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Many kinds of protocols have been designed to resolve the security and privacy problems of RFID systems. In this paper, we illustrate a new RFID authentication protocol based on Trivium, inspired from the Challenge-Response based RFID authentication protocol for distributed database environment. The proposed protocol can prevent many attacks including spoofing attack, replay attack, tracking and desynchronization. Furthermore, it improves the efficiency of searching on the back-up database to make the protocol more applicable.