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As the radio frequency identification (RFID) technology continues to evolve and mature, RFID tags can be implemented in a wide range of applications. Due to the shared wireless medium between the RFID reader and the RFID tag, however, adversaries can launch various attacks on the RFID system. The privacy and security issues of RFID are getting more and more important. To thwart different types of attacks, we propose a novel Anonymous RFID Authentication Protocol, termed ARAP, which can accomplish the authentication without disclosing real IDs of the participating tags and provide strong privacy and security protection of the RFID users. ARAP offers the anonymity of tags in addition to tag unlocatability and untrackability. It is also resistant to a wide range of attacks. Compared with the previous researches, the major advantages of ARAP are that ARAP can withstand physical attack, de-synchronization attack, disclosure attack and cloning attack, and also can provide anonymity and mutual authentication. We believe that our protocol is attractive to RFID applications.