Efficient and Privacy-Preserving Argmax Approximation Using Homomorphic Encryption for Neural Networks

Efficient and Privacy-Preserving Argmax Approximation Using Homomorphic Encryption for Neural Networks | 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 Efficient and Privacy-Preserving Argmax Approximation Using Homomorphic Encryption for Neural Networks Jagadeesh Sai D This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6878548/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 Privacy-preserving neural networks represent a compelling approach for enabling secure training and inference without compromising user data confidentiality. Fully Homomorphic Encryption (FHE) is a cornerstone technology in this domain, as it permits computation over encrypted data. However, FHE inherently supports only addition and multiplication operations, making the implementation of non-linear functions—such as activation, Argmax, and max-pooling—particularly challenging when applied to cipher texts. This work addresses the complexity of executing the Argmax operation homomorphically, which is essential for identifying the index of the maximum element in a dataset. Building upon existing methods that employ compositions of low-degree minimax polynomials to approximate non-linear functions like sign and Argmax, we introduce a refined homomorphic Argmax approximation algorithm. Our approach enhances both accuracy and efficiency through a multi-phase design comprising rotation accumulation, tree-based comparisons, normalization, and final output selection. We integrate the proposed approximation algorithm into a neural network architecture and conduct comparative evaluations. The results demonstrate that our method not only yields a modest improvement in prediction accuracy but also reduces inference latency by 58%, primarily due to the optimization of homomorphic sign and rotation operations. Privacy-preserving neural networks Fully homomorphic encryption (FHE) Non-linear function approximation Homomorphic Argmax Secure neural inference Encrypted computation Polynomial approximation Confidential deep learning 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. 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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-6878548","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":611734100,"identity":"82a26ec7-f48a-46d0-98c6-cbae81ef556e","order_by":0,"name":"Jagadeesh Sai D","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYDCCAwcYGBIqgAxmEI+NaC1nQFqYidYCxIxtDFBriNHCd/D4ww8P522zN2/nP8DwoewwYS2SB84YSyRuu5045zAzA+OMc0RoMThwhgGkJUEC6Bdm3jaitBx//CNxzm17sJa/xGk5YCaR2HCbcQZICyMxWoB+MbNIOHY7EajF4GDPuXTCWvhuHH9880cN0GH8Bx8++FFmTVgLg8QBBPsALkWogL+BOHWjYBSMglEwggEAP98/UrEzwFsAAAAASUVORK5CYII=","orcid":"","institution":"Ramaiah Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Jagadeesh","middleName":"Sai","lastName":"D","suffix":""}],"badges":[],"createdAt":"2025-06-12 09:08:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6878548/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6878548/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105565787,"identity":"08445213-f7fa-4ac2-ba0a-444ed6a6a479","added_by":"auto","created_at":"2026-03-27 12:54:23","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":976905,"visible":true,"origin":"","legend":"","description":"","filename":"EfficientandPrivacyPreservingArgmaxApproximationUsingHomomorphicEncryptionforNeuralNetworks.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6878548/v1_covered_f9ec54de-dc8a-475b-bd31-3d24a5fc2121.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Efficient and Privacy-Preserving Argmax Approximation Using Homomorphic Encryption for Neural Networks","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":"Privacy-preserving neural networks, Fully homomorphic encryption (FHE), Non-linear function approximation, Homomorphic Argmax, Secure neural inference, Encrypted computation, Polynomial approximation, Confidential deep learning","lastPublishedDoi":"10.21203/rs.3.rs-6878548/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6878548/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePrivacy-preserving neural networks represent a compelling approach for enabling secure training and inference without compromising user data confidentiality. Fully Homomorphic Encryption (FHE) is a cornerstone technology in this domain, as it permits computation over encrypted data. However, FHE inherently supports only addition and multiplication operations, making the implementation of non-linear functions\u0026mdash;such as activation, Argmax, and max-pooling\u0026mdash;particularly challenging when applied to cipher texts.\u003c/p\u003e \u003cp\u003eThis work addresses the complexity of executing the Argmax operation homomorphically, which is essential for identifying the index of the maximum element in a dataset. Building upon existing methods that employ compositions of low-degree minimax polynomials to approximate non-linear functions like sign and Argmax, we introduce a refined homomorphic Argmax approximation algorithm. Our approach enhances both accuracy and efficiency through a multi-phase design comprising rotation accumulation, tree-based comparisons, normalization, and final output selection.\u003c/p\u003e \u003cp\u003eWe integrate the proposed approximation algorithm into a neural network architecture and conduct comparative evaluations. The results demonstrate that our method not only yields a modest improvement in prediction accuracy but also reduces inference latency by 58%, primarily due to the optimization of homomorphic sign and rotation operations.\u003c/p\u003e","manuscriptTitle":"Efficient and Privacy-Preserving Argmax Approximation Using Homomorphic Encryption for Neural Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-26 02:40:46","doi":"10.21203/rs.3.rs-6878548/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","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}}],"origin":"","ownerIdentity":"c5423e12-f3a7-491a-8673-8e888653f0d8","owner":[],"postedDate":"March 26th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-26T02:40:46+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-26 02:40:46","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6878548","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6878548","identity":"rs-6878548","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}