{"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/integer-factorization-by-sieving-the-delta","title":"Integer Factorization By Sieving The Delta","arxiv_id":"2109.09599","date":"2021-09-20","proceeding":null,"authors":["Vishal Mudgal"],"abstract":"Let $n = \\mathrm{p}\\!\\cdot\\!\\mathrm{q}$ (p < q) and $\\Delta = \\lvert p-q \\rvert$, where p,q are odd integers, then, it is hypothesized that factorizing this composite n will take O(1) time once the steady state value is reached for any $\\Delta$ in $zone_0$ of some observation deck (od) with specific dial settings. We also introduce a new factorization approach by looking for $\\Delta$ in different $\\Delta$ sieve zones. Once $\\Delta$ is found and $n$ is already given, one can easily find the factors of this composite n from any one of the following quadratic equations: $p^2 + p\\Delta -n = 0$ or $q^2 -q\\Delta -n = 0$. The new factorization approach does not rely on congruence of squares or any special properties of n, p or q and is only based on sieving the $\\Delta$. In addition, some other new factorization approaches are also discussed. Finally, a new trapdoor function is presented which is leveraged to encrypt and decrypt a message with different keys. The most fascinating part of the discovery is how addition is used in factorization of a semiprime number by making it yield the difference of its prime factors.","url_abs":"https://arxiv.org/abs/2109.09599v1","url_pdf":"https://arxiv.org/pdf/2109.09599v1.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":"integer-factorization-by-sieving-the-delta","repo_url":"https://github.com/vdeltasieve/arjun","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}