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In recent years, the Internet of Things (IoT) has exploded in popularity. The smart home, as an important facet of IoT, has gained its focus for smart intelligent systems. As users communicate with smart devices over an insecure communication medium, the sensitive information exchanged among them becomes vulnerable to an adversary. Thus, there is a great thrust in developing an anonymous authentication scheme to provide secure communication for smart home environments. Most recently, an anonymous authentication scheme for smart home environments with provable security has been proposed in the literature. In this paper, we analyze the recent scheme to highlight its several vulnerabilities. We then address the security drawbacks and present a more secure and robust authentication scheme that overcomes the drawbacks found in the analyzed scheme, while incorporating its advantages too. Finally, through a detailed comparative study, we demonstrate that the proposed scheme provides significantly better security and more functionality features with comparable communication and computational overheads with similar schemes.