{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T19:36:18Z","timestamp":1776800178685,"version":"3.51.2"},"reference-count":21,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,10,19]],"date-time":"2016-10-19T00:00:00Z","timestamp":1476835200000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000781","name":"European Research Council","doi-asserted-by":"publisher","award":["ERC-2013-StG-335086-LATTAC"],"award-info":[{"award-number":["ERC-2013-StG-335086-LATTAC"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ERC-2013-StG-335086-LATTAC"],"award-info":[{"award-number":["ERC-2013-StG-335086-LATTAC"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the selected polynomials can be modelled in terms of size and root properties. We propose a new kind of polynomial for GNFS: with a new degree of freedom, we further improve the size property. We demonstrate the efficiency of our algorithm by exhibiting a better polynomial than the one used for the factorization of RSA-768 and a polynomial for RSA-1024 that outperforms the best published one.<\/p>","DOI":"10.1090\/mcom3048","type":"journal-article","created":{"date-parts":[[2015,2,18]],"date-time":"2015-02-18T09:42:20Z","timestamp":1424252540000},"page":"861-873","source":"Crossref","is-referenced-by-count":7,"title":["Better polynomials for GNFS"],"prefix":"10.1090","volume":"85","author":[{"given":"Shi","family":"Bai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cyril","family":"Bouvier","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexander","family":"Kruppa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Zimmermann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2015,10,19]]},"reference":[{"key":"1","unstructured":"S. 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Boender, Factoring large integers with the quadratic sieve, PhD thesis, Leiden University, 1997."},{"key":"6","isbn-type":"print","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1007\/BFb0091539","article-title":"Factoring integers with the number field sieve","author":"Buhler, J. P.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/3540570136"},{"key":"7","isbn-type":"print","first-page":"267","article-title":"Smooth numbers: computational number theory and beyond","author":"Granville, Andrew","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780521808545"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"411","DOI":"10.5802\/jtnb.101","article-title":"Integers without large prime factors","volume":"5","author":"Hildebrand, Adolf","year":"1993","journal-title":"J. Th\\'{e}or. Nombres Bordeaux","ISSN":"https:\/\/id.crossref.org\/issn\/1246-7405","issn-type":"print"},{"issue":"256","key":"9","doi-asserted-by":"publisher","first-page":"2037","DOI":"10.1090\/S0025-5718-06-01870-9","article-title":"On polynomial selection for the general number field sieve","volume":"75","author":"Kleinjung, Thorsten","year":"2006","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"10","unstructured":"T. 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Murphy, Polynomial selection for the number field sieve integer factorisation algorithm, PhD thesis, The Australian National University, 1999."},{"key":"14","isbn-type":"print","first-page":"199","article-title":"On quadratic polynomials for the number field sieve","author":"Murphy, Brian","year":"1998","ISBN":"https:\/\/id.crossref.org\/isbn\/9813083921"},{"key":"15","unstructured":"J. Papadopoulos, Call for volunteers: RSA768 polynomial selection, 2011. \\url{http:\/\/www.mersenneforum.org\/showthread.php?t=15540}."},{"key":"16","unstructured":"J. Papadopoulos, Msieve v1.48, 2011, \\url{http:\/\/sourceforge.net\/projects\/msieve}."},{"key":"17","isbn-type":"print","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/BFb0091538","article-title":"The lattice sieve","author":"Pollard, J. 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Kleinjung, Cofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024 bit integers, \\url{http:\/\/www.hyperelliptic.org\/tanja\/SHARCS\/talks06\/thorsten.pdf}, 2005."}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-03048-8\/S0025-5718-2015-03048-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-03048-8\/S0025-5718-2015-03048-8.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:42:21Z","timestamp":1776796941000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2016-85-298\/S0025-5718-2015-03048-8\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,10,19]]},"references-count":21,"journal-issue":{"issue":"298","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["S0025-5718-2015-03048-8"],"URL":"https:\/\/doi.org\/10.1090\/mcom3048","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":[[2015,10,19]]}}}