A method for constructing post-quantum EDS algorithms with small signature and public key sizes based on finite noncommutative associative algebras with two hidden groups

A method for constructing post-quantum EDS algorithms with small signature and public key sizes based on finite noncommutative associative algebras with two hidden groups | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A method for constructing post-quantum EDS algorithms with small signature and public key sizes based on finite noncommutative associative algebras with two hidden groups Alexey Petrenko, Natalie Grigorieva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7943157/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper presents a novel methodology for constructing post-quantum digital signature algorithms based on finite noncommutative associative algebras. The proposed approach enhances signature randomization by leveraging the algebraic interaction of two hidden noncommutative groups and chaotic mappings, resulting in both compact key representations and increased cryptographic robustness. A core contribution is the implementation of evolutionary algorithms for the automated design of multiplication tables, ensuring associativity and optimized performance. One-time exponent parameters b and n are generated using logistic mappings to introduce chaos, thereby impeding statistical cryptanalysis even in scenarios involving bulk signature analysis. Experimental evaluation confirms the exponential complexity of attack models under optimized parameters, while also validating efficient real-world implementation using Python and NumPy. This work is the first to systematically apply evolutionary search to the generation of algebraic structures for digital signatures, demonstrating practical post-quantum security and computational feasibility. post-quantum cryptography noncommutative associative algebras double randomization of signature chaotic maps evolutionary algorithms hidden commutative groups quantum stability digital signature algebraic structure key generation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7943157","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":546782484,"identity":"d1fdb90c-021f-4731-b0b2-fa999580a40d","order_by":0,"name":"Alexey Petrenko","email":"","orcid":"","institution":"Sirius University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Alexey","middleName":"","lastName":"Petrenko","suffix":""},{"id":546782485,"identity":"00da05e7-5b42-469a-b031-176b6bacf0f7","order_by":1,"name":"Natalie 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maps, evolutionary algorithms, hidden commutative groups, quantum stability, digital signature, algebraic structure, key generation","lastPublishedDoi":"10.21203/rs.3.rs-7943157/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7943157/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper presents a novel methodology for constructing post-quantum digital signature algorithms based on finite noncommutative associative algebras. The proposed approach enhances signature randomization by leveraging the algebraic interaction of two hidden noncommutative groups and chaotic mappings, resulting in both compact key representations and increased cryptographic robustness. A core contribution is the implementation of evolutionary algorithms for the automated design of multiplication tables, ensuring associativity and optimized performance. One-time exponent parameters b and n are generated using logistic mappings to introduce chaos, thereby impeding statistical cryptanalysis even in scenarios involving bulk signature analysis. Experimental evaluation confirms the exponential complexity of attack models under optimized parameters, while also validating efficient real-world implementation using Python and NumPy. 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