User authentication plays very role in computing system.In this thesis,firstly we studied Smart Card and user authentication and smart card based authentication and some existed protocol for smart card authentication and after that we did cryptanalysis of one of the existed protocol and we show that authentication protocol of Younghwa An is suffered from some major attacks.In the recent decades,in order to achieve high-degree security many researchers are introducing multifactor authentication schemes replacing by conventional password-based remote authentication protocol schemes these days.In the year of 2010,Li and Hwang proposed biometric-based authentication scheme using the smart card.Later on,Das showed that the scheme cannot stand with denial of services attack & also having low efficiency.Then proposed a new protocol to overcome the flaws of prior scheme.In 2012,Younghwa An.substantiate that Das’ s proposed protocol doesn’t provide mutual authentication.In 2014,Cao and Ge pointed that Younghwa’s protocol is still susceptible to replay attack and unable to provide user anonymity,while an adversary can perform the re-registration by intercepting user identity IDx in the login phase.In this thesis,firstly we deeply describe smart card,biometrics,and cryptography and the we will discuss related schemes,which have been proposed recently and then we will analyze the Cao and Ge’s scheme and show that their protocol is still cannot stand with password guessing and traceability attacks.