Abstract: Radio frequency identification (RFID) is a wireless automatic identification and data capture technology that uses radio signals to identify a product, animal or person without the need for physical access or line of sight. The wide deployment of RFID systems in a variety of applications has raised many concerns about the security and privacy. RFID authentication protocol can implement the identification between the reader and the tag, and ensure only legitimate reader to access the tag’s data. Because of cost constraints of the tag, the design of lightweight RFID authentication protocol is the main challenge. In order to achieve the unpredictability of privacy, the tag requires at least having the ability of pseudorandom function (PRF). In this paper, a framework of RFID lightweight authentication protocol based on PRF is described abstractly. Based on the implementation of message authentication function F\-i, a new RFID lightweight authentication protocol, ELAP, is proposed. Compared with the existing protocol, the new protocol can achieve mutual authentication between reader and tag, and resistant to all known attacks. In the efficiency, the tag need only two-time message digest computing, thus the computational cost of the tag is the minimum.