{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T10:52:51Z","timestamp":1780051971927,"version":"3.53.1"},"reference-count":19,"publisher":"American Mathematical Society (AMS)","issue":"261","license":[{"start":{"date-parts":[[2008,5,14]],"date-time":"2008-05-14T00:00:00Z","timestamp":1210723200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We present a detailed analysis of SQUFOF, Daniel Shanks\u2019 Square Form Factorization algorithm. We give the average time and space requirements for SQUFOF. We analyze the effect of multipliers, either used for a single factorization or when racing the algorithm in parallel.<\/p>","DOI":"10.1090\/s0025-5718-07-02010-8","type":"journal-article","created":{"date-parts":[[2007,10,29]],"date-time":"2007-10-29T06:30:33Z","timestamp":1193639433000},"page":"551-588","source":"Crossref","is-referenced-by-count":6,"title":["Square form factorization"],"prefix":"10.1090","volume":"77","author":[{"given":"Jason","family":"Gower","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"suffix":"Jr.","given":"Samuel","family":"Wagstaff","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2007,5,14]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"183","DOI":"10.2307\/2005475","article-title":"A method of factoring and the factorization of \ud835\udc39\u2087","volume":"29","author":"Morrison, Michael A.","year":"1975","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"2","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4542-1","volume-title":"Binary quadratic forms","author":"Buell, Duncan A.","year":"1989","ISBN":"https:\/\/id.crossref.org\/isbn\/0387970371"},{"key":"3","series-title":"Graduate Texts in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02945-9","volume-title":"A course in computational algebraic number theory","volume":"138","author":"Cohen, Henri","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540556400"},{"key":"4","volume-title":"A second course in number theory","author":"Cohn, Harvey","year":"1962"},{"key":"5","unstructured":"Jason E. Gower. Square form factorization. Ph.D. thesis, Purdue University, December 2004."},{"key":"6","unstructured":"David Joyner and Stephen McMath. \\url{http:\/\/cadigweb.ew.usna.edu\/ wdj\/mcmath\/}."},{"key":"7","volume-title":"Continued fractions","author":"Khinchin, A. Ya.","year":"1964"},{"key":"8","isbn-type":"print","first-page":"123","article-title":"On the calculation of regulators and class numbers of quadratic fields","author":"Lenstra, H. W., Jr.","year":"1982","ISBN":"https:\/\/id.crossref.org\/isbn\/0521285135"},{"key":"9","unstructured":"J. S. Milne. Algebraic Number Theory, 1998. available at \\url{http:\/\/www.math.lsa.umich.edu\/ jmilne}."},{"key":"10","isbn-type":"print","volume-title":"An introduction to the theory of numbers","author":"Niven, Ivan","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0471625469","edition":"5"},{"key":"11","series-title":"Progress in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0251-6","volume-title":"Prime numbers and computer methods for factorization","volume":"126","author":"Riesel, Hans","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0817637435","edition":"2"},{"key":"12","unstructured":"D. Shanks. Analysis and Improvement of the Continued Fraction Method of Factorization. Abstract 720-10-43. Amer. Math. Soc. Notices, 22:A\u201368, 1975."},{"key":"13","unstructured":"Daniel Shanks. An Attempt to Factor \ud835\udc41=1002742628021. Manuscript, 3 pages, available at [6]."},{"key":"14","unstructured":"Daniel Shanks. Notes for Analysis and Improvement of the Continued Fraction Method of Factorization. Manuscript, 15 pages, available at [6]."},{"key":"15","unstructured":"Daniel Shanks. SQUFOF Notes. Manuscript, 30 pages, available at [6]."},{"key":"16","first-page":"415","article-title":"Class number, a theory of factorization, and genera","author":"Shanks, Daniel","year":"1971"},{"key":"17","first-page":"217","article-title":"The infrastructure of a real quadratic field and its applications","author":"Shanks, Daniel","year":"1972"},{"key":"18","first-page":"51","article-title":"Five number-theoretic algorithms","author":"Shanks, Daniel","year":"1973"},{"key":"19","series-title":"Computational Mathematics Series","isbn-type":"print","volume-title":"Cryptanalysis of number theoretic ciphers","author":"Wagstaff, Samuel S., Jr.","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/1584881534"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2008-77-261\/S0025-5718-07-02010-8\/S0025-5718-07-02010-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2008-77-261\/S0025-5718-07-02010-8\/S0025-5718-07-02010-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:10:58Z","timestamp":1776784258000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2008-77-261\/S0025-5718-07-02010-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,14]]},"references-count":19,"journal-issue":{"issue":"261","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["S0025-5718-07-02010-8"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-07-02010-8","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2007,5,14]]}}}