{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T06:31:33Z","timestamp":1772346693899,"version":"3.50.1"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2019,5,30]],"date-time":"2019-05-30T00:00:00Z","timestamp":1559174400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2019,5,30]]},"abstract":"<jats:p>\n            Let\n            <jats:italic>q<\/jats:italic>\n            be a prime power and let F\n            <jats:sub>\n              <jats:italic>q<\/jats:italic>\n            <\/jats:sub>\n            be a field with\n            <jats:italic>q<\/jats:italic>\n            elements. Let\n            <jats:italic>f<\/jats:italic>\n            and\n            <jats:italic>g<\/jats:italic>\n            be irreducible polynomials in F\n            <jats:sub>\n              <jats:italic>q<\/jats:italic>\n            <\/jats:sub>\n            [\n            <jats:italic>X<\/jats:italic>\n            ], with deg\n            <jats:italic>f<\/jats:italic>\n            dividing deg\n            <jats:italic>g.<\/jats:italic>\n            Define\n            <jats:italic>k<\/jats:italic>\n            = F\n            <jats:sub>\n              <jats:italic>q<\/jats:italic>\n            <\/jats:sub>\n            [\n            <jats:italic>X<\/jats:italic>\n            ]\/\n            <jats:italic>f<\/jats:italic>\n            and\n            <jats:italic>K<\/jats:italic>\n            = F\n            <jats:sub>\n              <jats:italic>q<\/jats:italic>\n            <\/jats:sub>\n            [\n            <jats:italic>X<\/jats:italic>\n            ]\/\n            <jats:italic>g<\/jats:italic>\n            , then there is an embedding\n            <jats:italic>\u03d5<\/jats:italic>\n            :\n            <jats:italic>k<\/jats:italic>\n            [EQUATION]\n            <jats:italic>K<\/jats:italic>\n            , unique up to F\n            <jats:sub>\n              <jats:italic>q<\/jats:italic>\n            <\/jats:sub>\n            -automorphisms of\n            <jats:italic>k.<\/jats:italic>\n            Our goal is to describe algorithms to efficiently represent and evaluate one such embedding.\n          <\/jats:p>","DOI":"10.1145\/3338637.3338639","type":"journal-article","created":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T12:37:11Z","timestamp":1559306231000},"page":"117-119","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Computing isomorphisms and embeddings of finite fields"],"prefix":"10.1145","volume":"52","author":[{"given":"Ludovic","family":"Brieulle","sequence":"first","affiliation":[{"name":"Universit\u00e9 d'Aix-Marseille"}]},{"given":"Luca","family":"De Feo","sequence":"additional","affiliation":[{"name":"Universit\u00e9 de Versailles and Inria, Paris Saclay"}]},{"given":"Javad","family":"Doliskani","sequence":"additional","affiliation":[{"name":"University of Waterloo"}]},{"given":"Jean Pierre","family":"Flori","sequence":"additional","affiliation":[{"name":"Agence Nationale de la S\u00e9curit\u00e9 des Syst\u00e8mes d'Information"}]},{"given":"\u00c9ric","family":"Schost","sequence":"additional","affiliation":[{"name":"University of Waterloo"}]}],"member":"320","published-online":{"date-parts":[[2019,5,30]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1006\/ffta.2001.0344"},{"key":"e_1_2_1_2_1","volume-title":"Explicit computation of isomorphisms between finite fields. Revised version. https:\/\/www.math.u-bordeaux.fr\/~ballombe\/fpisom.ps","author":"Allombert Bill","year":"2002","unstructured":"Bill Allombert . Explicit computation of isomorphisms between finite fields. Revised version. https:\/\/www.math.u-bordeaux.fr\/~ballombe\/fpisom.ps , 2002 . Bill Allombert. Explicit computation of isomorphisms between finite fields. Revised version. https:\/\/www.math.u-bordeaux.fr\/~ballombe\/fpisom.ps, 2002."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1997.0138"},{"key":"e_1_2_1_5_1","volume-title":"the Sage Mathematics Software System (Version 7.2.0)","author":"Developers The Sage","year":"2016","unstructured":"The Sage Developers . SageMath , the Sage Mathematics Software System (Version 7.2.0) , 2016 . http:\/\/www.sagemath.org. The Sage Developers. 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Pinch. Recognising elements of finite fields. In Cryptography and Coding II, pages 193--197. Oxford University Press, 1992."},{"key":"e_1_2_1_9_1","volume-title":"Efficient computation of isomorphisms between finite fields. personal communication","author":"Rains Eric M.","year":"1996","unstructured":"Eric M. Rains . Efficient computation of isomorphisms between finite fields. personal communication , 1996 . Eric M. Rains. Efficient computation of isomorphisms between finite fields. personal communication, 1996."},{"key":"e_1_2_1_10_1","volume-title":"version 2.7.1","author":"The PARI Group","year":"2014","unstructured":"The PARI Group , Bordeaux. PARI\/GP , version 2.7.1 , 2014 . The PARI Group, Bordeaux. PARI\/GP, version 2.7.1, 2014."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3338637.3338639","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3338637.3338639","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T23:44:47Z","timestamp":1750203887000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3338637.3338639"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,30]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,5,30]]}},"alternative-id":["10.1145\/3338637.3338639"],"URL":"https:\/\/doi.org\/10.1145\/3338637.3338639","relation":{},"ISSN":["1932-2240"],"issn-type":[{"value":"1932-2240","type":"print"}],"subject":[],"published":{"date-parts":[[2019,5,30]]},"assertion":[{"value":"2019-05-30","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}