Optimizing CRYSTALS-Dilithium in Rust: Radix-4 NTT and Assembly-level Comparison with Official C Implementation

Post-Quantum Cryptography (PQC) is becoming popular since it offers protection against quantum attacks. CRYSTALS-Dilithium is being considered as a promising NIST PQC standard candidate. It utilizes the Radix-2 Number Theoretic Transform (NTT). Its reliance on lattice-based cryptography and number-theoretic principles positions CRYSTALS-Dilithium as a strong contender for providing robust security in the era of quantum computing. Besides, the Radix-4 NTT divides polynomials into more parts than the Radix-2 NTT, making calculations more efficient by reusing values. In this paper, we improve the computational efficiency of CRYSTALS-Dilithium by implementing the Radix-4 NTT algorithm in both C and Rust programming languages. We verified the effectiveness through experiments in terms of signature and verification speeds. Additionally, we analyzed the assembly code generated by both languages to understand the performance differences.