Efficient Polynomial Arithmetic and Hash Modules for ML-DSA and ML-KEM Standards

In light of the emerging threat posed by quantum computers to current cryptographic standards, the National Institute of Standards and Technology has introduced the Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM) and Digital Signature Standards (ML-DSA). These standards are derived from the lattice-based cryptosystems, CRYSTALS-Kyber and Dilithium, which rely on the Module Learning with Errors assumption to enhance security. Therefore, the efficient hash and arithmetic modules are essential for implementing these schemes, as they are the most time-consuming phases. This paper presents an efficient hardware architecture that optimizes and unifies hash and arithmetic modules, specifically tailored to accelerate FPGA-based implementations of ML-KEM and ML-DSA. Our polynomial arithmetic module demonstrates an improvement in terms of latency while consuming comparable hardware resources compared to state-of-the-art studies. Additionally, we detail a Keccak-based hash module with four distinct modes, efficiently supporting both cryptographic schemes.