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A Signcryption proposed by Yuliang Zheng in 1997 is a hybrid public key primitive that combines a digital signature and an encryption. It provides more efficient method than a straightforward composition of a signature scheme with an encryption scheme. In a mobile communication environment, the authenticated key agreement protocol should be designed to have lower computational complexity and memory requirements. Therefore, in this paper, our proposed method that efficient authenticated key exchange protocol using Signcryption scheme and based on EC using Signcryption in mobile and wireless network. And we analyze computational cost and security requirements of proposed protocol.