φHash: A One-Way Hashing Algorithm Based on Alpay Algebra

φHash: A One-Way Hashing Algorithm Based on Alpay Algebra | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 27 May 2025 V1 Latest version Share on φHash: A One-Way Hashing Algorithm Based on Alpay Algebra Author : Faruk Alpay 0009-0009-2207-6528 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.174836949.92567592/v1 153 views 110 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract I introduce φHash, a novel one-way hash function defined entirely in the categorical framework of Alpay Algebra. In this setting, each input (finite or infinite sequence) is encoded as an object in a small cartesian-closed category A with a distinguished initial state I, and a transfinite evolution functor φ : A → A. Repeated application of φ with inputdependent updates yields a unique fixed-point object φ ∞ (I) that encapsulates the entire input data. The hash digest is then obtained by a universal φ-algebra "fold" (projection) onto an n-bit object in A. I formalize this construction axiomatically, prove determinism and one-wayness, and show that φHash resists both classical and quantum brute-force attacks. As illustrations, I symbolically compute φHash-256, φHash-512, and φHash-1024 of the word "alpay" within Alpay Algebra, verifying repeatability and irreversibility. Finally, I explain how φHash extends to arbitrary output lengths (including φHash-∞) via universal fold operators. Throughout, I rely solely on Faruk Alpay's foundational axioms and the SHA-256 standard for contrast. Supplementary Material File (hash__a_one_way_hashing_algorithm_based_on_alpay_algebra.pdf) Download 350.11 KB Information & Authors Information Version history V1 Version 1 27 May 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords alpay algebra category theory cryptographic hash functions fixed-point theory one-way functions post-quantum cryptography quantum resistance symbolic computation transfinite iteration universal fold operators Authors Affiliations Faruk Alpay 0009-0009-2207-6528 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 153 views 110 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Faruk Alpay. φHash: A One-Way Hashing Algorithm Based on Alpay Algebra. Authorea . 27 May 2025. 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