{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/fast-multiplication-of-large-integers","title":"Fast Multiplication of Large Integers: Implementation and Analysis of the DKSS Algorithm","arxiv_id":"1503.04955","date":"2015-03-17","proceeding":null,"authors":["Christoph Lüders"],"abstract":"The Sch\\\"onhage-Strassen algorithm (SSA) is the de-facto standard for multiplication of large integers. For $N$-bit numbers it has a time bound of $O(N \\cdot \\log N \\cdot \\log \\log N)$. De, Kurur, Saha and Saptharishi (DKSS) presented an asymptotically faster algorithm with a better time bound of $N \\cdot \\log N \\cdot 2^{O(\\log^* N)}$. In this diploma thesis, results of an implementation of DKSS multiplication are presented: run-time is about 30 times larger than SSA, while memory requirements are about 3.75 times higher than SSA. A possible crossover point is estimated to be out of reach even if we utilized the whole universe for computer memory.","url_abs":"http://arxiv.org/abs/1503.04955v1","url_pdf":"http://arxiv.org/pdf/1503.04955v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"fast-multiplication-of-large-integers","repo_url":"https://github.com/koii-network/deterministic-rsa-js","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"fast-multiplication-of-large-integers","repo_url":"https://github.com/open-koi/deterministic-rsa","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"fast-multiplication-of-large-integers","repo_url":"https://github.com/open-koi/deterministic-rsa-js","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}