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In this paper we propose two mutual authentication protocols for RFID systems. Generally, in RFID systems, a reader can authenticate tags in the real-time and batch modes. This paper proposes the first authentication protocol for the real-time mode. It also proposes an efficient robust mutual authentication protocol for the batch mode. Some significant characteristics of the protocols are forward security, tag anonymity, location privacy, low complexity on the back-end server, and scalability. To the best of our knowledge, our protocols offer the most enhanced security features in RFID mutual authentication protocols with respect to user privacy. In analyzing the protocols, we show how remarkable properties such as forward security and tag anonymity are guaranteed. It is also illustrated that our protocol is secure against several common attacks that RFID systems confront with.