Physical Unclonable Functions (PUFs) have gained widespread attention for their secure key storage, authentication, and anti-counterfeiting applications. While traditional PUFs based on Complementary Metal-Oxide-Semiconductor (CMOS) have been extensively studied, the emergence of memristors offers new opportunities due to their inherent device variations and distinctive resistive switching behaviors. This study explores the construction of reliable PUFs using self-rectifying analog BiFeO $_{3}$