The Fast Fourier Transform (FFT) is a fundamental algorithm used in a wide range of applications, from signal processing to cryptography. With the increasing use of embedded and mobile devices, the need to optimize FFT performance has become crucial. This study focuses on the implementation of FFT on an ARM Cortex-A72 processor, leveraging NEON instructions, which are part of the SIMD (Single Instruction, Multiple Data) set. NEON instructions enable parallel operations, resulting in a significant improvement in execution times. Through a comparative analysis between implementations with and without NEON, a 99.99% reduction in execution time was demonstrated when using NEON, highlighting its effectiveness in applications that require high-speed processing, such as post-quantum cryptography.