GSM(Global System for Mobile communications) that is the most popular standard for mobile phones, has more than 70% users in the world and the number of users increase continuously. However GSM system has the problem that cannot normally authenticate a user by the exposure of IMSI that is able to uniquely authenticate MS? during the user authentication procedure. In this paper? we provide security enhancement and user privacy by adopting a temporary id and an encryption scheme. Moreover we provide fast user authentication via architecture modification of the conventional GSM user authentication protocol.