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Wireless Sensor Networks have a wide spectrum of applications ranging from health care to war fare. Applications like network query, software updates, time synchronization and network management demand for broadcast security. In these applications if same key is used to encrypt every packet that we send, then various attacks can be launched to derive the key. In order to avoid this it is required to encrypt every packet using different key. In this paper we are proposing a method that is based on Shamir's secret sharing scheme, which ensures the freshness of the key. In the proposed method every packet is encrypted using different key and the key used for encryption is derived by the receiver using the additional information sent along with the packet.