In July 2020, the lattice-based CRYSTALS-Dilithium digital signature scheme has been chosen as one of the three third-round finalists in the post-quantum cryptography standardization process by the National Institute of Standards and Technology (NIST). In this work, we present the first Very High Speed Integrated Circuit Hardware Description Language (VHDL) implementation of the CRYSTALS-Dilithium signature scheme for Field-Programmable Gate Arrays (FPGAs). Due to our parallelization-based design requiring only low numbers of cycles, running at high frequency and using reasonable amount of hardware resources on FPGA, our implementation is able to sign 15832 messages per second and verify 10524 signatures per second. In particular, the signing algorithm requires 68461 Look-Up Tables (LUTs), 86295 Flip-Flops (FFs), and the verification algorithm takes 61738 LUTs and 34963 FFs on Virtex 7 UltraScale+ FPGAs. In this article, experimental results for each Dilithium security level are provided and our VHDL-based implementation is compared with related High-Level Synthesis (HLS)-based implementations. Our solution is ca 114 times faster (in the signing algorithm) and requires less hardware resources.

Kyber is one of the three finalists of the National Institute of Standards and Technology (NIST) post-quantum cryptography competition. This article presents an optimized Very High Speed Integrated Circuit Hardware Description Language (VHDL)-based implementation of the main components of the Kyber scheme, namely Number-Theoretic Transform (NTT) and Keccak. We focus specifically on NTT, Keccak and their derivatives since they largely determine Kyber's performance due to their wide involvement in each step of the scheme. Our high-speed implementation also takes into account the trade-off between the degree of parallelization and the resources utilization. The NTT component is more than 27\% faster than the state-of-the-art implementations. Furthermore, the optimization helps the algorithm to achieve 1 572 839 NTT operations per second.