Security and privacy are major threats for the RFID technology today. First, the RFID passive tags prevailing in most of the RFID applications are very limited in processing power, so they cannot perform complex computations. Second, there are no RFID authentication protocols that can support both scalability and privacy at low complexity cost. In this paper, we present an adaptation of NTRU public cryptosystem for low-cost RFID tags and new efficient asymmetrical challenge/response RFID mutual authentication protocol for low-cost RFID systems based on this NTRU's adaptation. Thanks to properties of the polynomial ring in which NTRU operates we have ensured that the tag encrypts challenges using only addition and right circular shifts. The proposed authentication protocol guarantees privacy, high scalability level and low implementation complexity. It takes advantages of NTRU and HMAC features, and is resistant to all the classical security attacks including replays, tracking, man in the middle attacks, etc.