A Quantum Stochastic Walk Approach to Dynamic Multipath Routing under Correlated Cryptographic Degradation

A Quantum Stochastic Walk Approach to Dynamic Multipath Routing under Correlated Cryptographic Degradation | 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 Article A Quantum Stochastic Walk Approach to Dynamic Multipath Routing under Correlated Cryptographic Degradation Chinmay Patwardhan, Shubhalaxmi Joshi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9320492/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 Classical multipath routing protocols, including Equal-Cost Multi-Path (ECMP) and Shortest Path First (SPF), optimize for physical link metrics and are mathematically incapable of representing correlated algorithmic failure across cryptographic primitives. As financial-grade network architectures migrate to Post-Quantum Cryptography (PQC) under NIST mandate, this representational gap introduces a systemic risk: a zero-day compromise of a lattice-based algorithm (e.g., Module Learning With Errors, Module-LWE) leaves classical load balancers routing traffic into cryptographically compromised paths while all physical links remain active. This paper presents a Quantum Stochastic Walk (QSW) control plane operating over a Software-Defined Network (SDN), designed to detect and respond to correlated cryptographic degradation events. The architecture encodes heterogeneous PQC overhead Kyber (lattice, low latency), SPHINCS+ (hash, medium latency), and McEliece (code, high latency) into a utility vector u, and captures shared failure probability via a dual-covariance matrix Σ that decomposes network-layer and cryptographic-layer correlations with equal weight. A discretized approximation of the Gorini-Kossakowski- Lindblad-Sudarshan (GKLS) master equation evolves a density matrix ρ over N = 30 logical routing paths, blending coherent quantum channel dynamics with a classical Google-matrix baseline at mixing parameter ω = 0.2. The coherent update (V ρtV †) and stochastic update together carry an O(N3) periteration complexity, tractable for physical port densities up to N = 128. Upon simulation of a lattice-compromise shock event, the QSW engine redistributed traffic away from the compromised cluster reducing lattice-path utilization from 43.7% to 25.3% and increasing hash-based and code-based path utilization to 40.4% and 34.2%, respectively while maintaining 100% packet reachability throughout the transition. GPU/CPU convergence was achieved in 8.32 ms under the shock state. A 50-stream Non-Homogeneous Poisson Process (NHPP) traffic load with micro-burst injection confirmed correct multipath saturation at 188 Mbit/s aggregate throughput. The Python-based OpenFlow update latency of tflow mod ≈ 42 ms is identified as the binding deployment constraint, arising from OS-level user/kernel-space serialization; the required production path is migration to a P4 programmable data plane with native C++ or SmartNIC execution of the O(N3) tensor operations. Physical sciences/Engineering Physical sciences/Mathematics and computing Physical sciences/Physics Quantum StochasticWalk Post-Quantum Cryptography Software-Defined Networking GKLS Master Equation Multipath Routing Correlated Failure Kyber SPHINCS+ McEliece OpenFlow P4 Non-Homogeneous Poisson Process Control Plane Latency 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. 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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-9320492","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":619085030,"identity":"7ba527ca-075d-4922-bad3-88162d52e50a","order_by":0,"name":"Chinmay Patwardhan","email":"data:image/png;base64,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","orcid":"","institution":"MIT World Peace University","correspondingAuthor":true,"prefix":"","firstName":"Chinmay","middleName":"","lastName":"Patwardhan","suffix":""},{"id":619085031,"identity":"bed6b9c5-1bcc-4f70-821a-ba652940198a","order_by":1,"name":"Shubhalaxmi Joshi","email":"","orcid":"","institution":"MIT World Peace University","correspondingAuthor":false,"prefix":"","firstName":"Shubhalaxmi","middleName":"","lastName":"Joshi","suffix":""}],"badges":[],"createdAt":"2026-04-04 12:38:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9320492/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9320492/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107909965,"identity":"a8b1e395-f4bc-4ae8-8e70-5eb9086a7f48","added_by":"auto","created_at":"2026-04-27 13:12:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":197293,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9320492/v1_covered_3c075cf5-47bd-4c44-b39b-0565f3f89914.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Quantum Stochastic Walk Approach to Dynamic Multipath\nRouting under Correlated Cryptographic Degradation","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":"Quantum StochasticWalk, Post-Quantum Cryptography, Software-Defined Networking, GKLS Master Equation, Multipath Routing, Correlated Failure, Kyber, SPHINCS+, McEliece, OpenFlow, P4, Non-Homogeneous Poisson Process, Control Plane Latency","lastPublishedDoi":"10.21203/rs.3.rs-9320492/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9320492/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eClassical multipath routing protocols, including Equal-Cost Multi-Path (ECMP) and Shortest Path First (SPF),\u003c/p\u003e\n\u003cp\u003eoptimize for physical link metrics and are mathematically incapable of representing correlated algorithmic failure across\u003c/p\u003e\n\u003cp\u003ecryptographic primitives. As financial-grade network architectures migrate to Post-Quantum Cryptography (PQC) under NIST mandate, this representational gap introduces a systemic risk: a zero-day compromise of a lattice-based algorithm (e.g., Module Learning With Errors, Module-LWE) leaves classical load balancers routing traffic into cryptographically compromised paths while all physical links remain active. This paper presents a Quantum Stochastic Walk (QSW) control plane operating over a Software-Defined Network (SDN), designed to detect and respond to correlated cryptographic degradation events. The architecture encodes heterogeneous PQC overhead Kyber (lattice, low latency), SPHINCS+ (hash, medium latency), and McEliece (code, high latency) into a utility vector u, and captures shared failure probability via a dual-covariance matrix Σ that decomposes network-layer and cryptographic-layer correlations with equal weight. A discretized approximation of the Gorini-Kossakowski- Lindblad-Sudarshan (GKLS) master equation evolves a density matrix ρ over N = 30 logical routing paths, blending coherent quantum channel dynamics with a classical Google-matrix baseline at mixing parameter ω = 0.2. The coherent update (V ρtV †) and stochastic update together carry an O(N3) periteration complexity, tractable for physical port densities up to N = 128. Upon simulation of a lattice-compromise shock event, the QSW engine redistributed traffic away from the compromised cluster reducing lattice-path utilization from 43.7% to 25.3% and increasing hash-based and code-based path utilization to 40.4% and 34.2%, respectively while maintaining 100% packet\u003c/p\u003e\n\u003cp\u003ereachability throughout the transition. GPU/CPU convergence was achieved in 8.32 ms under the shock state. A 50-stream\u003c/p\u003e\n\u003cp\u003eNon-Homogeneous Poisson Process (NHPP) traffic load with micro-burst injection confirmed correct multipath saturation at\u003c/p\u003e\n\u003cp\u003e188 Mbit/s aggregate throughput. The Python-based OpenFlow update latency of tflow mod ≈ 42 ms is identified as the binding deployment constraint, arising from OS-level user/kernel-space serialization; the required production path is migration to a P4 programmable data plane with native C++ or SmartNIC execution of the O(N3) tensor operations.\u003c/p\u003e","manuscriptTitle":"A Quantum Stochastic Walk Approach to Dynamic Multipath\nRouting under Correlated Cryptographic Degradation","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-10 03:25:49","doi":"10.21203/rs.3.rs-9320492/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":"06e084b3-43af-4d0d-bc08-88bbebaa8180","owner":[],"postedDate":"April 10th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":65878284,"name":"Physical sciences/Engineering"},{"id":65878285,"name":"Physical sciences/Mathematics and computing"},{"id":65878286,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-05-10T13:39:41+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-10 03:25:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9320492","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9320492","identity":"rs-9320492","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}