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The authentication and key agreement (AKA) protocol of Universal Mobile Telecommunication System (UMTS), which is proposed to solve the vulnerabilities found in Global System for Mobile Communications (GSM) systems, is still vulnerable to redirection and man-in-the-middle attacks. An adversary can mount these attacks to eavesdrop or mischarge the subscribers in the system. In this paper, we propose a secure AKA (S-AKA) protocol to cope with these problems. The S-AKA protocol can reduce bandwidth consumption and the number of messages required in authenticating mobile subscribers. We also give the formal proof of the S-AKA protocol to guarantee its robustness.