Beyond Fixed Maps: Robust and Flexible Chaotic PRNGs Applied to Image Encryption

Beyond Fixed Maps: Robust and Flexible Chaotic PRNGs Applied to Image Encryption | 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 Beyond Fixed Maps: Robust and Flexible Chaotic PRNGs Applied to Image Encryption Milad Mohammadian, Bahadin Azizinasab, Mohammad Saeed Khayaty, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7117936/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 Chaos-based Pseudo-Random Number Generators (PRNGs) have achieved considerable attention due to their inherent randomness and deterministic properties. However, reliance on a single chaotic map may yield insufficient randomness because of intrinsic structural patterns. To mitigate this limitation, a proposed PRNG framework employs multiple state variables from chaotic systems and incorporates an XOR operation to improve bit randomness. This method exhibits high flexibility, permitting integration of any chaotic map contingent upon specific computational resources and application needs. In contrast to conventional chaos-based PRNGs, which are limited by fixed maps, the present approach offers enhanced adaptability. The proposed framework was implemented using four chaotic maps, including the one-dimensional logistic map, the two-dimensional logistic map, the two-dimensional hénon map, and the three-dimensional Lorenz system. Extensive evaluations, including NIST, TestU01, key sensitivity analysis, autocorrelation tests, time complexity assessments, and Monte Carlo (\pi) estimation, were conducted to verify the quality of the proposed algorithm. Cryptographic applicability was further evaluated through the implementation of a two-phase image-encryption scheme. Each RGB channel undergoes a PRNG‐driven permutation to disrupt pixel adjacency, followed by multi‐round diffusion based on neighboring intensities and key bits. Uniform histograms, near‐zero pixel correlations, high Number of Pixels Change Rate and Unified Average Changing Intensity values, and perfect decryption verify that our flexible PRNG framework provides robust security and lossless reversibility in image processing. The results confirmed its strong randomness, high sensitivity to initial conditions, and computational efficiency. Pseudo-random number generator Chaos theory NIST Logistic map H´enon map Lorenz system Image encryption 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-7117936","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":486179419,"identity":"db5d682c-84d4-4611-ba19-2a2b17e7f436","order_by":0,"name":"Milad Mohammadian","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Milad","middleName":"","lastName":"Mohammadian","suffix":""},{"id":486179420,"identity":"fc768d4b-9331-4429-b199-1d082a5e7cdd","order_by":1,"name":"Bahadin Azizinasab","email":"","orcid":"","institution":"University of Guilan","correspondingAuthor":false,"prefix":"","firstName":"Bahadin","middleName":"","lastName":"Azizinasab","suffix":""},{"id":486179421,"identity":"5fc1fe9a-681f-461c-b27e-2aa60504b524","order_by":2,"name":"Mohammad Saeed Khayaty","email":"","orcid":"","institution":"University of Tabriz","correspondingAuthor":false,"prefix":"","firstName":"Mohammad","middleName":"Saeed","lastName":"Khayaty","suffix":""},{"id":486179422,"identity":"03d54067-cb8f-4f9a-884a-e2b7001cb5ad","order_by":3,"name":"Mosleh Yousefi","email":"","orcid":"","institution":"University of Guilan","correspondingAuthor":false,"prefix":"","firstName":"Mosleh","middleName":"","lastName":"Yousefi","suffix":""},{"id":486179423,"identity":"3e9cb85a-bf9f-4704-92fc-b113bd2a291a","order_by":4,"name":"Sheida Mohammadpour","email":"","orcid":"","institution":"Shahid Beheshti University","correspondingAuthor":false,"prefix":"","firstName":"Sheida","middleName":"","lastName":"Mohammadpour","suffix":""},{"id":486179424,"identity":"c4055292-c832-4ba8-8595-bef14a5b0aa6","order_by":5,"name":"Bahman Ahmadi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA1UlEQVRIiWNgGAWjYBACAwYGNiDFzMOPEGNuIE6LZAMzlM/ASJwWBoMDxGoxZ2B+9uhGjbWM8Y38YxIfd/yRY5BuxK/FsoHN3DjnWDqP2Y1kNsmZZwyMGWQOEnDYAQYz6Ry2w2Att3nbDBIbJBIJaWH/Jp3z7zCP8Qyglr9tBvVEaOExk85tO8xjIAHUwthmkMBASItlM0+ZdG5fOo/EmcfmP3vbjA3bCGkxZ2/fJp3zzdqevz3xscHPNjl5fonkA3i1MDCjC7DhVz8KRsEoGAWjgBgAAKSMPwQXyLI5AAAAAElFTkSuQmCC","orcid":"","institution":"University of Twente","correspondingAuthor":true,"prefix":"","firstName":"Bahman","middleName":"","lastName":"Ahmadi","suffix":""}],"badges":[],"createdAt":"2025-07-14 07:08:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7117936/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7117936/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":102295215,"identity":"25a129f4-4bbf-4279-8204-eaad4275d962","added_by":"auto","created_at":"2026-02-10 10:09:55","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":20058792,"visible":true,"origin":"","legend":"","description":"","filename":"MiladND.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7117936/v1_covered_1d692a10-5735-44db-b9d8-416d7c8716a6.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Beyond Fixed Maps: Robust and Flexible Chaotic PRNGs Applied to Image Encryption","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Pseudo-random number generator, Chaos theory, NIST, Logistic map, H´enon map, Lorenz system, Image encryption","lastPublishedDoi":"10.21203/rs.3.rs-7117936/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7117936/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Chaos-based Pseudo-Random Number Generators (PRNGs) have achieved considerable attention due to their inherent randomness and deterministic properties. However, reliance on a single chaotic map may yield insufficient randomness because of intrinsic structural patterns. To mitigate this limitation, a proposed PRNG framework employs multiple state variables from chaotic systems and incorporates an XOR operation to improve bit randomness. This method exhibits high flexibility, permitting integration of any chaotic map contingent upon specific computational resources and application needs. In contrast to conventional chaos-based PRNGs, which are limited by fixed maps, the present approach offers enhanced adaptability. The proposed framework was implemented using four chaotic maps, including the one-dimensional logistic map, the two-dimensional logistic map, the two-dimensional hénon map, and the three-dimensional Lorenz system. 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