{"paper_id":"2e26baa1-e8b8-4820-bdd6-86fe8e5b94bc","body_text":"Corpus-Driven Oracle Construction for Quantum Key-Recovery Attacks on Monoalphabetic Substitution Ciphers | 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 Corpus-Driven Oracle Construction for Quantum Key-Recovery Attacks on Monoalphabetic Substitution Ciphers Alessio Di Santo, Gabriella Lanziani This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9156135/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 12 You are reading this latest preprint version Abstract We study the quantum key-recovery complexity of monoalphabeticsubstitution ciphers by constructing Grover search oracles fromcharacter trigram language models built on four Renaissance Italianplaintext corpora.The central quantity is the marked key fraction P good ---the proportion of substitution keys whosedecryption satisfies a statistical plausibility criterion---whichdirectly governs both classical exhaustive-search cost and Groveroracle call count. Working over a 23-letter alphabet, empirical estimation shows thatoracle call counts range from 3 to 31, orders of magnitude belowprior overstated claims, while classical exhaustive search requiresup to 426 trials at the strictest threshold.To validate these analytical projections, the alphabet is reduced to seven letters, making all 5040 keys enumerable and enabling direct statevector simulation of Grover amplitude amplification. The simulation confirms quantum speedups of 2×--9× over random exhaustive search at most thresholds, and exposes empirically an intrinsic limitation of Grover’s algorithm in the discrete setting, discrete resonance failure : at one threshold the standard iteration formula predicts 2 optimal iterations, while the true discrete optimum requires 24, making quantum search four times slower than classical at that point. Exact enumeration further establishes that P good is strictly invariant with cipher length for a fixed alphabet, qualifying apparent length-dependence in the analytical sweep as a sampling artifact.Parallel quadratic unconstrained binary optimization experimentsshow an inverted failure pattern relative to the Grover case,demonstrating that the two attack paradigms are sensitive tocomplementary properties of the key-score landscape. MSC Classification: 94A60 , 68Q12 , 94A45 , 68P25 Physical sciences/Mathematics and computing Physical sciences/Physics Monoalphabetic Substitution Cipher Quantum Key-Recovery Attack Grover's Algorithm Amplitude Amplification Oracle Complexity n-gram Language Model QUBO Annealing Discrete Resonance Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 27 Apr, 2026 Reviews received at journal 24 Apr, 2026 Reviewers agreed at journal 23 Apr, 2026 Reviews received at journal 19 Apr, 2026 Reviews received at journal 17 Apr, 2026 Reviewers agreed at journal 10 Apr, 2026 Reviewers agreed at journal 27 Mar, 2026 Reviewers invited by journal 24 Mar, 2026 Editor invited by journal 23 Mar, 2026 Editor assigned by journal 19 Mar, 2026 Submission checks completed at journal 19 Mar, 2026 First submitted to journal 18 Mar, 2026 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-9156135\",\"acceptedTermsAndConditions\":true,\"allowDirectSubmit\":false,\"archivedVersions\":[],\"articleType\":\"Article\",\"associatedPublications\":[],\"authors\":[{\"id\":611655424,\"identity\":\"4a52e5af-9681-43f4-96ae-2a0dcf807fe2\",\"order_by\":0,\"name\":\"Alessio Di Santo\",\"email\":\"data:image/png;base64,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\",\"orcid\":\"\",\"institution\":\"University of L'Aquila\",\"correspondingAuthor\":true,\"prefix\":\"\",\"firstName\":\"Alessio\",\"middleName\":\"Di\",\"lastName\":\"Santo\",\"suffix\":\"\"},{\"id\":611655425,\"identity\":\"3b836d68-a8d2-4442-8bc1-0fe3745701f8\",\"order_by\":1,\"name\":\"Gabriella Lanziani\",\"email\":\"\",\"orcid\":\"\",\"institution\":\"\",\"correspondingAuthor\":false,\"prefix\":\"\",\"firstName\":\"Gabriella\",\"middleName\":\"\",\"lastName\":\"Lanziani\",\"suffix\":\"\"}],\"badges\":[],\"createdAt\":\"2026-03-18 07:40:50\",\"currentVersionCode\":1,\"declarations\":\"\",\"doi\":\"10.21203/rs.3.rs-9156135/v1\",\"doiUrl\":\"https://doi.org/10.21203/rs.3.rs-9156135/v1\",\"draftVersion\":[],\"editorialEvents\":[],\"editorialNote\":\"\",\"failedWorkflow\":false,\"files\":[{\"id\":105566526,\"identity\":\"5ca1b070-134c-4502-b657-5a8046ff8d44\",\"added_by\":\"auto\",\"created_at\":\"2026-03-27 12:56:37\",\"extension\":\"pdf\",\"order_by\":1,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":2234295,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"CorpusDrivenOracleConstructionforQuantumKeyRecoveryAttacksonMonoalphabeticSubstitutionCiphers.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-9156135/v1_covered_748e1363-99a5-41b3-95ac-42e9a5327cc1.pdf\"}],\"financialInterests\":\"No competing interests reported.