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We propose two efficient mutual authentication and key exchange protocols (MAKEPs) namely (1) server-specific and (2) linear MAKEPs. They are suitable for establishing secure communications between a low-power wireless device (client) and a powerful base station (server) under different system requirements. These protocols reduce the computational burden of the client while still maintaining a required level of security and a good amount of scalability for most wireless communications applications. We discuss their security and also demonstrate that they can be implemented efficiently.