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Security and privacy concerns pose significant obstacles to the widespread adoption of IoT technology. One potential solution to address these concerns is the implementation of cryptographic protocols on resource-constrained IoT edge nodes. However, the limited resources available on these nodes make it challenging to effectively deploy such protocols. In cryptographic systems, finite-field multiplication plays a pivotal role, with its efficiency directly impacting overall performance. To tackle these challenges, we propose an innovative and compact bit-serial systolic layout specifically designed for Montgomery multiplication in the binary-extended field. This novel multiplier structure boasts regular cell architectures and localized communication connections, making it particularly well suited for VLSI implementation. Through a comprehensive complexity analysis, our suggested design demonstrates significant improvements in both area and area–time complexities when compared to existing competitive bit-serial multiplier structures. This makes it an ideal choice for cryptographic systems operating under strict area utilization constraints, such as resource-constrained IoT nodes and tiny embedded devices.