Efficient Hardware RNS Decomposition for Post-Quantum Signature Scheme FALCON

The recently announced National Institute of Standards and Technology (NIST) Post-quantum cryptography (PQC) third-round standardization process has released its candidates to be standardized and FALCON is one of them. On the other hand, however, very few hardware implementation works for FALCON have been released due to its very complicated computation procedure and intensive complexity. With this background, in this paper, we propose an efficient hardware structure to implement residue numeral system (RNS) decomposition within NTRUSolve (a key arithmetic component for key generation of FALCON). In total, we have proposed three stages of coherent interdependent efforts to finish the proposed work. First, we have identified the necessary algorithmic operation related to RNS decomposition. Then, we have innovatively designed a hardware structure to realize these algorithms. Finally, field-programmable gate array (FPGA)-based implementation has been carried out to verify the superior performance of the proposed hardware structure. For instance, the proposed hardware design involves at least 3.91x faster operational time than the software implementation. To the authors' best knowledge, this is the first paper about the hardware acceleration of RNS decomposition for FALCON, and we hope the outcome of this work will facilitate the research in this area.