With the rapid proliferation of Internet of Things (IoT) devices, ensuring secure and reliable device authentication has become paramount. Physically Unclonable Functions (PUFs) provide a promising hardware-based alternative to conventional key storage by exploiting intrinsic manufacturing variations. This paper presents a Verilog-based Ring Oscillator PUF (RO-PUF) design that ensures a one-to-one mapping between PUF responses and cryptographic keys. We improve uniqueness and output stability by comparing paired oscillator frequencies and hashing the resulting response using a deterministic SHA-256-based mechanism. The design is validated through simulation using Vivado 2024.2, and is suitable for FPGA implementation to evaluate real-time performance and hardware efficiency, and results demonstrate consistent key generation with high entropy and no key duplication for repeated PUFresponses.