Four-Pixel Sum-Preserving Encryption Using the Chaotic Map for High Thumbnail-Preserving Image Security

Four-Pixel Sum-Preserving Encryption Using the Chaotic Map for High Thumbnail-Preserving Image Security | 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 Four-Pixel Sum-Preserving Encryption Using the Chaotic Map for High Thumbnail-Preserving Image Security Chia-Hung Kao, Guan-Zhen Chen, Yi-You Hou, Teh-Lu Liao This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8425176/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 21 You are reading this latest preprint version Abstract In cloud environments, traditional image encryption techniques often protect privacy at the expense of usability. To address this problem, thumbnail-preserving encryption (TPE) has been developed. In TPE, all information is hidden except for a recognizable low-resolution thumbnail of the encrypted image. This paper proposes a four-pixel sum-preserving encryption (SPE) method based on the use of a chaotic map. The method specifically addresses the problem of unencrypted residual pixels that arises with existing TPE schemes, particularly the three-pixel SPE scheme. This problem stems from the fact that pixel group sizes (which are powers of three) are not integer divisors of typical image block sizes (which are powers of two). The proposed method also offers higher security, algorithmic robustness, and computational efficiency. A sum-preserving substitution operation ensures that the sum of the pixel values in each encrypted four-pixel group is unchanged after encryption, guaranteeing perfect reversibility. Experimental results demonstrated that the design effectively hides the high-frequency details of an image while producing a recognizable thumbnail. Furthermore, the use of four-pixel SPE ensures a large key space and high sensitivity, resulting in high resistance to statistical and brute-force attacks. Physical sciences/Engineering Physical sciences/Mathematics and computing Four-pixel encryption logistic chaotic mapping sum-preserving encryption (SPE) thumbnail-preserving encryption (TPE) Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 16 Jan, 2026 Reviews received at journal 15 Jan, 2026 Reviews received at journal 13 Jan, 2026 Reviews received at journal 13 Jan, 2026 Reviews received at journal 12 Jan, 2026 Reviewers agreed at journal 11 Jan, 2026 Reviewers agreed at journal 11 Jan, 2026 Reviewers agreed at journal 09 Jan, 2026 Reviewers agreed at journal 09 Jan, 2026 Reviewers agreed at journal 08 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviews received at journal 07 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers agreed at journal 07 Jan, 2026 Reviewers agreed at journal 06 Jan, 2026 Reviewers invited by journal 06 Jan, 2026 Editor assigned by journal 06 Jan, 2026 Editor invited by journal 30 Dec, 2025 Submission checks completed at journal 25 Dec, 2025 First submitted to journal 25 Dec, 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-8425176","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":571130994,"identity":"c9eb54b0-b820-4441-8582-c8237aa09523","order_by":0,"name":"Chia-Hung Kao","email":"","orcid":"","institution":"National Cheng Kung University","correspondingAuthor":false,"prefix":"","firstName":"Chia-Hung","middleName":"","lastName":"Kao","suffix":""},{"id":571131000,"identity":"6820667c-ae47-41e9-914f-3d07b45f8d47","order_by":1,"name":"Guan-Zhen Chen","email":"","orcid":"","institution":"Air Force Institute of 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chaotic mapping, sum-preserving encryption (SPE), thumbnail-preserving encryption (TPE)","lastPublishedDoi":"10.21203/rs.3.rs-8425176/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8425176/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn cloud environments, traditional image encryption techniques often protect privacy at the expense of usability. To address this problem, thumbnail-preserving encryption (TPE) has been developed. In TPE, all information is hidden except for a recognizable low-resolution thumbnail of the encrypted image. This paper proposes a four-pixel sum-preserving encryption (SPE) method based on the use of a chaotic map. The method specifically addresses the problem of unencrypted residual pixels that arises with existing TPE schemes, particularly the three-pixel SPE scheme. This problem stems from the fact that pixel group sizes (which are powers of three) are not integer divisors of typical image block sizes (which are powers of two). The proposed method also offers higher security, algorithmic robustness, and computational efficiency. A sum-preserving substitution operation ensures that the sum of the pixel values in each encrypted four-pixel group is unchanged after encryption, guaranteeing perfect reversibility. Experimental results demonstrated that the design effectively hides the high-frequency details of an image while producing a recognizable thumbnail. Furthermore, the use of four-pixel SPE ensures a large key space and high sensitivity, resulting in high resistance to statistical and brute-force attacks.\u003c/p\u003e","manuscriptTitle":"Four-Pixel Sum-Preserving Encryption Using the Chaotic Map for High Thumbnail-Preserving Image Security","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-01-08 10:19:25","doi":"10.21203/rs.3.rs-8425176/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-16T05:31:26+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-15T09:47:28+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-14T03:49:54+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-14T00:41:54+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-13T00:33:09+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87738765519961694895037393826815156514","date":"2026-01-11T22:29:31+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"227278524826405686019324166869828062073","date":"2026-01-11T18:23:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"243417736824007910009821578697773278049","date":"2026-01-09T08:31:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"83788078584512748699831857639923183842","date":"2026-01-09T05:28:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"339388663876147505119270953425649841975","date":"2026-01-08T12:44:16+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"255120682466934346999700557426294344499","date":"2026-01-08T00:35:43+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-01-07T11:38:20+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"245235857455559893875783368487620510356","date":"2026-01-07T10:24:52+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"215828360429412822559106318498278207106","date":"2026-01-07T06:17:22+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"134004587255979784244138820076208218452","date":"2026-01-07T05:08:41+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"87738765519961694895037393826815156514","date":"2026-01-07T04:59:45+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-01-07T04:48:35+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-01-07T03:53:16+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-30T06:15:15+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-25T13:41:33+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-12-25T13:34:22+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":"752be2c9-e03f-44d0-8041-e7d9ad22a2e1","owner":[],"postedDate":"January 8th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":60776429,"name":"Physical sciences/Engineering"},{"id":60776430,"name":"Physical sciences/Mathematics and computing"}],"tags":[],"updatedAt":"2026-03-30T04:54:34+00:00","versionOfRecord":[],"versionCreatedAt":"2026-01-08 10:19:25","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8425176","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8425176","identity":"rs-8425176","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}