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The extensive application of the Internet of Things (IoT) and artificial intelligence technology has greatly promoted the construction and development of smart cities. Smart home as the foundation of smart cities can optimize home lifestyles. However, users access the smart home system through public channels, and the transmitted information is vulnerable to attack by attackers, and the privacy and data security of the home user will be difficult to be guaranteed. Therefore, how to protect users' data and privacy security becomes critical. In this paper, we design a provably secure authentication scheme for the smart home environment, which ensures that only legitimate users can use smart devices. We use the informal model to verify the security of the scheme and formally analyze the security and correctness of the scheme through the Real or Random model. Finally, through the comparison of security and performance analysis, it is proven that our scheme has higher security under similar performance. [ABSTRACT FROM AUTHOR]