Remote scheme for password authentication based on theory of quadratic residues

We propose a remote password authentication scheme based on quadratic residues. In our scheme, any legal user can freely choose his own password in the card initialization phase. Using his password and smart card which contains identity and other information, he can then log into the system successfully. According to our analysis, intruders cannot obtain any secret information from the public information, or derive any password from intercepted messages. In addition, our scheme can withstand the attack of replaying previously intercepted log-in requests.