Smart home technology is one of the significant emerging applications in the Internet of Things that facilitates the user to control home devices in the remote manner. In this context, investigating and addressing IoT security issues is highly challenging as the operating strategies of IoT application differs due to their heterogeneity characteristics. At this juncture, an authentication mechanism with anonymity and efficiency is necessary for facilitating secure communication in the smart home scenario, since the user or home communication channels are generally determined to be highly insecure. In this paper, Similarity Learning-Based Supervised Discrete Hash Signature Scheme (SLSDHS) is proposed for achieving secure user during the process of smart home authentication. It leverages the mutual association between possible semantic labels in order to learn maximized more stable hash codes, which is a predominant improvement over the traditional hash code approaches. The communication overhead and computation overhead of the proposed SLSDHS is identified to be considerably minimized compared to the benchmarked schemes used for comparison. The security analysis of the proposed SLSDHS scheme evaluated using informal analysis, formal analysis, and AVIPSA tool-based model checks confirmed its predominance with respect to automated testing of internet security protocols.