High-Radix/Mixed-Radix NTT Multiplication Algorithm/Architecture Co-Design Over Fermat Modulus - Xing, Yile; Li, Guangyan; Ye, Zewen; Luk, Ryan W. L.; Chen, Donglong; Yan, Hong; Cheung, Ray C. C. (IEEE transactions on computers, 2025)
Polynomial multiplication using Number Theoretic Transform (NTT) is crucial in lattice-based post-quantum cryptography (PQC) and fully homomorphic encryption (FHE), with modulus q q<inline-graphic xlink:href="chen-ieq1-3590972.gif"/> significantly affecting performance. Fermat moduli of the form 2^{2^{n}}+1 22n+1<inline-graphic xlink:href="chen-ieq2-3590972.gif"/> , such as 65537, offer efficiency gains due to simplified modular reduction and powers-of-2 twiddle factors in NTT. While Fermat moduli have been directly applied or explored for incorporation into existing schemes, Fermat NTT-based polynomial multiplication designs remain underexplored in fully exploiting the benefits of Fermat moduli. This work presents a high-radix/mixed-radix NTT architecture tailored for Fermat moduli, which improves the utilization of the powers-of-2 twiddle factors in large transform sizes. In most cases, our design achieves a 30%-85% reduction in DSP area-time product (ATP) and a 70%-100% reduction in BRAM ATP compared to state-of-the-art designs with smaller or equivalent modulus, while maintaining competitive LUT and FF ATP, underscoring the potential of Fermat NTT-based polynomial multipliers in lattice-based cryptography.