{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:14:01Z","timestamp":1760058841643,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T00:00:00Z","timestamp":1745884800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>We present a new construction of a one-time pad (OTP) with inherent diffusive properties and a redundancy injection mechanism that benefits from them. The construction is based on interpreting the plaintext and key as members of a permutation group in the Lehmer code representation after conversion to factoradic. The so-constructed OTP translates any perturbation of the ciphertext to an unpredictable, metrically large random perturbation of the plaintext. This allows us to provide unconditional integrity assurance without extra key material. The redundancy is injected using Foata\u2019s \u201cpun\u201d: the reading of the one-line representation as the cyclic one; we call this Pseudo Foata Injection. We obtain algorithms of quadratic complexity that implement both mechanisms.<\/jats:p>","DOI":"10.3390\/cryptography9020027","type":"journal-article","created":{"date-parts":[[2025,4,29]],"date-time":"2025-04-29T09:00:39Z","timestamp":1745917239000},"page":"27","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-Degenerate One-Time Pad and Unconditional Integrity of Perfectly Secret Messages"],"prefix":"10.3390","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8796-6542","authenticated-orcid":false,"given":"Alex","family":"Shafarenko","sequence":"first","affiliation":[{"name":"College Lane, University of Hertfordshire, Hatfield AL10 9AB, UK"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication Theory of Secrecy Systems?","volume":"4","author":"Shanon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","unstructured":"Vernam, G. (1919). Secret Signaling System Patent. (No. 1,310,719), U.S. Patent."},{"key":"ref_3","unstructured":"Abidin, A., and Larsson, J.\u00c5. (2011, January 20\u201322). New universal hash functions. Proceedings of the Research in Cryptology: 4th Western European Workshop, WEWoRC 2011, Weimar, Germany. Revised Selected Papers 4."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1090\/psapm\/010\/0113289","article-title":"Teaching combinatorial tricks to a computer","volume":"10","author":"Lehmer","year":"1960","journal-title":"Proc. Symp. Appl. Math."},{"key":"ref_5","unstructured":"Knuth, D. (1997). Volume 2: Seminumerical Algorithms. The Art of Computer Programming, Addison-Wesley."},{"key":"ref_6","first-page":"173","article-title":"Metrics on Permutations, a Survey","volume":"23","author":"Deza","year":"1998","journal-title":"J. Comb. Inf. Sys. 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Unconditionally secure authentication schemes and practical and theoretical consequences. Proceedings of the Conference on the Theory and Application of Cryptographic Techniques, Linz, Austria."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Carter, J.L., and Wegman, M.N. (1977, January 2\u20134). Universal classes of hash functions. Proceedings of the Ninth Annual ACM Symposium on Theory of Computing, Boulder, CO, USA.","DOI":"10.1145\/800105.803400"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/0022-0000(81)90033-7","article-title":"New hash functions and their use in authentication and set equality","volume":"22","author":"Wegman","year":"1981","journal-title":"J. Comput. Syst. Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"075203","DOI":"10.1088\/1612-202X\/ac6a60","article-title":"On the robustness of information-theoretic authentication in quantum cryptography","volume":"19","author":"Molotkov","year":"2022","journal-title":"Laser Phys. Lett."},{"key":"ref_15","unstructured":"Krawczyk, H. (1994, January 21\u201325). LFSR-based hashing and authentication. Proceedings of the Annual International Cryptology Conference, Santa Barbara, CA, USA."}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/2\/27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:24:10Z","timestamp":1760030650000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/9\/2\/27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,29]]},"references-count":15,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,6]]}},"alternative-id":["cryptography9020027"],"URL":"https:\/\/doi.org\/10.3390\/cryptography9020027","relation":{},"ISSN":["2410-387X"],"issn-type":[{"type":"electronic","value":"2410-387X"}],"subject":[],"published":{"date-parts":[[2025,4,29]]}}}