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Mobile Edge Computing (MEC) accommodates processing and data storage and manipulation capabilities across the scope of wireless network. In MEC environment, MEC servers along with the computing and storage capabilities are distributed at the edge of the network. However, due to the broad range of wireless communication, the fulfillment of security requirements still remain a challenging task in the for MEC environment. With the expeditious traffic expansion and growing end user requirements, the classic security protocols cannot encounter the innovative requirements of lightweightness and real-time communication. To meet these requirements, we have proposed an authentication protocol for the MEC environment. Our proposed protocol stipulates secure and efficient communication for all of the intended entities. Meanwhile, during its execution user anonymity remains intact. Moreover, our protocol is proven to be secure under the assumptions of formal security model. Additionally in this article, we have described the security properties of our protocol that it offers resistance against impersonation, session key computation and forward and backward secrecy attacks. The comparative analysis of time consumption and computation overheads are presented at the end of the paper, which is an evidence that our proposed protocol outperforms prior to various existing MEC protocols.