A comprehensive guideline for choosing parameters in the Eschenauer-Gligor key predistribution

The Eschenauer-Gligor random key predistribution scheme is well known as the standard approach to secure communication in large-scale wireless sensor networks. The performance of the scheme has received considerable attention in the literature, yet there is still a lack of a comprehensive and rigorous guideline for identifying all possible combinations of scheme parameters to ensure an occurring probability p for the event that each sensor is directly connected to at least k neighboring sensors, for arbitrary k and p. This paper fills the gap and provides fundamental guidelines on choosing parameters of the scheme. We also significantly improve a recent result in [Zhao et al., IEEE Transactions on Automatic Control 2016].