Area and Power Efficient FFT/IFFT Processor for FALCON Post-Quantum Cryptography

Abstract

Quantum computing is an emerging technology on the verge of reshaping industries, while simultaneously challenging existing cryptographic algorithms. FALCON, a recent standard quantum-resistant digital signature, presents a challenging hardware implementation due to its extensive non-integer polynomial operations, necessitating FFT over the ring <inline-formula><tex-math notation="LaTeX">$\mathbb {Q}[x]/(x^{n}+1)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi mathvariant="double-struck">Q</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mi>x</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msup><mml:mi>x</mml:mi><mml:mi>n</mml:mi></mml:msup><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math><inline-graphic xlink:href="alsuhli-ieq1-3407124.gif"/></alternatives></inline-formula>. This paper introduces an ultra-low-power and compact processor tailored for FFT/IFFT operations over the ring for efficient FALCON implementation. The proposed processor incorporates various optimization techniques, including twiddle factor compression and conflict-free scheduling. In an ASIC implementation using a 22 nm GF process, the proposed processor demonstrates an area occupancy of 0.15 mm<inline-formula><tex-math notation="LaTeX">$^{2}$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="alsuhli-ieq2-3407124.gif"/></alternatives></inline-formula> and a power consumption of 12.6 mW/28.1 mW at an operating frequency of 167 MHz/500 MHz for the non-pipelined/pipelined version of the processor. Since a hardware implementation of FFT/IFFT over the ring is currently non-existent, the execution time achieved by this processor is compared to the reference software implementation of FFT/IFFT of FALCON on a Raspberry Pi 4 with Cortex-A72, where the proposed pipelined processor achieves a speedup up to 3.8×. Furthermore, in comparison to dedicated state-of-the-art hardware accelerators for classic FFT, the pipelined architecture occupies 42% less area and consumes 64% less power, on average. The quantified speedup in the context of FALCON suggests that the proposed hardware design offers a promising solution for the efficient implementation of FALCON.