\",\"formattedTitle\":\"Corpus-Driven Oracle Construction for Quantum Key-Recovery Attacks on Monoalphabetic Substitution Ciphers\",\"fulltext\":[],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":false,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":false,\"isAuthorSuppliedPdf\":true,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":true,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true},\"keywords\":\"Monoalphabetic Substitution Cipher, Quantum Key-Recovery Attack, Grover's Algorithm, Amplitude Amplification, Oracle Complexity, n-gram Language Model, QUBO Annealing, Discrete Resonance\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-9156135/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-9156135/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eWe study the quantum key-recovery complexity of monoalphabeticsubstitution ciphers by constructing Grover search oracles fromcharacter trigram language models built on four Renaissance Italianplaintext corpora.The central quantity is the \\u003cem\\u003emarked key fraction\\u003c/em\\u003e \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003egood\\u003c/sub\\u003e---the proportion of substitution keys whosedecryption satisfies a statistical plausibility criterion---whichdirectly governs both classical exhaustive-search cost and Groveroracle call count. Working over a 23-letter alphabet, empirical estimation shows thatoracle call counts range from 3 to 31, orders of magnitude belowprior overstated claims, while classical exhaustive search requiresup to 426 trials at the strictest threshold.To validate these analytical projections, the alphabet is reduced to seven letters, making all 5040 keys enumerable and enabling direct statevector simulation of Grover amplitude amplification. The simulation confirms quantum speedups of 2×--9× over random exhaustive search at most thresholds, and exposes empirically an intrinsic limitation of Grover’s algorithm in the discrete setting, \\u003cem\\u003ediscrete resonance failure\\u003c/em\\u003e: at one threshold the standard iteration formula predicts 2 optimal iterations, while the true discrete optimum requires 24, making quantum search four times \\u003cem\\u003eslower\\u003c/em\\u003e than classical at that point. Exact enumeration further establishes that \\u003cem\\u003eP\\u003c/em\\u003e\\u003csub\\u003egood\\u003c/sub\\u003e is strictly invariant with cipher length for a fixed alphabet, qualifying apparent length-dependence in the analytical sweep as a sampling artifact.Parallel quadratic unconstrained binary optimization experimentsshow an inverted failure pattern relative to the Grover case,demonstrating that the two attack paradigms are sensitive tocomplementary properties of the key-score landscape.\\u003c/p\\u003e\\n\\u003cp\\u003eMSC Classification: 94A60 , 68Q12 , 94A45 , 68P25\\u003c/p\\u003e\",\"manuscriptTitle\":\"Corpus-Driven Oracle Construction for Quantum Key-Recovery Attacks on Monoalphabetic Substitution Ciphers\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2026-03-26 06:27:34\",\"doi\":\"10.21203/rs.3.rs-9156135/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Revision requested\",\"date\":\"2026-04-27T09:30:31+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2026-04-24T05:50:56+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"70434759219232438517911687925434026855\",\"date\":\"2026-04-24T03:23:10+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2026-04-20T02:46:30+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"editorInvitedReview\",\"content\":\"\",\"date\":\"2026-04-18T01:50:21+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"325986664537829606398045398628679781904\",\"date\":\"2026-04-10T09:27:12+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"234438230798527341452480936102564745519\",\"date\":\"2026-03-27T11:25:54+00:00\",\"index\":\"hide\",\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2026-03-24T09:25:18+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvited\",\"content\":\"\",\"date\":\"2026-03-23T12:22:05+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2026-03-19T05:38:58+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"checksComplete\",\"content\":\"\",\"date\":\"2026-03-19T05:38:34+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Scientific Reports\",\"date\":\"2026-03-18T07:31:16+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"scientific-reports\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"scirep\",\"sideBox\":\"Learn more about [Scientific Reports](http://www.nature.com/srep/)\",\"snPcode\":\"\",\"submissionUrl\":\"\",\"title\":\"Scientific Reports\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"stoa\",\"reportingPortfolio\":\"Scientific Reports\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":true}}],\"origin\":\"\",\"ownerIdentity\":\"b6cd8cb4-8fa6-4bb3-97f8-3f5861b0940e\",\"owner\":[],\"postedDate\":\"March 26th, 2026\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"under-review\",\"subjectAreas\":[{\"id\":65081005,\"name\":\"Physical sciences/Mathematics and computing\"},{\"id\":65081006,\"name\":\"Physical sciences/Physics\"}],\"tags\":[],\"updatedAt\":\"2026-05-14T06:08:59+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2026-03-26 06:27:34\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-9156135\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-9156135\",\"identity\":\"rs-9156135\",\"version\":[\"v1\"]},\"buildId\":\"XKTyCvWXoU3ODBz1xrDgd\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}