Chakravyuha: A Scheme to Resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher

Chakravyuha: A Scheme to Resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher | 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 Chakravyuha: A Scheme to Resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher Subrata Nandi, Srinivasan Krishnaswamy, Nitesh Narayana GS, Pianki Mitra This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4228602/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 In LFSR-based stream ciphers, the knowledge of the feedback equation of the LFSR plays a critical role in most attacks. In word-based stream ciphers such as those in the SNOW series, even if the feedback configuration is hidden, knowing the characteristic polynomial of the state transition matrix of the LFSR enables the attacker to create a feedback equation over GF(2).This, in turn, can be used to launch Fast Correlation Attacks. In this work, we propose a method for hiding both the feedback equation of a word-based LFSR and the characteristic polynomial of the state transition matrix. Here, we employ az-primitive σ-LFSR whose characteristic polynomial is randomly sampled from the distribution of primitive polynomials over GF(2) of the appropriate degree. We propose an algorithm for locating z-primitive σ-LFSR configurations of a given degree. Further, an invertible matrix is generated from the key. This is then employed to generate a public parameter to retrieve the feedback configuration using the key. If the key size is $n$- bits, the process of retrieving the feedback equation from the public parameter has an average time complexity O(2 n−1 ). The proposed method has been tested on SNOW 3G for resistance to Fast Correlation Attacks. In addition to that, the scheme withstands other attacks like Algebraic Attacks, Distinguishing Attacks, Guess and Determine Attacks. We have demonstrated that the security of SNOW 2.0 and SNOW 3G increases from 128 bits to 256 bits 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. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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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-4228602","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":289642584,"identity":"17511ae3-adb3-466e-bec2-526e85b255bf","order_by":0,"name":"Subrata Nandi","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYFACHgRTIqFCAsaVIKAlAabljAQPD2laGNtQbMUO5GfkHvvw84cdgzn72YM3Hs6zkLHnX8D44QeDRR4uLQY38pJn9iQkM1j25CVbJG4DOkziAbNkD4NEMU4tEjnGDDwJzAwGB3LMJCBaDjBIAx2Z2IDTYTnGjH8S6hkMzr8BapkD1sL8G58Whhs5xsw8CYeBLgTZ0gDUwt/AhtcWgzPvkpll0o7zGNx4Y2yRcAyo5QZjm2WPAR6HteceZnxjUy1ncD7H8OaPmjp79v7Dh2/8qKjD7TAoQE4DIMUGBNSjAv4DJCkfBaNgFIyC4Q8AOghLsTmyFWcAAAAASUVORK5CYII=","orcid":"","institution":"Indian Institute of Technology Guwahati","correspondingAuthor":true,"prefix":"","firstName":"Subrata","middleName":"","lastName":"Nandi","suffix":""},{"id":289642585,"identity":"a6040b8f-a968-4926-b3a7-5cae607b80e9","order_by":1,"name":"Srinivasan Krishnaswamy","email":"","orcid":"","institution":"Indian Institute of Technology Guwahati","correspondingAuthor":false,"prefix":"","firstName":"Srinivasan","middleName":"","lastName":"Krishnaswamy","suffix":""},{"id":289642588,"identity":"b22009cc-30e3-442f-b3da-41e871025ee1","order_by":2,"name":"Nitesh Narayana GS","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Nitesh","middleName":"Narayana","lastName":"GS","suffix":""},{"id":289642589,"identity":"e26145a7-ff74-4449-9779-9c7941acd2f8","order_by":3,"name":"Pianki Mitra","email":"","orcid":"","institution":"Indian Institute of Technology Guwahati","correspondingAuthor":false,"prefix":"","firstName":"Pianki","middleName":"","lastName":"Mitra","suffix":""}],"badges":[],"createdAt":"2024-04-06 19:44:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4228602/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4228602/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":69284228,"identity":"78937a84-585f-450a-9bc8-328a262f232b","added_by":"auto","created_at":"2024-11-18 19:20:01","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":578554,"visible":true,"origin":"","legend":"","description":"","filename":"MainArticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4228602/v1_covered_f3c2c44d-22cd-4e26-813f-6f9b8b6b7471.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Chakravyuha: A Scheme to Resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-4228602/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4228602/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn LFSR-based stream ciphers, the knowledge of the feedback equation of the LFSR plays a critical role in most attacks. In word-based stream ciphers such as those in the SNOW series, even if the feedback configuration is hidden, knowing the characteristic polynomial of the state transition matrix of the LFSR enables the attacker to create a feedback equation over GF(2).This, in turn, can be used to launch Fast Correlation Attacks. In this work, we propose a method for hiding both the feedback equation of a word-based LFSR and the characteristic polynomial of the state transition matrix. Here, we employ az-primitive σ-LFSR whose characteristic polynomial is randomly sampled from the distribution of primitive polynomials over GF(2) of the appropriate degree. We propose an algorithm for locating z-primitive σ-LFSR configurations of a given degree. Further, an invertible matrix is generated from the key. This is then employed to generate a public parameter to retrieve the feedback configuration using the key. If the key size is $n$- bits, the process of retrieving the feedback equation from the public parameter has an average time complexity O(2\u003csup\u003en−1\u003c/sup\u003e). The proposed method has been tested on SNOW 3G for resistance to Fast Correlation Attacks. In addition to that, the scheme withstands other attacks like Algebraic Attacks, Distinguishing Attacks, Guess and Determine Attacks. We have demonstrated that the security of SNOW 2.0 and SNOW 3G increases from 128 bits to 256 bits\u003c/p\u003e","manuscriptTitle":"Chakravyuha: A Scheme to Resist Fast Correlation Attack for Word Oriented LFSR based Stream Cipher","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-12 02:44:41","doi":"10.21203/rs.3.rs-4228602/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":"61877374-48f5-4e0d-8675-d0d811e86910","owner":[],"postedDate":"April 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-11-18T18:21:52+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-12 02:44:41","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4228602","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4228602","identity":"rs-4228602","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}