An efficient and effective matrix and transformation based Cryptographic algorithm

An efficient and effective matrix and transformation based Cryptographic algorithm | 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 An efficient and effective matrix and transformation based Cryptographic algorithm Abobakkar Siddeeq, Muhammad Asif, Hassan Khan, Samardin Jebran This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6585441/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 In this paper, we demonstrated the application of the Abaoub Shkheam transform, the Gupta integral transform, and the matrix decomposition of the non-singular matrix to improve the security of two-way communication. In 2024, Khalat et al. utilized the matrix-based technique to examine the word ”[weather]” in the form of a third-order matrix solution and using the Abaoub Shkheam transform [14]. In this work, we have extended the work of Khalat et al. and the new cryptography procedure is established for the sentence ”THE FLOWERS ARE SO COLORFUL” and compared the results with two transformations, namely the Abaoub Shkheam transform and the Gupta integral transform. The purpose of this study, is to develop a technique for data encryption and decryption utilizing matrix decomposition, Gupta integral transform and Abaoub Shkheam transform. For encryption, select the plain text as the original data and transfer it to encrypted text using the hyperbolic function and lower triangular matrix for encryption. Secondly, for decryption using the inverse suggested transformations, a hyperbolic function and the upper triangular matrix. The current procedure can be understand easily by using tabular data. Cryptography Encryption Decryption Gupta integral transform Abaoub Shkheam transform lower and upper triangular matrices 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-6585441","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":451779946,"identity":"b8b6a5f5-5196-4759-a3ef-2dea799506be","order_by":0,"name":"Abobakkar Siddeeq","email":"","orcid":"","institution":"Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Abobakkar","middleName":"","lastName":"Siddeeq","suffix":""},{"id":451779947,"identity":"5ce66c4e-0273-4ccb-b25b-f9c5099fbe82","order_by":1,"name":"Muhammad Asif","email":"","orcid":"","institution":"Imam Mohammad ibn Saud Islamic University","correspondingAuthor":false,"prefix":"","firstName":"Muhammad","middleName":"","lastName":"Asif","suffix":""},{"id":451779949,"identity":"c719394f-7aba-4f3a-89b9-e00e98e3231b","order_by":2,"name":"Hassan Khan","email":"","orcid":"","institution":"Wali Khan University Mardan","correspondingAuthor":false,"prefix":"","firstName":"Hassan","middleName":"","lastName":"Khan","suffix":""},{"id":451779952,"identity":"ca323fe3-9b8c-49e0-8b8c-68ebdb7d44f7","order_by":3,"name":"Samardin Jebran","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABCklEQVRIiWNgGAWjYBAC9gYeJB6PAYOcBJgBlsKuhRFdizFcC88BorQwMCTOIKilvffYh587GOz5px1+9uFNwZ30mTMSGB+8bWOQ58Gug4Gx51zyzN4zQMNvpxnPnGPwLHe2RAKz4dw2BsMeXFpm5Bgz8LYxJDDcTjBm5jE4nDtPIoFNGijCuB+XlvlvjBn/tjHYy99O/wzSki4nkcD+G6jFHpctgjN4jJlBZm64nQO2JUEaaAtIJBGXFmmevGRm2TaJxI23c4oZ5xgcNpzZ87BZcs45iWRcWvjYzx5mfNtmYy93O30zw5s/h+Uljicf/PCmzMYWlxYokEDxXwO6yCgYBaNgFIwCEgEAosNTU5p5NeQAAAAASUVORK5CYII=","orcid":"","institution":"Kabul University","correspondingAuthor":true,"prefix":"","firstName":"Samardin","middleName":"","lastName":"Jebran","suffix":""}],"badges":[],"createdAt":"2025-05-03 18:23:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6585441/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6585441/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[],"financialInterests":"No competing interests reported.","formattedTitle":"An efficient and effective matrix and transformation based Cryptographic algorithm","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"Cryptography, Encryption, Decryption, Gupta integral transform, Abaoub Shkheam transform, lower and upper triangular matrices","lastPublishedDoi":"10.21203/rs.3.rs-6585441/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6585441/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, we demonstrated the application of the Abaoub Shkheam transform, the Gupta integral transform, and the matrix decomposition of the non-singular matrix to improve the security of two-way communication. 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