A Unified Hardware Accelerator for Fast Fourier Transform and Number Theoretic Transform

Abstract: The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most widely used algorithm in digital signal processing. In this work, we demonstrate a unified hardware accelerator supporting both 512-point complex FFT as well as 256-point NTT for the recently standardized NIST post-quantum key encapsulation and digital signature algorithms ML-KEM and ML-DSA respectively. Our proposed architecture effectively utilizes the arithmetic circuitry required for complex FFT, and the only additional circuits required are for modular reduction along with modifications in the control logic. Our implementation achieves performance comparable to state-of-the-art ML-KEM / ML-DSA NTT accelerators on FPGA, thus demonstrating how an FFT accelerator can be augmented to support NTT and the unified hardware can be used for both digital signal processing and post-quantum lattice-based cryptography applications.