The double authentication (DA) scheme presented in D. Huang et al., (2003) is designed to provide security against impersonation attack to link state routing protocol at a lower computational cost as compared to the existing schemes, such as, digital signature scheme S. Murphy et al. (1997). In this paper, we present a key distribution scheme that can be used for generating and distributing keys to provide DA. This scheme leads to a storage complexity for each router that varies linearly with the number of routers in the network in the worst case (fully connected network with n nodes). Moreover, for router with four or less average number of links, the storage complexity falls below log/sub 2/n. This scheme also increases the security robustness of DA as the subverted routers can collude only if they are neighbors.