# A High-Level Synthesis Approach to the Software/Hardware Codesign of NTT-based Post-Quantum Cryptography Algorithms

### Abstract

Due to an emerging threat of quantum computing, one of the major challenges facing the cryptographic community is a timely transition from traditional public-key cryptosystems, such as RSA and Elliptic Curve Cryptography, to a new class of algorithms, collectively referred to as Post-QuantumCryptography (PQC). Several promising candidates for a new PQC standard can have their software and hardware implementations accelerated using the Num-ber Theoretic Transform (NTT). In this paper, we present an improved hardware architecture for NTT,with the hardware-friendly modular reduction, and demonstrate that this architecture can be efficiently implemented in hardware using High-Level Synthesis(HLS). The novel feature of the proposed architecture is an original memory write-back scheme, which assists in preparing coefficients for performing later NTT stages, saving memory storage used for precomputed constants. Our design is the most efficient for the case when $log_2N$ is even. The latency of our proposed architecture is approximately equal to $(N log_2N+ 3N)/4$ clock cycles. As a proof of concept, we implemented the NTT operation for several parameter sets used in the PQC algorithms NewHope, FALCON, qTESLA, and CRYSTALS-DILITHIUM.

Publication
A High-Level Synthesis Approach to the Software/Hardware Codesign of NTT-based Post-Quantum Cryptography Algorithms