TY - JOUR AU - Alkim, Erdem AU - Hwang, Vincent AU - Yang, Bo-Yin PY - 2022/08/31 Y2 - 2024/03/29 TI - Multi-Parameter Support with NTTs for NTRU and NTRU Prime on Cortex-M4 JF - IACR Transactions on Cryptographic Hardware and Embedded Systems JA - TCHES VL - 2022 IS - 4 SE - Articles DO - 10.46586/tches.v2022.i4.349-371 UR - https://tches.iacr.org/index.php/TCHES/article/view/9823 SP - 349-371 AB - <p>We propose NTT implementations with each supporting at least one parameter of NTRU and one parameter of NTRU Prime. Our implementations are based on size-1440, size-1536, and size-1728 convolutions without algebraic assumptions on the target polynomial rings. We also propose several improvements for the NTT computation. Firstly, we introduce dedicated radix-(2, 3) butterflies combining Good–Thomas FFT and vector-radix FFT. In general, there are six dedicated radix-(2, 3) butterflies and they together support implicit permutations. Secondly, for odd prime radices, we show that the multiplications for one output can be replaced with additions/subtractions. We demonstrate the idea for radix-3 and show how to extend it to any odd prime. Our improvement also applies to radix-(2, 3) butterflies. Thirdly, we implement an incomplete version of Good–Thomas FFT for addressing potential code size issues. For NTRU, our polynomial multiplications outperform the state-of-the-art by 2.8%−10.3%. For NTRU Prime, our polynomial multiplications are slower than the state-of-the-art. However, the SotA exploits the specific structure of coefficient rings or polynomial moduli, while our NTT-based multiplications exploit neither and apply across different schemes. This reduces the engineering effort, including testing and verification.</p> ER -