Efficient Image Encryption Approach by Lorenz Chaotic Maps, SHA-256, and Discrete-Time Quantum Walks

Efficient Image Encryption Approach by Lorenz Chaotic Maps, SHA-256, and Discrete-Time Quantum Walks | 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 Article Efficient Image Encryption Approach by Lorenz Chaotic Maps, SHA-256, and Discrete-Time Quantum Walks M. Karmany, A. Moawad, M. Abaza, A. Mansour, A. Alfalou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7710829/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 19 You are reading this latest preprint version Abstract This paper describes a novel image encryption scheme that combines Lorenz chaotic maps, the secure Hash Algorithm 256 (SHA-256), and Discrete-Time Quantum Walks (DTQWs). It exploits their sensitivity to their initial conditions, their innate capacity to produce complex randomness, and their adaptability for rapid computational procedures. The chaotic sequences resulting from the Lorenz maps undergoes are utilized in bitwise modular addition operations, for diffusion. DTQWs develop dynamic Substitution Boxes (S-Boxes), that increase confusion by modifying the adaptability of rows/columns. To achieve stronger security, SHA-256 is used to encrypt the plaintext in successive stages, producing hash-dependent quantum coin rotation angles and thereby injects plaintext sensitivity into S-Box construction. It guarantees high-level randomness, low correlation coefficients close to zero, and high immunity to statistical and differential attacks. Outcomes demonstrate better security and computation efficiency compared to available methods, qualifying it as an efficient and reliable solution for secure image transmission within present-day communication systems. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Image Encryption Lorenz Chaotic Systems SHA-256 Discrete Time Quantum Walk (DTQW) Modular Addition S-Box Substitution Statistical Security Analysis Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 19 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 14 Oct, 2025 Reviews received at journal 14 Oct, 2025 Reviews received at journal 12 Oct, 2025 Reviews received at journal 10 Oct, 2025 Reviews received at journal 10 Oct, 2025 Reviewers agreed at journal 08 Oct, 2025 Reviewers agreed at journal 08 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers agreed at journal 07 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviews received at journal 06 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviewers agreed at journal 06 Oct, 2025 Reviewers invited by journal 06 Oct, 2025 Editor assigned by journal 29 Sep, 2025 Submission checks completed at journal 28 Sep, 2025 First submitted to journal 25 Sep, 2025 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-7710829","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":529414351,"identity":"89c0d219-7d57-4231-aed8-79dc03110b04","order_by":0,"name":"M. 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Walks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Image Encryption, Lorenz Chaotic Systems, SHA-256, Discrete Time Quantum Walk (DTQW), Modular Addition, S-Box Substitution, Statistical Security Analysis","lastPublishedDoi":"10.21203/rs.3.rs-7710829/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7710829/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper describes a novel image encryption scheme that combines Lorenz chaotic maps, the secure Hash Algorithm 256 (SHA-256), and Discrete-Time Quantum Walks (DTQWs). It exploits their sensitivity to their initial conditions, their innate capacity to produce complex randomness, and their adaptability for rapid computational procedures. The chaotic sequences resulting from the Lorenz maps undergoes are utilized in bitwise modular addition operations, for diffusion. DTQWs develop dynamic Substitution Boxes (S-Boxes), that increase confusion by modifying the adaptability of rows/columns. To achieve stronger security, SHA-256 is used to encrypt the plaintext in successive stages, producing hash-dependent quantum coin rotation angles and thereby injects plaintext sensitivity into S-Box construction. It guarantees high-level randomness, low correlation coefficients close to zero, and high immunity to statistical and differential attacks. Outcomes demonstrate better security and computation efficiency compared to available methods, qualifying it as an efficient and reliable solution for secure image transmission within present-day communication systems.\u003c/p\u003e","manuscriptTitle":"Efficient Image Encryption Approach by Lorenz Chaotic Maps, SHA-256, and Discrete-Time Quantum Walks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-17 04:22:25","doi":"10.21203/rs.3.rs-7710829/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-10-14T10:56:24+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-14T08:32:18+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-13T03:09:20+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-11T01:57:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-10T23:07:51+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"129110134288506260259110303454804944102","date":"2025-10-08T09:48:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"319412907133577196759944953654739719783","date":"2025-10-08T08:45:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"188996892989337144215485820941637419834","date":"2025-10-07T15:32:04+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"94893087160970321194394939941702754954","date":"2025-10-07T07:46:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"12799338297669129571505024784905038785","date":"2025-10-06T13:58:55+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-06T12:54:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"160876382573856829264634382068898214426","date":"2025-10-06T11:34:07+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"243417736824007910009821578697773278049","date":"2025-10-06T10:35:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"243796022262228222580087286393057725381","date":"2025-10-06T10:11:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87738765519961694895037393826815156514","date":"2025-10-06T10:04:21+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-06T09:41:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-09-29T09:33:55+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-09-29T00:39:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-09-25T08:44:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"73c0eb59-0c63-4304-a998-dd810346be5e","owner":[],"postedDate":"October 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":56270628,"name":"Physical sciences/Engineering"},{"id":56270629,"name":"Physical sciences/Mathematics and computing"},{"id":56270630,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-01-26T16:01:27+00:00","versionOfRecord":{"articleIdentity":"rs-7710829","link":"https://doi.org/10.1038/s41598-025-33365-0","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-19 15:58:18","publishedOnDateReadable":"January 19th, 2026"},"versionCreatedAt":"2025-10-17 04:22:25","video":"","vorDoi":"10.1038/s41598-025-33365-0","vorDoiUrl":"https://doi.org/10.1038/s41598-025-33365-0","workflowStages":[]},"version":"v1","identity":"rs-7710829","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7710829","identity":"rs-7710829","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}