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Although TESLA can provide the crucial broadcast authentication, it also introduces some problems (such as large verification delay) that limit its application in a large wireless sensor network due to the resource constraints. In this paper, we present a localized broadcast authentication protocol, namely L-TESLA, to address these problems. We consider a large sensor network where a few trusted and better secured nodes are deployed. We find that these trusted nodes can help divide sensor nodes in the network into several subsets, and coordinate broadcast authentication in the subsets. Thereby, all sensor nodes can verify a broadcast message as if they were in a small network. A secure protocol is developed to identify the subsets according to the deployment of the trusted nodes. The simulation results illustrate that a significant reduction in the average verification delay can be achieved in our scheme.