{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,10]],"date-time":"2025-12-10T12:43:41Z","timestamp":1765370621572,"version":"3.44.0"},"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>Constructing and implementing isogeny-based cryptographic primitives is an active research. In particular, performing length-n isogenies walks over quadratic field extensions of Fp plays an exciting role in some constructions, including Hash functions, Verifiable Delay Functions, Key-Encapsulation Mechanisms, and generic proof systems for isogeny knowledge. Remarkably, many isogeny-based constructions, for efficiency, perform 2-isogenies through square root calculations.This work analyzes the idea of using 3-isogenies instead of 2-isogenies, which replaces the requirement of calculating square roots with cube roots. Performing length-m 3-isogenies allows shorter isogeny walks than when employing length-n 2-isogenies since a cube root calculation costs essentially the same as computing a square root, and we require 3m \u2248 2n to provide the same security level.We propose an efficient mapping from arbitrary supersingular Montgomery curves defined over Fp2 to the 3-isogeny curve model from Castryck, Decru, and Vercauteren (Asiacrypt 2020); a deterministic algorithm to compute all order-3 points on arbitrary supersingular Montgomery curves, and an efficient algorithm to compute length-m 3-isogeny chains.We improve the length-m 3-isogeny walks required by the KEM from Nakagawa and Onuki (CRYPTO 2024) by using our results and introducing more suitable parameter sets that are friendly with C-code implementations. In particular, our experiments illustrate an improvement between 26.41% and 35.60% in savings when calculating length-m 3-isogeny chains and using our proposed parameters instead of those proposed by Nakagawa and Onuki (CRYPTO 2024).Finally, we enhance the key generation of CTIDH-2048 by including radical 3-isogeny chains over the basefield Fp, reducing the overhead of finding a 3-torsion basis as required in some instantiations of the CSIDH protocol. Our experiments illustrate the advantage of radical 3 isogenies in the key generation of CTIDH-2048, with an improvement up to 4 times faster than the original CTIDH.<\/jats:p>","DOI":"10.46586\/tches.v2025.i4.644-666","type":"journal-article","created":{"date-parts":[[2025,9,5]],"date-time":"2025-09-05T13:05:11Z","timestamp":1757077511000},"page":"644-666","source":"Crossref","is-referenced-by-count":1,"title":["Let us walk on the 3-isogeny graph: efficient, fast, and simple"],"prefix":"10.46586","volume":"2025","author":[{"given":"Jes\u00fas-Javier","family":"Chi-Dom\u00ednguez","sequence":"first","affiliation":[]},{"given":"Eduardo","family":"Ochoa-Jim\u00e9nez","sequence":"additional","affiliation":[]},{"given":"Ricardo-Neftal\u00ed","family":"Pontaza-Rodas","sequence":"additional","affiliation":[]}],"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\/12424\/12152","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/tches.iacr.org\/index.php\/TCHES\/article\/download\/12424\/12152","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\/12424"}},"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.i4.644-666","relation":{},"ISSN":["2569-2925"],"issn-type":[{"type":"electronic","value":"2569-2925"}],"subject":[],"published":{"date-parts":[[2025,9,5]]}}}