On the gradual deployment of random pairwise key distribution schemes   (Extended Version)
  In the context of wireless sensor networks, the pairwise key distribution scheme of Chan et al. has several advantages over other key distribution schemes including the original scheme of Eschenauer and Gligor. However, this offline pairwise key distribution mechanism requires that the network size be set in advance, and involves all sensor nodes simultaneously. Here, we address this issue by describing an implementation of the pairwise scheme that supports the gradual deployment of sensor nodes in several consecutive phases. We discuss the key ring size needed to maintain the secure connectivity throughout all the deployment phases. In particular we show that the number of keys at each sensor node can be taken to be $O(\log n)$ in order to achieve secure connectivity (with high probability). 
Osman Yagan and Armand M. Makowski
cs.CR cs.DM cs.IT math.IT