by Chan et al. have been widely studied in the literature. Yet, there is a lack of a formal analysis on how to control the parameters of the two schemes to ensure connectivity of a sensor network with a certain probability, especially when the wireless links are unreliable. This paper fills the gap and provides fundamental guidelines on choosing the scheme parameters.