ESPM-D: Efficient Sparse Polynomial Multiplication for Dilithium on ARM Cortex-M4 and Apple M2

Dilithium is a lattice-based digital signature scheme standardized by the NIST post-quantum cryptography (PQC) project. In this study, we focus on developing efficient sparse polynomial multiplication implementations of Dilithium for ARM Cortex-M4 and Apple M2, which are both based on the ARM architecture. The ARM Cortex-M4 is commonly utilized in resource-constrained devices such as sensors. Conversely, the Apple M2 is typically found on mobile devices, emphasizing high performance and versatility. Accordingly, our optimization strategies differ between ARM Cortex-M4 and Apple M2. We prioritize optimizing stack usage for the former while enhancing computational efficiency for the latter. Our optimized sparse polynomial multiplication achieves significant speedups of up to 30 compared to the state-of-the-art Number-Theoretic Transform (NTT) implementation. Additionally, we integrate the sparse polynomial multiplication with the infinity norm judgments in the Dilithium signing process, further enhancing signing efficiency. Our optimized implementation not only reduces stack usage by 10.8 Dilithium3, and Dilithium5, respectively, but also enhances signing performance by 0.4 Furthermore, we optimize polynomial sampling, rounding functions, and polynomial packing and unpacking using ARM Cortex-M4 DSP instructions, resulting in a 0.4 procedures. On the MacBook Air 2022, our Dilithium implementation achieves 10 to 11 work sets new performance records for Dilithium on both ARM Cortex-M4 and Apple M2 platforms.