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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 log2n. This scheme also increases the security robustness of DA as the subverted routers can collude only if they are neighbors.