Physically unclonable functions (PUFs) are advanced physical security measures that offer fundamental, unclonable appraisals of physical objects, providing an effective defense against hardware vulnerability breaches. They function as unique digital hardware fingerprints. This study discusses previous methods adopted for improving hardware security via PUF technology, with a specific focus on PUF circuits implemented on FPGA boards. Hardware security is assumed to be enhanced by adding a memristor to the ring oscillator PUF circuit and implementing these authentication architectures on FPGA boards. Additionally, this study explores methods for improving the main performance metrics for FPGA-based memristive-ring oscillator PUFs, including uniqueness, uniformity, and reliability. The study was founded on many scientific studies selected according to specific criteria. This study aims to assess and contrast these studies to achieve substantial enhancements in the security of devices on the basis of the obtained results. Upon comparing the findings, it was revealed that the proposed techniques, which provide flexibility and adaptability in dealing with memristive-PUF circuits to improve security services, displayed a distinct enhancement in security performance compared with other research that did not include any references to memristors. As an essential part of the authentication architecture, performance metrics involving memristor technology are verified in this study, with a uniqueness of 48.57%, uniformity of 51.43%, and bit-aliasing of 51.43%. These outcomes demonstrate the validation of memristor-based physical unclonable functions (M-PUF) against encryption and verification within a certified key exchange and tests.