An Evidence-Driven Classification Framework forShor’s Algorithm: Implementations,Optimizations, and Cryptographic Impact

An Evidence-Driven Classification Framework forShor’s Algorithm: Implementations,Optimizations, and Cryptographic Impact | 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 Evidence-Driven Classification Framework forShor’s Algorithm: Implementations,Optimizations, and Cryptographic Impact ANDERSON FERNANDES PEREIRA DOS SANTOS This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8553610/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 Shor’s algorithm remains the most important example of quantum advantage,with significant implications for integer factorization and public-key cryptog-raphy. Despite its well-established theoretical foundations, practical realizationis constrained by circuit depth, quantum arithmetic overhead, noise sensitivity,verification complexity, and fault-tolerance requirements. This paper introducesQ Class, an evolutionary-applicable, function-oriented, evidence-based classifi-cation system for assessing the practical evolution, maturity, and cryptographicrelevance of Shor’s algorithm. The framework is validated through a systematicmapping of literature published since Shor’s original 1994 paper. It offers thepractical evolution of Shor’s algorithm a new direction rather than algorithmicnovelty, highlighting persistent bottlenecks and research priorities. Shor’s Algorithm Quantum Factoring Classification Framework Quantum Circuit Implementation Cryptographic Impact Full Text Additional Declarations No competing interests reported. Supplementary Files AnEvidenceDrivenClassificationFrameworkforShorsAlgorithmImplementationsOptimizationsandCryptographicImpactImages.zip 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-8553610","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":571616962,"identity":"c65caab8-7060-43b6-9f72-f1eb719ab4fd","order_by":0,"name":"ANDERSON FERNANDES PEREIRA DOS SANTOS","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzklEQVRIiWNgGAWjYHACAzDJzwymDkC5xGiRbCZZi8EBYrXwz27e+Ljij02e8XHuxAcMFXcYzKUP4NcicedYseHZtrRis8O8mw0YzjxjsOxLIGDNjRwzycaGw4nbDvNuk2BsO8xgcIaADvkbOeY/G/4cTtzczLv9B+M/IrQYAG1hbGA7nLiBmXcbA2MDEVoMb6QVSza2pSXOAPpFIuHYMx7LHgJa5G4kb/zY8Mcmsb//7MYPH2ruyJnzENCCChIYGEjTMApGwSgYBaMAOwAABtZGpDUfiRcAAAAASUVORK5CYII=","orcid":"","institution":"Military Institute of Engineering","correspondingAuthor":true,"prefix":"","firstName":"ANDERSON","middleName":"FERNANDES PEREIRA DOS","lastName":"SANTOS","suffix":""}],"badges":[],"createdAt":"2026-01-08 16:23:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8553610/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8553610/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":100022955,"identity":"c13c6e28-f5de-43c0-9fda-f6998067ec57","added_by":"auto","created_at":"2026-01-12 08:10:44","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":2727,"visible":true,"origin":"","legend":"","description":"","filename":"b79f310cb6e24574ba8bd034a32169d2.json","url":"https://assets-eu.researchsquare.com/files/rs-8553610/v1/043d497e0d92acd8a0c6d357.json"},{"id":103050507,"identity":"4cd2d0c4-8b20-4d52-b645-9ce1915cb39a","added_by":"auto","created_at":"2026-02-20 07:50:18","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":613495,"visible":true,"origin":"","legend":"","description":"","filename":"AnEvidenceDrivenClassificationFrameworkforShorsAlgorithmImplementationsOptimizationsandCryptographicImpact.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8553610/v1_covered_972c24cb-b131-4449-9fd7-15150c7da17d.pdf"},{"id":100022914,"identity":"8c020ff2-563d-4661-b1f0-44e9800a9e55","added_by":"auto","created_at":"2026-01-12 08:10:42","extension":"zip","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":154275,"visible":true,"origin":"","legend":"","description":"","filename":"AnEvidenceDrivenClassificationFrameworkforShorsAlgorithmImplementationsOptimizationsandCryptographicImpactImages.zip","url":"https://assets-eu.researchsquare.com/files/rs-8553610/v1/68771db26f29ae5f584712fa.zip"}],"financialInterests":"No competing interests reported.","formattedTitle":"An Evidence-Driven Classification Framework forShor’s Algorithm: Implementations,Optimizations, and Cryptographic Impact","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":"Shor’s Algorithm, Quantum Factoring, Classification Framework, Quantum Circuit Implementation, Cryptographic Impact","lastPublishedDoi":"10.21203/rs.3.rs-8553610/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8553610/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Shor’s algorithm remains the most important example of quantum advantage,with significant implications for integer factorization and public-key cryptog-raphy. 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