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User identification is an important access control mechanism for client-server networking architectures. The concept of single sign-on can allow legal users to use the unitary token to access different service providers in distributed computer networks. Recently, some user identification schemes have been proposed for distributed computer networks. Unfortunately, most existing schemes cannot preserve user anonymity when possible attacks occur. Also, the additional time-synchronized mechanisms they use may cause extensive overhead costs. To overcome these drawbacks, we propose a secure single sign-on mechanism that is efficient, secure, and suitable for mobile devices in distributed computer networks.