Low-Energy NTT and INTT Architectures for Image Encryption and Decryption

The number theoretic transform (NTT) and its inverse (INTT) are efficient mathematical tools for polynomial multiplication, making them highly suitable for cryptographic applications such as image encryption and decryption. This work presents novel hardware architectures for NTT and INTT, designed explicitly for energy-efficient image encryption. Our primary contributions include the introduction of an approximate radix-2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> logarithm (AxRLL-16) based on a leading one detector (LOD) and Radix-16 encoder, which optimizes modular reduction operations by significantly reducing computational complexity. The NTT and INTT proposals are synthesized under a 65nm technology and achieve substantial improvements in power, area, and energy efficiency. Compared to state-of-the-art designs, our NTT and INTT implementations exhibit over 96.13% areasavings and 96.88% power-savings, with energy consumption reduced by up to 207 times.