{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:20:05Z","timestamp":1777645205810,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"4","license":[{"start":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T00:00:00Z","timestamp":1427846400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2015,4]]},"abstract":"<jats:p>\n                    Given a square-free integer \u0394 &lt; 0, we present an algorithm constructing a pair of primes p and q such that q|p + 1 \u2212 t and 4p \u2212 t\n                    <jats:sup>2<\/jats:sup>\n                    = \u0394f\n                    <jats:sup>2<\/jats:sup>\n                    , where |t| \u2264 2\u221ap for some integers f, t. Together with a CM method presented in the paper, such primes p and q are used for a construction of an elliptic curve E over a finite field $\\mathbb{F}_p$ such that the order of E is divisible by a large prime. It is shown that our algorithm works in polynomial time.\n                  <\/jats:p>","DOI":"10.3233\/fi-2015-1161","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T01:25:53Z","timestamp":1575336353000},"page":"331-343","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["An Algorithmic Construction of Finite Elliptic Curves of Order Divisible by a Large Prime"],"prefix":"10.1177","volume":"136","author":[{"given":"Maciej","family":"Grze\u015bkowiak","sequence":"first","affiliation":[{"name":"Adam Mickiewicz University, Faculty of Mathematics and Computer Science, Umultowska 87, 61-614 Pozna\u0144, Poland. maciejg@amu.edu.pl"}]}],"member":"179","published-online":{"date-parts":[[2015,4,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1161","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2015-1161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:37Z","timestamp":1777444297000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2015-1161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4]]},"references-count":0,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2015,4]]}},"alternative-id":["10.3233\/FI-2015-1161"],"URL":"https:\/\/doi.org\/10.3233\/fi-2015-1161","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,4]]}}}