Owing to the fast progress of mobile communication technologies and the ubiquity of mobile networks, users can communicate with each other anytime and anywhere as long as they carry their smart and tiny mobile phones. This convenient communication service is quite popular and gradually joins in the people¡¦s life. Nevertheless, lots of attacks, such as the men-in-the-middle attacks and the replay attacks, are seriously threatening the security of the mobile networks and affecting the quality of the service simultaneously. Many security mechanisms for mobile communication have been introduced in the literature. Among these mechanisms, authentication plays a very important role in the entire mobile network system and acts as the first defense against the attackers since it can ensure the correctness of the identities of communication entities before they engage in any other communication activities. Therefore, to guarantee the quality of this advanced service, an efficient (especially, user efficient) and secure authentication scheme is urgently desired. In this thesis, we will propose a robust authentication scheme for mobile communication systems. Not only does the proposed scheme achieve mutual authentication, but also it greatly reduces the computation and communication cost of mobile users as compared with the existing authentication schemes.