ECO-CRYSTALS: Efficient Cryptography CRYSTALS on Standard RISC-V ISA

The field of post-quantum cryptography (PQC) is continuously evolving. Many researchers are exploring efficient PQC implementation on various platforms, including x86, ARM, FPGA, GPU, etc. In this paper, we present an Efficient CryptOgraphy CRYSTALS (ECO-CRYSTALS) implementation on standard 64-bit RISC-V Instruction Set Architecture (ISA). The target schemes are two winners of the National Institute of Standards and Technology (NIST) PQC competition: CRYSTALS-Kyber and CRYSTALS-Dilithium, where the two most time-consuming operations are Keccak and polynomial multiplication. Notably, this paper is the first highly-optimized assembly software implementation to deploy Kyber and Dilithium on the 64-bit RISC-V ISA. Firstly, we propose a better scheduling strategy for Keccak, which is specifically tailored for the 64-bit dual-issue RISC-V architecture. Our 24-round Keccak permutation (Keccak-$p$[1600,24]) achieves a 59.18% speed-up compared to the reference implementation. Secondly, we apply two modular arithmetic (Montgomery arithmetic and Plantard arithmetic) in the polynomial multiplication of Kyber and Dilithium to get a better lazy reduction. Then, we propose a flexible dual-instruction-issue scheme of Number Theoretic Transform (NTT). As for the matrix-vector multiplication, we introduce a row-to-column processing methodology to minimize the expensive memory access operations. Compared to the reference implementation, we obtain a speedup of 53.85%$\thicksim$85.57% for NTT, matrix-vector multiplication, and INTT in our ECO-CRYSTALS. Finally, the ECO-CRYSTALS implementation for key generation, encapsulation, and decapsulation in Kyber achieves 399k, 448k, and 479k cycles respectively, achieving speedups of 60.82%, 63.93%, and 65.56% compared to the NIST reference implementation. Similarly, the ECO-CRYSTALS implementation for key generation, sign, and verify in Dilithium reaches 1 364k, 3 191k, and 1 369k cycles, showcasing speedups of 54.84%, 64.98%, and 57.20%, respectively.