Broadcast authentication is one of the most fundamental services in Wireless Sensor Network (WSNs) that is being used to secure the application from different attacks like passive and active attacks, diverse layer attacks, cryptographic attacks and Denial of service (DoS) attacks. Security has become the most forefronts of network management and implementation. Digital Signature (DS) and Timed Efficient Stream Loss-tolerant Authentication (TESLA) are used in Wireless Sensor Networks to provide broadcast authentication, but still both are vulnerable to DoS attacks, attackers keep on broadcasting forged messages which will cause extra cost on the network due to power consumption. This will drain the nodes' energy, which will eventually reduce the network lifetime.In this paper we present approaches that are trying to defend against or contain such DoS attacks. We propose new scheme in receiver sensor node to recognize the forged message before authenticating the broadcast message to avoid the many unnecessary operations and to conserve the node's energy. The new proposed scheme uses a dynamic window (Wang et al., 2007) on the receiver side and reduces the DoS attacks to affect only a small part of the network. In this way we can reduce the energy consumption in order to increase the network lifetime and minimize the delay of broadcast messages.