This paper presents an approach related to authenticate mutually a RFID (Radio Frequency Identification) tag from a RFID reader by using the cryptography based on Elliptic curve. Our proposal mutual authentication lies on the Elliptic curve discrete logarithm problem, which is considered the core in order to fight against all of attacks like replay attack, forgery attack and man-in-the-middle attack. Scientifically, we prove not only the accuracy and the security of our approach, but also its performance in the mutual authentication between a RFID tag and a reader. .
