{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T12:40:43Z","timestamp":1767789643025,"version":"3.49.0"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T00:00:00Z","timestamp":1767744000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T00:00:00Z","timestamp":1767744000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Scientific Research Deanship at the University of Ha\u2019il, Saudi Arabia","award":["RG-23 143"],"award-info":[{"award-number":["RG-23 143"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Supercomput"],"DOI":"10.1007\/s11227-025-08179-6","type":"journal-article","created":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T07:13:04Z","timestamp":1767769984000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Performance enhancement of Fermat factorization algorithm on multicore systems"],"prefix":"10.1007","volume":"82","author":[{"given":"Yasser","family":"Kotb","sequence":"first","affiliation":[]},{"given":"Khaled A.","family":"Fathy","sequence":"additional","affiliation":[]},{"given":"Ibrahim M.","family":"Alseadoon","sequence":"additional","affiliation":[]},{"given":"Mohamed A. G.","family":"Hazber","sequence":"additional","affiliation":[]},{"given":"Hazem M.","family":"Bahig","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,1,7]]},"reference":[{"key":"8179_CR1","doi-asserted-by":"publisher","unstructured":"Lenstra A (2017) General Purpose Integer Factoring. In: Bos JW, Lenstra AK, eds. Topics in Computational Number Theory Inspired by Peter L. Montgomery. Cambridge University Press, https:\/\/doi.org\/10.1017\/9781316271575","DOI":"10.1017\/9781316271575"},{"key":"8179_CR2","doi-asserted-by":"publisher","unstructured":"Hoffstein J, Pipher J, Silverman J (2014) Integer Factorization and RSA. In: An Introduction to Mathematical Cryptography. Undergraduate Texts in Mathematics, Springer, 117\u2013191, https:\/\/doi.org\/10.1007\/978-1-4939-1711-2-3","DOI":"10.1007\/978-1-4939-1711-2-3"},{"key":"8179_CR3","doi-asserted-by":"publisher","unstructured":"Rubinstein-Salzedo SC, Algorithms F, Testing P (2018) In: Cryptography. Springer Undergraduate Mathematics Series. Springer. Cham. https:\/\/doi.org\/10.1007\/978-3-319-94818-8-13","DOI":"10.1007\/978-3-319-94818-8-13"},{"key":"8179_CR4","doi-asserted-by":"publisher","first-page":"1897","DOI":"10.3390\/sym14091897","volume":"14","author":"H Bahig","year":"2022","unstructured":"Bahig H, Nassr D, Mahdi M, Bahig H (2022) Small private exponent attacks on RSA using continued fractions and multicore systems. Symmetry 14:1897. https:\/\/doi.org\/10.3390\/sym14091897","journal-title":"Symmetry"},{"key":"8179_CR5","doi-asserted-by":"publisher","first-page":"86","DOI":"10.37394\/23205.2025.24.8","volume":"24","author":"Zihan Guan","year":"2025","unstructured":"Guan Zihan, Zhuang Xiaodong, Mastorakis Nikos E (2025) Optimization of quadratic sieve algorithm implementation for large integer factorization. WSEAS Trans Comput 24:86\u201391. https:\/\/doi.org\/10.37394\/23205.2025.24.8","journal-title":"WSEAS Trans Comput"},{"key":"8179_CR6","unstructured":"B\u00f6ck Hanno (2023) Fermat factorization in the wild. Cryptology ePrint Archive, Paper 2023\/026, https:\/\/eprint.iacr.org\/2023\/026"},{"issue":"12","key":"8179_CR7","doi-asserted-by":"publisher","first-page":"340","DOI":"10.14569\/IJACSA.2020.0111242","volume":"11","author":"H Bahig","year":"2020","unstructured":"Bahig H, Mahdi M, Alutaibi K, AlGhadhban A, Bahig H (2020) Performance analysis of Fermat factorization algorithms. Int J Adv Comput Sci Appl 11(12):340\u2013350. https:\/\/doi.org\/10.14569\/IJACSA.2020.0111242","journal-title":"Int J Adv Comput Sci Appl"},{"key":"8179_CR8","doi-asserted-by":"publisher","first-page":"1203","DOI":"10.3390\/math11051203","volume":"11","author":"AM Zaki","year":"2023","unstructured":"Zaki AM, Bakr ME, Alsahangiti AM, Khosa SK, Fathy KA (2023) Acceleration of wheel factoring techniques. Mathematics 11:1203. https:\/\/doi.org\/10.3390\/math11051203","journal-title":"Mathematics"},{"key":"8179_CR9","doi-asserted-by":"publisher","first-page":"15730","DOI":"10.1007\/s11227-022-04470-y","volume":"78","author":"H