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Fog computing (FC) is an infrastructure consisting of decentralized computing, where computing resources such as storage, applications, and data are scattered among the cloud and data source. Fog computing inherits similar privacy and security concerns present in cloud computing, such as authentication and key management issues. Recently, Wazid et al. presented a scheme of authentication key exchange for fog computing called SAKA-FC to address these issues. We analyzed and identified that the SAKA-FC suffers from some severe vulnerabilities. Furthermore, we presented an improved scheme to mitigate these problems while retaining its strengths. The formal security analysis of the proposed scheme is validated through BAN logic. At the same time, the AVISPA tool is employed for automated formal security verification. Informal security analysis is conducted to attest that the proposal can confront the …