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Injecting false data attack is a well known serious threat to wireless sensor network, for which an adversary reports bogus information to sink causing error decision at upper level and energy waste in en-route nodes. In this paper, we propose a novel bandwidth-efficient cooperative authentication (BECAN) scheme for filtering injected false data. Based on the random graph characteristics of sensor node deployment and the cooperative bit-compressed authentication technique, the proposed BECAN scheme can save energy by early detecting and filtering the majority of injected false data with minor extra overheads at the en-route nodes. In addition, only a very small fraction of injected false data needs to be checked by the sink, which thus largely reduces the burden of the sink. Both theoretical and simulation results are given to demonstrate the effectiveness of the proposed scheme in terms of high filtering probability and energy saving.