Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption

Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption | 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 Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption Yang Gao, Quan Gang, Soamar Homsi, Wujie Wen, Liqiang Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4473301/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 Despite the enormous technical and financial advantages of cloud computing, security and privacy have always been the primary concerns for adopting cloud computing facilities, especially for government agencies and commercial sectors with high-security requirements. Homomorphic Encryption (HE) has recently emerged as an effective tool in ensuring privacy and security for sensitive applications by allowing computing on encrypted data. One major obstacle to employing HE-based computation, however, is its excessive computational cost, which can be orders of magnitude higher than its counterpart based on the plaintext. In this paper, we study the problem of how to reduce the HE-based computational cost for general Matrix Multiplication (MM), i.e., a fundamental building block for numerous practical applications, by taking advantage of the Single Instruction Multiple Data (SIMD) operations supported by HE schemes. Specifically, we develop a novel element-wise algorithm for general matrix multiplication, based on which we propose two HE-based General Matrix Multiplication (HEGMM) Approved for Public Release on 06 Mar 2024. Distribution is Unlimited. Case Number: 2024-0184 (original case number(s): AFRL-2024-0944) algorithms to reduce the HE computation cost. Our experimental results show that our algorithms can significantly outperform the state-of-the-art approaches of HE-based matrix multiplication. Homomorphic Encryption privacy protection Matrix Multiplication Cloud Computing Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 21 Jun, 2024 Reviews received at journal 20 Jun, 2024 Reviews received at journal 16 Jun, 2024 Reviewers agreed at journal 12 Jun, 2024 Reviews received at journal 12 Jun, 2024 Reviews received at journal 11 Jun, 2024 Reviewers agreed at journal 06 Jun, 2024 Reviewers agreed at journal 04 Jun, 2024 Reviewers agreed at journal 01 Jun, 2024 Reviewers agreed at journal 31 May, 2024 Reviewers agreed at journal 31 May, 2024 Reviewers agreed at journal 31 May, 2024 Reviewers agreed at journal 31 May, 2024 Reviewers agreed at journal 31 May, 2024 Reviewers agreed at journal 30 May, 2024 Reviewers agreed at journal 30 May, 2024 Reviewers agreed at journal 30 May, 2024 Reviewers invited by journal 30 May, 2024 Editor assigned by journal 29 May, 2024 Submission checks completed at journal 29 May, 2024 First submitted to journal 24 May, 2024 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-4473301","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":312619851,"identity":"660fc3ff-c089-41ea-89c7-c57738a0d810","order_by":0,"name":"Yang Gao","email":"","orcid":"","institution":"University of Central Florida","correspondingAuthor":false,"prefix":"","firstName":"Yang","middleName":"","lastName":"Gao","suffix":""},{"id":312619852,"identity":"a2f4a094-2c2e-4cc2-9141-d3aa9246cd48","order_by":1,"name":"Quan Gang","email":"","orcid":"","institution":"Florida International University","correspondingAuthor":false,"prefix":"","firstName":"Quan","middleName":"","lastName":"Gang","suffix":""},{"id":312619853,"identity":"fe2276cc-d131-4a0e-afdf-120e05b7b4f0","order_by":2,"name":"Soamar Homsi","email":"","orcid":"","institution":"United States Air Force Research Laboratory","correspondingAuthor":false,"prefix":"","firstName":"Soamar","middleName":"","lastName":"Homsi","suffix":""},{"id":312619854,"identity":"96d41ba6-c703-4ba9-a19b-5c83afe68e62","order_by":3,"name":"Wujie Wen","email":"","orcid":"","institution":"Lehigh University","correspondingAuthor":false,"prefix":"","firstName":"Wujie","middleName":"","lastName":"Wen","suffix":""},{"id":312619855,"identity":"840861a3-2630-4eed-9498-6c9147f7911e","order_by":4,"name":"Liqiang Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA7UlEQVRIiWNgGAWjYBACPmYGhgNw3gcGBn4gZYBXCxuyFsYZDAySDQS1IHOYeYjSws688cDPHbUMBsfPHn5t22YnwcDevE0Cv8PYCg72njnOYHAmL806ty1ZgoHnWBkBLTwGB3jbjjGYHcgxM85tO1DHIJFjRlDLwb8gLeffmBlbth2QYJB/Q1jLYd62GgazGznGjxlBWiR4CGlhKzgs23aAx/7GGzPGnnPJEmw8acUW+LTw8x/e/PFtW52cZH+O8YcfZXYS/OyHN97Ap4UBEguHeUA2gt3Dhl81XEsdiMH8gQjVo2AUjIJRMAIBAJdoQqrRTKTmAAAAAElFTkSuQmCC","orcid":"","institution":"University of Central Florida","correspondingAuthor":true,"prefix":"","firstName":"Liqiang","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2024-05-24 15:18:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4473301/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4473301/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58097557,"identity":"1f5bd7ee-2ba1-4943-b0a0-73bd489b4b89","added_by":"auto","created_at":"2024-06-11 06:05:22","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1083715,"visible":true,"origin":"","legend":"","description":"","filename":"qtpjxbpccppybfxnqcfkqyyhbmvvxqzq.