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Lightweight authentication protocols are necessary in the RFID system because tags are lack of computational resources and communication ability. Many researchers have proposed some authentication protocols which only use lightweight operations, such as XOR, hash operation and so on. In this paper, we analyze some authentication protocols. Especially, we analyze a forward secure RFID privacy protection scheme proposed by Ohkubo et al and find its weakness. Afterwards, we propose an improved forward secure RFID privacy protection scheme and analyze it. It is low-cost and suitable for inexpensive tags. Moreover, it not only provides one-way authentication and forward security but also resists replay attack.