Paper 2025/1322

Generation of Fast Finite Field Arithmetic for Cortex-M4 with ECDH and SQIsign Applications

Abstract

Finite field arithmetic is central to several cryptographic algorithms on embedded devices like the ARM Cortex-M4, particularly for elliptic curve and isogeny-based cryptography. However, rapid algorithm evolution, driven by initiatives such as NIST’s post-quantum standardization, might frequently render hand-optimized implementations obsolete. We address this challenge with m4-modarith, a library generating C code with inline assembly for the Cortex-M4 that rivals custom-tuned assembly, enabling agile development in this ever-changing landscape. Our generated modular multiplications obtains fast performances, competitive with hand-optimized assembly implementations published in the literature, even outperforming some of them for Curve25519. Two contributions are pivotal to this success. First, we introduce a novel multiplication strategy that matches the memory access complexity of the operand caching method while being applicable to a larger cache size for Cortex-M4 implementations. Second, we generalize an efficient pseudo-Mersenne reduction strategy, and formally prove its correctness and applicability for most primes of cryptographic interest. Our generator allowed agile optimization of SQIsign’s NIST PQC Round 2 submission, improving level 1 verification from 123 Mcycles to only 54 Mcycles, a $2.3\times$ speedup. As an additional case study, we use our generator to improve performance of portable implementations of RFC~7748 by up to $2.2\times$.