{"paper":{"title":"Module Lattice Security (Part IV): Probabilistic Polynomial Quantum Attack on Module-LWE over 2-Power Cyclotomics","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR","math.CO","math.RA"],"primary_cat":"quant-ph","authors_text":"Ming-Xing Luo","submitted_at":"2026-05-17T12:16:04Z","abstract_excerpt":"We present a quantum attack on ML-KEM and related 2-power cyclotomic lattice schemes. Combining with Parts I-III, we provide an algorithm and verify the resulting approximation factor satisfies $\\gamma \\le 21 < q/2=1665$ for ML-KEM-1024, with a success probability $\\ge 0.99$. We apply a tower decomposition of the Principal Ideal Problem (PIP) through the chain $\\Q \\subset \\Q(\\zeta_8) \\subset \\cdots \\subset \\Q(\\zeta_{2^k})$ which yields a polynomial-time quantum algorithm costing $O(n^3 \\log^2 n)$ gates, $O(n^2 \\log n)$ qubits, and $\\mathrm{poly}(n)$ classical bit operations. We extend the anal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17412","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17412/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-19T21:41:57.744870Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.689694Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"38c201d78df700008436eb53cd68c0a8a4d46bf4a1faa87e7afb7a389f7b61e4"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}