Exact Formulae for Resilience in Random Key Predistribution Schemes

As wireless sensor networks are often deployed in adverse or hostile environments, key management schemes are required for sensor nodes. The random key predistribution (RKP) scheme is a probabilistic key management scheme where each node is preloaded with a subset of keys that are randomly selected from a pool of keys. If a pair of neighbor nodes have a common key, it can be used to establish a secure link between the nodes. The q-composite RKP scheme requires that a pair of neighbor nodes have at least q common keys for a secure link. In this article, we show that the previous security analysis (i.e., resilience against node capture) of the q-composite RKP scheme is inaccurate and present new formulae for resilience in the RKP scheme and the q-composite RKP scheme.