{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:14:43Z","timestamp":1777644883300,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2013,8,1]],"date-time":"2013-08-01T00:00:00Z","timestamp":1375315200000},"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":[[2013,8]]},"abstract":"<jats:p>\n                    Atkin's algorithm [2] for computing square roots in $Z^*_p$ , where p is a prime such that p \u2261 5 mod 8, has been extended by M\u00fcller [15] for the case p \u2261 9 mod 16. In this paper we extend Atkin's algorithm to the general case p \u2261 2\n                    <jats:sup>s<\/jats:sup>\n                    + 1 mod 2\n                    <jats:sup>s<\/jats:sup>\n                    + 1, for any s \u2265 2, thus providing a complete solution for the case p \u2261 1 mod 4. Complexity analysis and comparisons with other methods are also provided.\n                  <\/jats:p>","DOI":"10.3233\/fi-2013-853","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:27:32Z","timestamp":1575332852000},"page":"71-94","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["A Complete Generalization of Atkin's Square Root Algorithm"],"prefix":"10.1177","volume":"125","author":[{"given":"Armand Stefan","family":"Rotaru","sequence":"first","affiliation":[{"name":"Institute of Computer Science, Romanian Academy, Carol I no. 8, 700505 Iasi, Romania. armand.rotaru@iit.academiaromana-is.ro"}]},{"given":"Sorin","family":"Iftene","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Alexandru Ioan Cuza University, General Berthelot no. 16, 700483 Iasi, Romania. siftene@info.uaic.ro"}]}],"member":"179","published-online":{"date-parts":[[2013,8,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2013-853","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2013-853","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:30:37Z","timestamp":1777444237000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2013-853"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,8]]}},"alternative-id":["10.3233\/FI-2013-853"],"URL":"https:\/\/doi.org\/10.3233\/fi-2013-853","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,8]]}}}