Quantum Cryptanalysis on Feistel Variants in Related-Key Settings

Quantum Cryptanalysis on Feistel Variants in Related-Key Settings | 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 Quantum Cryptanalysis on Feistel Variants in Related-Key Settings Xiaoyu Wang, Siwei Chen, Zejun Xiang, Shasha Zhang, Xiangyong Zeng This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4699945/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 05 Nov, 2025 Read the published version in Quantum Information Processing → Version 1 posted 9 You are reading this latest preprint version Abstract Simon’s algorithm is a well-known quantum algorithm that can achieve exponential acceleration. This paper studies the applications of Simon’s algorithm in analyzing the security of Feistel variants, several well-known cryptographic structures derived from the Feistel structure. Specifically, we study quantum related-key attacks on Feistel variants in the setting that adversaries can only control part of the key difference in quantum superposition. We delve into observing the quantum related-key attacks on the balanced Feistel structure given by Cid \textit{et al.} and slightly improve the existing method to design periodic functions, ultimately providing a new approach to building periodic functions in single-key settings. Based on these results, we propose a general technique to construct quantum related-key distinguishers exploiting the quantum single-key distinguishers construction technique. As applications of our proposed technique, we demonstrate how to construct new polynomial-time quantum related-key chosen-plaintext distinguishers on several Feistel variants: Feistel-KF, SM4-like, MARS-like, Type-1/2/3 generalized Feistel-KF structures. Simon’s Algorithm Periodic Functions Related-key Attacks Generalized Feistel Structures Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 05 Nov, 2025 Read the published version in Quantum Information Processing → Version 1 posted Editorial decision: Revision requested 07 Apr, 2025 Reviews received at journal 07 Apr, 2025 Reviews received at journal 28 Mar, 2025 Reviewers agreed at journal 24 Mar, 2025 Reviewers agreed at journal 13 Sep, 2024 Reviewers invited by journal 28 Jul, 2024 Editor assigned by journal 08 Jul, 2024 Submission checks completed at journal 08 Jul, 2024 First submitted to journal 07 Jul, 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. 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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-4699945","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":335385645,"identity":"ea750e52-ead0-4331-8f9e-92d691083987","order_by":0,"name":"Xiaoyu Wang","email":"","orcid":"","institution":"Hubei University","correspondingAuthor":false,"prefix":"","firstName":"Xiaoyu","middleName":"","lastName":"Wang","suffix":""},{"id":335385648,"identity":"e4771d5c-edbd-4d2c-86bb-3e3d4a0280ec","order_by":1,"name":"Siwei Chen","email":"","orcid":"","institution":"Hubei University","correspondingAuthor":false,"prefix":"","firstName":"Siwei","middleName":"","lastName":"Chen","suffix":""},{"id":335385651,"identity":"aec918d9-e1c6-4abc-8e86-aa31c5a65d12","order_by":2,"name":"Zejun Xiang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9UlEQVRIiWNgGAWjYDACZjjFfIyBsQHETiBaC1sakVoQgMeMOC0Gx5mfPfzyx4bd4HbPt8e8Ow4z8LPnGDD83IFbi2Qzm7mxDE8as8Gds9uNec8cZpDseWPA2HsGtxZ+ZgYzaQmJw8wGN3K3SfO2HWYwuJFjwMzYhlsLGzP7N2kJg/9ALTnPwFrsCWnhZ+Yxk/yQcACkhQ1iiwQBLZLNPGXSDAeSmSVvpJlJzj2TziNx5lnBwV48WgzOH98m+eOPXTLfjeRnEm93WMvxtydvfPATjxYQYOZhYEiGcXhAxAH8GhgYGH8wMNgRUjQKRsEoGAUjGAAA+lhJ2MGVkYMAAAAASUVORK5CYII=","orcid":"","institution":"Hubei University","correspondingAuthor":true,"prefix":"","firstName":"Zejun","middleName":"","lastName":"Xiang","suffix":""},{"id":335385653,"identity":"bc2e9e72-42b1-4c1d-9ff9-8a9e3a13a279","order_by":3,"name":"Shasha Zhang","email":"","orcid":"","institution":"Hubei University","correspondingAuthor":false,"prefix":"","firstName":"Shasha","middleName":"","lastName":"Zhang","suffix":""},{"id":335385654,"identity":"baaa8666-34e3-4c99-b4fa-1ba21f862e27","order_by":4,"name":"Xiangyong Zeng","email":"","orcid":"","institution":"Hubei University","correspondingAuthor":false,"prefix":"","firstName":"Xiangyong","middleName":"","lastName":"Zeng","suffix":""}],"badges":[],"createdAt":"2024-07-07 11:14:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4699945/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4699945/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11128-025-04975-4","type":"published","date":"2025-11-05T15:57:19+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":95563988,"identity":"a8255fcd-58f7-49d9-84c8-bcbdc8659f57","added_by":"auto","created_at":"2025-11-10 16:06:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2644323,"visible":true,"origin":"","legend":"","description":"","filename":"QuantumCryptanalysisonFeistelVariantsinRelatedKeySettings.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4699945/v1_covered_e8000f8c-6a0a-4291-9f3c-4aa8ab0c5bda.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Quantum Cryptanalysis on Feistel Variants in Related-Key Settings","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":"quantum-information-processing","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"qinp","sideBox":"Learn more about [Quantum Information Processing](http://link.springer.com/journal/11128)","snPcode":"11128","submissionUrl":"https://submission.nature.com/new-submission/11128/3","title":"Quantum Information Processing","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Simon’s Algorithm, Periodic Functions, Related-key Attacks, Generalized Feistel Structures","lastPublishedDoi":"10.21203/rs.3.rs-4699945/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4699945/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Simon’s algorithm is a well-known quantum algorithm that can achieve exponential acceleration. 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