{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T17:26:05Z","timestamp":1772645165562,"version":"3.50.1"},"reference-count":0,"publisher":"Universitatsbibliothek der Ruhr-Universitat Bochum","issue":"4","license":[{"start":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T00:00:00Z","timestamp":1757030400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["TCHES"],"abstract":"<jats:p>Finite field arithmetic is central to several cryptographic algorithms on embedded devices like the ARM Cortex-M4, particularly for elliptic curve and isogenybased cryptography. However, rapid algorithm evolution, driven by initiatives such as NIST\u2019s 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\u2019s NIST PQC Round 2 submission, improving level 1 verification from 123 Mcycles to only 54 Mcycles, a 2.3x speedup. As an additional case study, we use our generator to improve performance of portable implementations of RFC 7748 by up to 2.2x.<\/jats:p>","DOI":"10.46586\/tches.v2025.i4.588-620","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T13:05:11Z","timestamp":1757077511000},"page":"588-620","source":"Crossref","is-referenced-by-count":1,"title":["Generation of Fast Finite Field Arithmetic forCortex-M4 with ECDH and SQIsign Applications"],"prefix":"10.46586","volume":"2025","author":[{"given":"Felix Carvalho","family":"Rodrigues","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D\u00e9cio","family":"Gazzoni Filho","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gora","family":"Adj","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Isaac A.","family":"Canales-Mart\u00ednez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge","family":"Ch\u00e1vez-Saab","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julio","family":"L\u00f3pez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Scott","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco","family":"Rodr\u00edguez-Henr\u00edquez","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25480","published-online":{"date-parts":[[2025,9,5]]},"container-title":["IACR Transactions on Cryptographic Hardware and Embedded Systems"],"original-title":[],"link":[{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/download\/12422\/12150","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/download\/12422\/12150","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T13:05:11Z","timestamp":1757077511000},"score":1,"resource":{"primary":{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/view\/12422"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,5]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,9,5]]}},"URL":"https:\/\/doi.org\/10.46586\/tches.v2025.i4.588-620","relation":{},"ISSN":["2569-2925"],"issn-type":[{"value":"2569-2925","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,5]]}}}