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Sensor networks are often deployed in unattended environments, thus leaving these networks vulnerable to false data injection attacks in which an adversary injects false data into the network with the goal of deceiving the base station or depleting the resources of the relaying nodes. Standard authentication mechanisms cannot prevent this attack if the adversary has compromised one or a small number of sensor nodes. In this paper, we present an interleaved hop-by-hop authentication scheme that guarantees that the base station will detect any injected false data packets when no more than a certain number t nodes are compromised. Further, our scheme provides an upper bound B for the number of hops that a false data packet could be forwarded before it is detected and dropped, given that there are up to t colluding compromised nodes. We show that in the worst case B is O(t2). Through performance analysis, we show that our scheme is efficient with respect to the security it provides, and it also allows a tradeoff between security and performance.