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In order to help the WSN achieve better performance against DDoS attacks in broadcast authentication, a new strategy based on DBP-MSP and safe routing is proposed in this paper. By introducing puzzle difficulty level k decided by the base station in DBP-MSP, the strategy can properly cut down computational consumption of the sender for solving a puzzle especially when the broadcast workload in WSN is not heavy, which properly controls the energy consumption of the sender. By introducing the broadcast state table which is updated by the base station according to messages from nodes, the receiver can verify the puzzle solution by the message the base station returns by searching the table. DDoS attacks to broadcast authentication protocol can be prevented by this kind of weak authenticator. In addition, by introducing a key chain distribution scheme where the base station passes the one way key chains to the sender every time intervals, the storage and computation burden on the sender can be reduced, as well as better security performance for the one-way key chain. The simulation indicates that the new strategy can solve the limitation that a powerful sender with large memory resource is required in the basic MSP strategy, as well as achieving better performance in dealing with DDoS attacks. Hence, Our strategy is more secure and has wider applicable area in the WSN than the basic MSP strategy.