RFID system (Radio-Frequency Identification) is a technology for automated identification of objects and people. Human beings are smart enough to identify an object under a variety of challenge circumstances. RFID systems are emerging as one of the most pervasive computing technologies. But there are still a large number of problems that are to be addressed. One of the fundamental issues still to be addressed is privacy, which concludes association threat, location threat, preference threat, constellation threat, transaction threat, action threat and breadcrumb threat (Kim, J., Yang, C, Jeon, J,2007). Misbehaviours of both readers and tags will lead to attacks to the system. The common attacks on the readers, tags and the air interface between them comprise: Tracking or Tracing, Tamper, Clandestine Scanning, Counterfeit Tags, Cloning Tags, Eavesdropping, Replay, man-in-the-middle attack, Spoofing, Differential power analysis, Timing Attacks, Denial of Service, Physical Attacking and so on (P. Cuenca and L. Orozco-Barbosa, 2006.),(Kim, J., Yang, C, Jeon, J, 2007). Due to scarceness of resources most of the proposed protocols were designed using symmetric key cryptographic algorithms. However, it has been shown that it is inevitable to use public-key cryptographic algorithms to satisfy these requirements. A number of mechanisms have been devised to overcome the problems related to security and privacy issue of RFID systems. In this paper we propose three anonymous RFID authentication protocols and prove that they are secure in the traditional cryptographic framework. Our model allows most of the threats that apply to RFIDs systems including, denial of service, impersonation, malicious traceability, information leakage through power analysis and active man-in-the middle attacks. Our protocols are efficient and scalable.