{"paper_id":"063b38ae-1cdc-439a-b3c3-a286741a220c","body_text":"Gamma Statistic Kakutani Fixed Point and Equilibrium Generative Adversarial Network Based Secure Steganography | 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 Gamma Statistic Kakutani Fixed Point and Equilibrium Generative Adversarial Network Based Secure Steganography Gahan A V, Geetha D Devanagavi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5031105/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 Images have been frequently utilized as ideal conditions for hiding information through the employment of steganography algorithms. The information for hiding ranges between document digitization, another secret image where hidden data is said to be embedded without the intervention of humans. Until now, an abundance of steganography algorithms are found in the state-of-the-art works, as well as steganalysis techniques, dedicated to hidden information detection in files.Present-day Steganography algorithms depend on machine learning (ML) and deep learning (DL) for embedding as much as secret text images as probableas reducing visual changes in a given input image (i.e., cover image) with improved accuracy.However, the embedding rate and bit error rate were focused minimally. Following this direction, this article endeavors to exemplify that a Generative Adversarial Network (GAN) can be utilized to enhance the potentiality of spatial domain steganalysis method and to position secret text message information with minimal image alteration (i.e., improving the embedding rate and bit error rate) significantly. In this work, a method called, Gamma Statistic Kakutani Fixed-point and Equilibrium Generative Adversarial Network-based (GSKF-EGAN) secure steganography is proposed. First, a Gamma Statistic Histogram Equalization-based Preprocessing model is designed by fine-tuning the gamma coefficient and equalization for both the cover image and secret text image to circumvent high peak and ensure optimal illumination simultaneously. Second, the Kakutani Fixed-point and Equilibrium Generative Adversarial Network-based Steganography model is designed with the processed images as input. Here by employing the Kakutani Fixed-point ensures a significant embedding rate during the embedding process and using Strategic Equilibrium for validation ensures minimum distortion or bit error rate during the extraction process. Also, experimental results reveal that retrieved secret message data generated by the GSKF-EGAN method with minimum distortion or bit error rate, therefore enhancing retrieved image quality with a higher embedding rate than those generated by conventional image Steganography techniques. Image Steganography Gamma Statistic Histogram Equalization Machine Learning Deep Learning Kakutani Fixed-point Equilibrium Generative Adversarial Network 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-5031105\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":true,\"archivedVersions\":[],\"articleType\":\"Research Article\",\"associatedPublications\":[],\"authors\":[{\"id\":350998163,\"identity\":\"e4e980a3-55bd-4f0f-b81e-d81c653c77c7\",\"order_by\":0,\"name\":\"Gahan A V\",\"email\":\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8UlEQVRIiWNgGAWjYHACxgMMBTB2BRCzA4UaCOg5wGAAY55hYOBhJkkLYxsRWvhnnzEAarFL3N7ee/DDx3k2ifuZmQ8+nMFgJ6eLQ5/EuRyQluTEOWfOJUvO3JaW2MPMlmy4gSHZ2OwADmvO8IC0MOfOkMgxY+bddhiohcdM8gHDgcRtOLTIQ7TU586Qf2PG/HcOEVoMIFoOA23hMWNmbIBq2YBHi+EZtoIDCQbH62fw5BhL9hxLM+45DPTLDAPcfpE7w7zxwYeKamMJ9jOGH37U2Mi2tzcffNhTYSeH0/sgkIDFwXiUj4JRMApGwSggCACpPFkFJJ3olQAAAABJRU5ErkJggg==\",\"orcid\":\"\",\"institution\":\"REVA University\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Gahan\",\"middleName\":\"A\",\"lastName\":\"V\",\"suffix\":\"\"},{\"id\":350998164,\"identity\":\"849cbdee-9d64-4216-baa3-f1c01eb5a0db\",\"order_by\":1,\"name\":\"Geetha D Devanagavi\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"REVA University\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Geetha\",\"middleName\":\"D\",\"lastName\":\"Devanagavi\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2024-09-04 11:12:54\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-5031105/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-5031105/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":84721899,\"identity\":\"748747d4-41bc-45ca-98a8-ee7d69cdc9b8\",\"added_by\":\"auto\",\"created_at\":\"2025-06-16 15:09:06\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":868186,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"Article.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-5031105/v1_covered_b0b1c116-9581-4f67-8c47-9463ef4ae8aa.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"\\u003cp\\u003eGamma Statistic Kakutani Fixed Point and Equilibrium Generative Adversarial Network Based Secure Steganography\\u003c/p\\u003e\",\"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\":\"info@researchsquare.com\",\"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\":\"Image Steganography, Gamma Statistic, Histogram Equalization, Machine Learning, Deep Learning, Kakutani Fixed-point, Equilibrium Generative Adversarial Network\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-5031105/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-5031105/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"Images have been frequently utilized as ideal conditions for hiding information through the employment of steganography algorithms. 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