Complex dynamics of a 2D Rosenbrock-Schwefel hyperchaotic map and its application to topology-evolving image encryption

Complex dynamics of a 2D Rosenbrock-Schwefel hyperchaotic map and its application to topology-evolving 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 Complex dynamics of a 2D Rosenbrock-Schwefel hyperchaotic map and its application to topology-evolving image encryption Wenjun Song, Hao Shen, Xuncai Zhang, Chengye Zou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9414004/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 Addressing the security vulnerabilities of digital image transmission and the limited chaotic ranges of existing schemes, this paper proposes a robust image encryption algorithm driven by a novel discrete dynamical system. The core contribution is the formulation of a two-dimensional Rosenbrock-Schwefel (2D-RS) hyperchaotic map. By coupling the Rosenbrock function's valley structure with the Schwefel function's multi-peak oscillations, dynamical analysis verifies that the 2D-RS map generates pseudo-random sequences with wider chaotic ranges, robust hyperchaoticity, and superior ergodicity. To overcome the limitations of traditional spatial scrambling, a bidirectional oscillatory permutation algorithm is designed utilizing a dynamic linked-list topology. This topology evolves continuously at the pixel level during encryption, significantly amplifying traversal path complexity and resisting structural cryptanalysis. Furthermore, a state-dependent adaptive diffusion mechanism is introduced to enforce strict plaintext sensitivity and ensure a global avalanche effect. Comprehensive signal processing evaluations confirm the scheme achieves near-ideal information entropy, minimal pixel correlation, and successfully thwarts standard differential and statistical attacks. Crucially, the algorithm exhibits outstanding robustness against data cropping and noise interference, validating its practical reliability for secure image transmission over non-ideal communication channels. 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-9414004","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":628290608,"identity":"0bf8cfe2-5628-4c8e-b0d7-48f596826166","order_by":0,"name":"Wenjun Song","email":"","orcid":"","institution":"Zhengzhou University of Light Industry","correspondingAuthor":false,"prefix":"","firstName":"Wenjun","middleName":"","lastName":"Song","suffix":""},{"id":628290609,"identity":"779f1735-d276-422e-a705-0a670e807d01","order_by":1,"name":"Hao Shen","email":"","orcid":"","institution":"Zhengzhou University of Light Industry","correspondingAuthor":false,"prefix":"","firstName":"Hao","middleName":"","lastName":"Shen","suffix":""},{"id":628290611,"identity":"6913a442-a269-466c-a043-dbf92b8753a7","order_by":2,"name":"Xuncai Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA80lEQVRIiWNgGAWjYDACCTiLsfEBwwEQI4F4Lc0GpGphYJMgSov87OZnD7+2Hc7jbz/cVl1w5jADP3uOAcPPHbi1MM45Zm4sc+ZwscSZxLbbM24cZpDseWPA2HsGtxZmiQQzaYmKw4kbGIBaeD4cZjC4kWPAzNiGWwubRPo3aQkDoBb+h23FIC32hLTwSOSYSX4A2SKR2MbMA3SYgQQBLRISOWXSDGfSE2fceNgsPeNMOo/EmWcFB3vxaJGfkb5N8mebdWJ/f/rDzwXHrOX425M3PviJRws4CHhgDJBLQYwD+DUAA/oHkpZRMApGwSgYBRgAALopUzjipzOvAAAAAElFTkSuQmCC","orcid":"","institution":"Zhengzhou University of Light Industry","correspondingAuthor":true,"prefix":"","firstName":"Xuncai","middleName":"","lastName":"Zhang","suffix":""},{"id":628290613,"identity":"d75ec721-3335-42fc-b14f-340a63b6eed0","order_by":3,"name":"Chengye Zou","email":"","orcid":"","institution":"Yanshan University","correspondingAuthor":false,"prefix":"","firstName":"Chengye","middleName":"","lastName":"Zou","suffix":""}],"badges":[],"createdAt":"2026-04-14 10:11:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9414004/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9414004/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":108350689,"identity":"f6b05764-3035-47df-b551-2385337c4629","added_by":"auto","created_at":"2026-05-03 10:24:58","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2054323,"visible":true,"origin":"","legend":"","description":"","filename":"Complexdynamicsofa2DRosenbrockSchwefelhyperchaoticmapanditsapplicationtotopologyevolvingimageencryption.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9414004/v1_covered_6a124dbb-e9c5-4ddc-9949-42a5f13c1588.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Complex dynamics of a 2D Rosenbrock-Schwefel hyperchaotic map and its application to topology-evolving 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":"","lastPublishedDoi":"10.21203/rs.3.rs-9414004/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9414004/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAddressing the security vulnerabilities of digital image transmission and the limited chaotic ranges of existing schemes, this paper proposes a robust image encryption algorithm driven by a novel discrete dynamical system. The core contribution is the formulation of a two-dimensional Rosenbrock-Schwefel (2D-RS) hyperchaotic map. By coupling the Rosenbrock function's valley structure with the Schwefel function's multi-peak oscillations, dynamical analysis verifies that the 2D-RS map generates pseudo-random sequences with wider chaotic ranges, robust hyperchaoticity, and superior ergodicity. To overcome the limitations of traditional spatial scrambling, a bidirectional oscillatory permutation algorithm is designed utilizing a dynamic linked-list topology. This topology evolves continuously at the pixel level during encryption, significantly amplifying traversal path complexity and resisting structural cryptanalysis. Furthermore, a state-dependent adaptive diffusion mechanism is introduced to enforce strict plaintext sensitivity and ensure a global avalanche effect. Comprehensive signal processing evaluations confirm the scheme achieves near-ideal information entropy, minimal pixel correlation, and successfully thwarts standard differential and statistical attacks. 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