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Since Hopper and Blum suggested the HB protocol which is based on the conjectured hardness of the LPN (Learning Parity in the Presence of Noise) problem in 2001, a family of light-weight authentication protocols has been developed for RFID (Radio Frequency Identification) system by many engineers. It was found that each algorithm had own weakness against new attacks so that more advanced protocols have been expanded in order to overcome the attacks. In this paper, we enhance the HB-MP and HB-MP+ protocol, called HB-MP++. Ultra low-weight and concrete function will be used to eliminate vulnerability of the conventional methods. We also provide the security and performance analysis of the proposed protocol.