{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T03:02:39Z","timestamp":1787281359997,"version":"build-2736575974"},"reference-count":34,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Algebra Geometry"],"published-print":{"date-parts":[[2022,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>This article provides new constant-time encodings [Formula: see text] to ordinary elliptic [Formula: see text]-curves [Formula: see text] of [Formula: see text]-invariants 0, 1728 having a small prime divisor of the Frobenius trace. Therefore all curves of [Formula: see text] are covered. This circumstance is also true for the Barreto\u2013Naehrig curves BN512, BN638 from the international cryptographic standards ISO\/IEC 15946-5, TCG Algorithm Registry, and FIDO ECDAA Algorithm. Many [Formula: see text] curves, as well as BN512, BN638, are not appropriate for the most efficient prior encodings. So, in fact, only the universal Shallue\u2013van de Woestijne one was previously applicable to them. However, this encoding (in contrast to the new ones) cannot be computed at the cost of one exponentiation in the field [Formula: see text].<\/jats:p>","DOI":"10.1137\/21m1441602","type":"journal-article","created":{"date-parts":[[2022,12,7]],"date-time":"2022-12-07T16:13:55Z","timestamp":1670429635000},"page":"600-617","source":"Crossref","is-referenced-by-count":4,"title":["Optimal Encodings to Elliptic Curves of \\(\\boldsymbol{j}\\)-Invariants 0, 1728"],"prefix":"10.1137","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4796-8989","authenticated-orcid":true,"given":"Dmitrii","family":"Koshelev","sequence":"first","affiliation":[{"name":"Computer Sciences and Networks Department, T\u00e9l\u00e9com Paris, Paris, France."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2022,12,9]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139012843"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1201\/9781315370170"},{"key":"ref3","doi-asserted-by":"crossref","unstructured":"A. Faz-Hernandez , \nS. Scott , \nN. Sullivan , \nR. S. Wahby , and \nC. A. Wood , Hashing to Elliptic Curves, 2022, https:\/\/datatracker.ietf.org\/doc\/draft-irtf-cfrg-hash-to-curve.","DOI":"10.17487\/RFC9380"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-2012-02606-8"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.46586\/tches.v2019.i4.154-179"},{"key":"ref6","unstructured":"D. Koshelev , Hashing to Elliptic Curves of j=0 and Quadratic Imaginary Orders of Class Number 2, preprint, paper 2020\/969, 2020,  https:\/\/eprint.iacr.org\/2020\/969."},{"key":"ref7","unstructured":"D. Boneh , \nS. Gorbunov , \nR. S. Wahby , \nH. Wee , \nC. A. Wood , and \nZ. Zhang , BLS Signatures, 2022, https:\/\/datatracker.ietf.org\/doc\/draft-irtf-cfrg-bls-signature."},{"key":"ref8","unstructured":"Y. Sakemi , \nT. Kobayashi , \nT. Saito , and \nR. S. Wahby , Pairing-Friendly Curves, 2022, https:\/\/datatracker.ietf.org\/doc\/draft-irtf-cfrg-pairing-friendly-curves."},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17455-1_17"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/168\/01690"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1093\/imrn\/rnp162"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-03356-8_18"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.11.003"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39059-3_14"},{"key":"ref15","first-page":"93","volume":"485","author":"Kani E.","year":"1997","journal-title":"J. Reine Angew. Math."},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-2011-039-3"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-45724-2_18"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09494-6"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1515\/form.2000.008"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157014000461"},{"key":"ref21","unstructured":"International Organization for Standardization\/International Electrotechnical Commission, Information Security \u2014  Cryptographic Techniques Based on Elliptic Curves \u2014 Part 5: Elliptic Curve Generation, ISO\/IEC 15946-5, 3rd ed. 2022, https:\/\/www.iso.org\/standard\/80241.html."},{"key":"ref22","unstructured":"Trusted Computing Group, TCG Algorithm Registry, 2020, https:\/\/trustedcomputinggroup.org\/resource\/tcg-algorithm-registry."},{"key":"ref23","unstructured":"FIDO Alliance, FIDO ECDAA Algorithm, 2018, https:\/\/fidoalliance.org\/specs\/fido-v2.0-id-20180227\/fido-ecdaa-algorithm-v2.0-id-20180227.html."},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/s12095-021-00478-y"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8368-9_12"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.5802\/aif.2430"},{"key":"ref27","doi-asserted-by":"crossref","unstructured":"D. Koshelev , Magma Code, 2022, https:\/\/github.com\/dishport\/Optimal-encodings-to-elliptic-curves-of-j-invariants-0-1728.","DOI":"10.1137\/21M1441602"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.4064\/aa171-4-5"},{"key":"ref30","unstructured":"T. Fisher , On Pairs of 17-Congruent Elliptic Curves, preprint, arXiv:2106:02033, 2021, https:\/\/arxiv.org\/abs\/2106.02033."},{"key":"ref31","unstructured":"D. Koshelev , Faster Indifferentiable Hashing to Elliptic   \\(\\mathbb{F}_{q^2}\\)  -Curves, preprint, paper 2021\/678, 2021, https:\/\/eprint.iacr.org\/2021\/678."},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdr039"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.4171\/RMI\/1269"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18487-1_42"}],"container-title":["SIAM Journal on Applied Algebra and Geometry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/21M1441602","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:22:36Z","timestamp":1787235756000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/21M1441602"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,9]]},"references-count":34,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,12,31]]}},"alternative-id":["10.1137\/21M1441602"],"URL":"https:\/\/doi.org\/10.1137\/21m1441602","relation":{},"ISSN":["2470-6566"],"issn-type":[{"value":"2470-6566","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,9]]}}}