Bounds on the differential uniformity of the Wan-Lidl polynomials

Bounds on the differential uniformity of the Wan-Lidl polynomials | 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 Bounds on the differential uniformity of the Wan-Lidl polynomials Li-An Chen, Robert S Coulter This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2176151/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 18 Mar, 2023 Read the published version in Cryptography and Communications → Version 1 posted 7 You are reading this latest preprint version Abstract We study the differential uniformity of the Wan-Lidl polynomials over finite fields. A general upper bound, independent of the order of the field, is established. Additional bounds are established in settings where one of the parameters is restricted. In particular, we establish a class of permutation polynomials which have differential uniformity at most 5 over fields of order $3\bmod 4$, irrespective of the field size. Computational results are also given. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 18 Mar, 2023 Read the published version in Cryptography and Communications → Version 1 posted Editorial decision: Accepted 31 Jan, 2023 Reviews received at journal 06 Nov, 2022 Reviewers agreed at journal 26 Oct, 2022 Reviewers invited by journal 26 Oct, 2022 Editor assigned by journal 21 Oct, 2022 Submission checks completed at journal 19 Oct, 2022 First submitted to journal 17 Oct, 2022 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-2176151","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":145611101,"identity":"8d3b89cb-b4a4-4471-84a7-f33b6d4e1219","order_by":0,"name":"Li-An Chen","email":"","orcid":"","institution":"University of Delaware","correspondingAuthor":false,"prefix":"","firstName":"Li-An","middleName":"","lastName":"Chen","suffix":""},{"id":145611102,"identity":"9c25734d-d40f-49de-988c-b5b6e06bec42","order_by":1,"name":"Robert S Coulter","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIie3LMQ6CQBCF4d3YS0ujXmEMJZcZQ7ENRBObLShITKDxAt4CbzCGBJo5AJXBhpoTENfSwuzSWexfTKZ4nxA+338myZytEPh5Vm6GzDQyRCwjh8KZBNUVmkk/Vd0lhurYWEshMxDxOat5RBKs7ATCFOhRYlb35pFl40pmVNAfJ5KzMykQoU8FycKBhNyeiFvc33gEwlZFVhJUl/ugc9ytu+Q1THm8sZLvcNnc5/P5fL96A+yPS5u4dSqOAAAAAElFTkSuQmCC","orcid":"","institution":"University of Delaware","correspondingAuthor":true,"prefix":"","firstName":"Robert","middleName":"S","lastName":"Coulter","suffix":""}],"badges":[],"createdAt":"2022-10-17 18:14:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2176151/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2176151/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s12095-023-00634-6","type":"published","date":"2023-03-18T20:02:25+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":28199013,"identity":"41578615-55ef-4cde-bb57-7ced02023747","added_by":"auto","created_at":"2022-10-24 19:28:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":215010,"visible":true,"origin":"","legend":"","description":"","filename":"WanLidlDUwithdeclaration.tex.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2176151/v1_covered.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Bounds on the differential uniformity of the Wan-Lidl polynomials","fulltext":[{"header":"Full Text","content":"This preprint is available for \u003ca href='/article/rs-2176151/latest.pdf' target='_blank'\u003edownload as a PDF\u003c/a\u003e."}],"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":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"cryptography-and-communications","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ccds","sideBox":"Learn more about [Cryptography and Communications](http://link.springer.com/journal/12095)","snPcode":"12095","submissionUrl":"https://submission.nature.com/new-submission/12095/3","title":"Cryptography and Communications","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2176151/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2176151/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"We study the differential uniformity of the Wan-Lidl polynomials over finite\nfields.\nA general upper bound, independent of the order of the field, is established.\nAdditional bounds are established in settings where one of the parameters is\nrestricted. 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