{"paper":{"title":"Equation Asymmetry: An Algebraic Framework for Unifying Secrecy and Covertness in Information-Theoretic Security","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Wang Hao, Zhang Kuang","submitted_at":"2026-06-09T03:35:33Z","abstract_excerpt":"This paper studies the algebraic structure underlying a broad class of information-theoretic security problems. We define the equation asymmetry degree (EAD) as $\\Phi = (n - r)/n$, where $n$ is the signal embedding dimension and $r$ is the effective rank of the adversary's observation matrix. This single parameter is shown to simultaneously govern both secrecy (measured by equivocation $H(M|Y_E)$) and covertness (measured by detection error probability $P_e$). On finite fields $\\mathbb{F}_q$, we establish the equivocation lower bound $H(M|Y_E) = \\min(k, n - r_E) \\log q$ with exact probabilisti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.10374","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/2606.10374/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}