Bahig","year":"2022","unstructured":"Bahig H, Nassr D, Mahdi M, Hazber M, Al-Utaibi K, Bahig H (2022) Speeding up wheel factoring method. J Supercomput 78:15730\u201315748. https:\/\/doi.org\/10.1007\/s11227-022-04470-y","journal-title":"J Supercomput"},{"key":"8179_CR10","doi-asserted-by":"publisher","first-page":"312","DOI":"10.3390\/sym14020312","volume":"14","author":"K Somsuk","year":"2022","unstructured":"Somsuk K (2022) An efficient variant of Pollard\u2019s $$p-1$$ for the case that all prime factors of the $$p-1$$ in B$$-$$smooth. Symmetry 14:312. https:\/\/doi.org\/10.3390\/sym14020312","journal-title":"Symmetry"},{"key":"8179_CR11","doi-asserted-by":"publisher","unstructured":"Somsuk K (2014) Algorithm NMIF, a using integer modulo 20\u2019s technique. In: International Computer Science and Engineering Conference (ICSEC), pp 312\u2013316. IEEE. https:\/\/doi.org\/10.1109\/ICSEC.2014.6978214","DOI":"10.1109\/ICSEC.2014.6978214"},{"key":"8179_CR12","doi-asserted-by":"publisher","first-page":"99","DOI":"10.6633\/IJNS.201701.19(1).11","volume":"19","author":"K Somsuk","year":"2017","unstructured":"Somsuk K, Tientanopajai K (2017) An improvement of Fermat\u2019s factorization by considering the last m digits of modulus to decrease computation time. Int J Netw Secur 19:99\u2013111. https:\/\/doi.org\/10.6633\/IJNS.201701.19(1).11","journal-title":"Int J Netw Secur"},{"key":"8179_CR13","doi-asserted-by":"publisher","first-page":"1469","DOI":"10.11591\/ijece.v10i2.pp1469-1476","volume":"10","author":"K Somsuk","year":"2020","unstructured":"Somsuk K (2020) The new integer factorization algorithm based on Fermat\u2019s factorization algorithm and Euler\u2019s theorem. Int J Electr Comput Eng 10:1469\u201376","journal-title":"Int J Electr Comput Eng"},{"issue":"4","key":"8179_CR14","doi-asserted-by":"publisher","first-page":"323","DOI":"10.14569\/IJACSA.2020.0110444","volume":"11","author":"H Bahig","year":"2020","unstructured":"Bahig H, Bahig H, Kotb Y (2020) Fermat factorization using a multi-core system. Int J Adv Comput Sci Appl 11(4):323\u2013330. https:\/\/doi.org\/10.14569\/IJACSA.2020.0110444","journal-title":"Int J Adv Comput Sci Appl"},{"issue":"4","key":"8179_CR15","doi-asserted-by":"publisher","first-page":"167","DOI":"10.17706\/jsw.16.4.167-173","volume":"16","author":"J Li","year":"2021","unstructured":"Li J, Liu M (2021) Parallel strategy to factorize Fermat numbers with implementation in Maple software. J Softw 16(4):167\u2013173","journal-title":"J Softw"},{"key":"8179_CR16","doi-asserted-by":"crossref","unstructured":"Bahig H (2022) Speeding up Fermat\u2019s factoring method using precomputation. Annals Emerg Technol Comput (AETiC) 6(2)","DOI":"10.33166\/AETiC.2022.02.004"},{"key":"8179_CR17","doi-asserted-by":"publisher","first-page":"2024ss0101","DOI":"10.31893\/multiscience.2024ss0101","volume":"6","author":"K Balasubramanian","year":"2023","unstructured":"Balasubramanian K, Pitchai MP (2023) A survey of Fermat factorization algorithms for factoring RSA composite numbers. Multidiscip Sci J 6:2024ss0101. https:\/\/doi.org\/10.31893\/multiscience.2024ss0101","journal-title":"Multidiscip Sci J"},{"key":"8179_CR18","unstructured":"OpenMP. https:\/\/www.openmp.org\/"},{"key":"8179_CR19","unstructured":"GMP. library, GNU multiple precision arithmetic library. https:\/\/gmplib.org\/"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-08179-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-08179-6","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-08179-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,7]],"date-time":"2026-01-07T07:13:07Z","timestamp":1767769987000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-08179-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,7]]},"references-count":19,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["8179"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-08179-6","relation":{},"ISSN":["1573-0484"],"issn-type":[{"value":"1573-0484","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,1,7]]},"assertion":[{"value":"14 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"49"}}