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Seamless roaming in the global mobility network (GLOMONET) is highly desirable for mobile users, although their proper authentication is challenging. This is because not only are wireless networks susceptible to attacks, but also mobile terminals have limited computational power. Recently, some authentication schemes with anonymity for the GLOMONET have been proposed. This paper shows some security weaknesses in those schemes. Furthermore, a lightweight and provably secure user authentication scheme with anonymity for the GLOMONET is proposed. It uses only symmetric cryptographic and hash operation primitives for secure authentication. Besides, it takes only four message exchanges among the user, foreign agent and home agent. We also demonstrate that this protocol enjoys important security attributes including prevention of various attacks, single registration, user anonymity, user friendly …