One of the most commonly used two-factor authentication mechanisms is based on smart card and user’s password. Throughout the years, there have been many schemes proposed, but most of them have already been found flawed due to the lack of formal security analysis. On the cryptanalysis of this type of schemes, in this paper, we further review two recently proposed schemes and show that their security claims are invalid. To address the current issue, we propose a new and simplified property set and a formal adversarial model for analyzing the security of this type of schemes. We believe that the property set and the adversarial model themselves are of independent interest. We then propose a new scheme and a generic construction framework. In particular, we show that a secure password based key exchange protocol can be transformed efficiently to a smartcard and password based two-factor authentication scheme provided that there exist pseudorandom functions and collision-resistant hash functions.