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Securing broadcast communication over sensor networks has become an important research challenge. Intuitively, broadcast communication has two important metrics: reliability and security. Though the reliability metric has drawn sufficient attention in the research community, the security metric has not. In this paper, we address both metrics with an emphasis on the former and address the denial-of-broadcast message attacks (DoBM) in sensor networks. We propose a novel tree-based model called the k-parent flooding tree model (k-FTM) and present algorithms for the construction of k-FTM. The proposed k-FTM is robust against DoBM. It enables the base station to detect DoBM very efficiently, even in the presence of a prudent adversary who focuses on remaining undetected by causing damage below the detection threshold. k-FTM is, to our best knowledge, the first fault-tolerant tree model that is both reliable and secure. Through simulations we confirm that our model achieves detection rates close to that of a static tree and a broadcast reliability close to that of blind flooding.