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In sensor networks, the adversaries can inject false data reports from compromising nodes. Previous approaches for filtering false reports share keys between the source node and its upstream nodes on the path to sink, and rely on intermediate nodes to verify the reports generated by downstream nodes in a probabilistic manner. As a result, false reports have to travel several hops before detected. Worse still, these schemes haven't balanced the overheads of all nodes in the process of keys distributing. In response to these, this paper proposes a cluster-based filtering scheme, in which nodes are grouped into clusters once deployed by employing some strong nodes act as cluster heads. We then proposed a distributed method of keys assignment by constructing a sink-rooted tree which comprises of all the cluster heads, guarantees that the keys of a source cluster are stored by several forwarding clusters close to it and thus to filter false reports generated by the source cluster during several hops during forwarding, further, the number of authentication keys held by the forwarding clusters getting smaller with the distance increase from the source cluster and thus to balance the keys stored by each forwarding cluster. Analysis and simulation results show that our scheme outperforms existing schemes in terms of overhead balance and filtering efficiency.