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The smart home is a crucial embodiment of the internet of things (IoT), which can facilitate users to access smart home services anytime and anywhere. Due to the limited resources of cloud computing, it cannot meet users' real-time needs. Therefore, edge computing emerges as the times require, providing users with better real-time access and storage. The application of edge computing in the smart home environment can enable users to enjoy smart home services. However, users and smart devices communicate through public channels, and malicious attackers may intercept information transmitted through public channels, resulting in user privacy disclosure. Therefore, it is a critical issue to protect the secure communication between users and smart devices in the smart home environment. Furthermore, authentication protocols in smart home environments also have some security challenges. In this paper, we propose an anonymous authentication protocol that applies edge computing to the smart home environment to protect communication security between entities. To protect the security of smart devices, we embed physical unclonable functions (PUF) into each smart device. Real-or-random model, informal security analysis, and ProVerif are adopted to verify the security of our protocol. Finally, we compare our protocol with existing protocols regarding security and performance. The comparison results demonstrate that our protocol has higher security and slightly better performance. [ABSTRACT FROM AUTHOR]