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4473301/v1_covered_712790c1-8311-4062-b776-4d167da08e84.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption","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":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Homomorphic Encryption, privacy protection, Matrix Multiplication, Cloud Computing","lastPublishedDoi":"10.21203/rs.3.rs-4473301/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4473301/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eDespite the enormous technical and financial advantages of cloud computing, security and privacy have always been the primary concerns for adopting cloud computing facilities, especially for government agencies and commercial sectors with high-security requirements. Homomorphic Encryption (HE) has recently emerged as an effective tool in ensuring privacy and security for sensitive applications by allowing computing on encrypted data. One major obstacle to employing HE-based computation, however, is its excessive computational cost, which can be orders of magnitude higher than its counterpart based on the plaintext. In this paper, we study the problem of how to reduce the HE-based computational cost for general Matrix Multiplication (MM), i.e., a fundamental building block for numerous practical applications, by taking advantage of the Single Instruction Multiple Data (SIMD) operations supported by HE schemes. Specifically, we develop a novel element-wise algorithm for general matrix multiplication, based on which we propose two HE-based General Matrix Multiplication (HEGMM) Approved for Public Release on 06 Mar 2024. Distribution is Unlimited. Case Number: 2024-0184 (original case number(s): AFRL-2024-0944) algorithms to reduce the HE computation cost. Our experimental results show that our algorithms can significantly outperform the state-of-the-art approaches of HE-based matrix multiplication.\u003c/p\u003e","manuscriptTitle":"Secure and Efficient General Matrix Multiplication On Cloud Using Homomorphic Encryption","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-11 05:57:13","doi":"10.21203/rs.3.rs-4473301/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-06-21T18:28:03+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-20T18:21:17+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-16T13:18:37+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"327654672456310921076319188725960799097","date":"2024-06-12T18:59:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-12T07:24:42+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-06-11T07:09:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"316406843178606655893563580679442704338","date":"2024-06-06T17:53:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"333070598758353912148274296036142184574","date":"2024-06-05T02:28:03+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"170532563545866073997621923251153774703","date":"2024-06-01T11:28:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"186747845334396682025368428231147984121","date":"2024-05-31T19:09:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"303964953765370722891462493039184492882","date":"2024-05-31T13:28:39+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"171621231707144028749888802854458715005","date":"2024-05-31T07:02:18+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"36270073838689114359583982243221357021","date":"2024-05-31T06:12:05+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"147788065432162790291126840506884076109","date":"2024-05-31T04:03:46+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"228180773271585073506691485356815863181","date":"2024-05-31T02:57:26+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"197814575830543946458889122141794494351","date":"2024-05-31T00:49:28+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"36220592726346022324971171547287358904","date":"2024-05-31T00:44:48+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-05-31T00:38:17+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-29T06:04:24+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-29T06:04:24+00:00","index":"","fulltext":""},{"type":"submitted","content":"The Journal of Supercomputing","date":"2024-05-24T15:17:02+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-journal-of-supercomputing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [The Journal of Supercomputing](https://www.springer.com/journal/11227)","snPcode":"11227","submissionUrl":"https://submission.nature.com/new-submission/11227/3","title":"The Journal of Supercomputing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"79a863fb-f175-4b9b-8091-d8e3df39cc08","owner":[],"postedDate":"June 11th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-08-02T20:45:07+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-11 05:57:13","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4473301","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4473301","identity":"rs-4473301","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}