{"paper":{"title":"A Framework of Variable-Length Source Encryption using Mutual Information Security Criterion: Universal Coding, Strong Converse Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Secure variable-length source encryption is possible exactly when the key rate is at least the source entropy rate, independent of the leakage bound","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bagus Santoso, Yasutada Oohama","submitted_at":"2026-05-07T18:05:21Z","abstract_excerpt":"In this paper we consider the variable-length lossless source coding for discrete memoryless sources. We proposes a new encryption framework for securely transmitting codewords over a noiseless channel. The proposed source encryption framework is based on the secure communication framework of the Shannon cipher system. In the proposed framework, we use the mutual information as a measure of information leakage to an adversary. We establish the necessary and sufficient condition for secure communication under the condition that the information leakage is upper bounded by a constant $\\delta\\in ("},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish the necessary and sufficient condition for secure communication under the condition that the information leakage is upper bounded by a constant δ∈(0,∞), thereby providing a complete solution to the problem. We also show that the obtained necessary and sufficient condition does not depend on the constant δ∈(0,∞), demonstrating that we have the strong converse coding theorem for the proposed framework of source encryption. We further prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text and those of the key used for the encryption.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The source is discrete memoryless and the transmission channel is noiseless; the framework inherits the Shannon cipher system model in which sender and receiver share a secret key whose distribution is independent of the source.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper gives necessary and sufficient conditions for secure variable-length source encryption under mutual information leakage bounded by any δ>0, proves these conditions are independent of δ (strong converse), and shows existence of universal encryption schemes for any source and key statistics.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Secure variable-length source encryption is possible exactly when the key rate is at least the source entropy rate, independent of the leakage bound","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"41446edf09b0745b21ffe9d0e7f5fe6dc09f787da910d4c05c1cc4c7a9903a31"},"source":{"id":"2605.06802","kind":"arxiv","version":3},"verdict":{"id":"d67afa60-6e7a-4383-83a6-f78fa9347e24","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T06:47:35.229611Z","strongest_claim":"We establish the necessary and sufficient condition for secure communication under the condition that the information leakage is upper bounded by a constant δ∈(0,∞), thereby providing a complete solution to the problem. We also show that the obtained necessary and sufficient condition does not depend on the constant δ∈(0,∞), demonstrating that we have the strong converse coding theorem for the proposed framework of source encryption. We further prove the existence of encryption/decryption schemes, which are universal in the sense that they work effectively for any distributions of the plain text and those of the key used for the encryption.","one_line_summary":"The paper gives necessary and sufficient conditions for secure variable-length source encryption under mutual information leakage bounded by any δ>0, proves these conditions are independent of δ (strong converse), and shows existence of universal encryption schemes for any source and key statistics.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The source is discrete memoryless and the transmission channel is noiseless; the framework inherits the Shannon cipher system model in which sender and receiver share a secret key whose distribution is independent of the source.","pith_extraction_headline":"Secure variable-length source encryption is possible exactly when the key rate is at least the source entropy rate, independent of the leakage bound"},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.06802/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T12:02:03.821213Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T07:36:02.444091Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T18:01:18.883056Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T12:23:06.797498Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"49af7b665b54b73dcb88cc1df5c32903c7d3d4cbf443503f482dbfdb5c6e932e"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"5512da4b0e1b57cb46baf3886030b1c0b721da7cd1d162f2df00cdf4aa1ba15c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}