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The developing next generation (4G) mobile communication system will offer us great convenience and huge opportunities of service creation with numerous security threats. As a critical security mechanism, user authentication and key agreement (AKA) schemes have received considerable attentions in recent years. In this paper, a AKA scheme (SPAKA) based on self-certified public-key is proposed for the coming 4G system to reduce the storage, computation and communicational load of existing public-key based user authentication schemes while improving the security of 3G AKA scheme. Three authentication protocols including first-time authentication, re-authentication and handoff authentication are designed respectively for different authentication scenarios. According to the performance analysis, our approach has outperformed related schemes by providing better flexibility and scalability while maintain the expected security and efficiency. Consequently, it is more appropriate for 4G wireless system.