{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:52Z","timestamp":1760242252173,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,3,7]],"date-time":"2017-03-07T00:00:00Z","timestamp":1488844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science and Technology Foundation of Guizhou Province, China","award":["LKS [2013] 35"],"award-info":[{"award-number":["LKS [2013] 35"]}]},{"name":"the Guangxi University Science and Technology Research Project","award":["2013YB193"],"award-info":[{"award-number":["2013YB193"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper we introduce two normalized versions of non-perfect security for private-key encryption: one version in the framework of Shannon entropy, another version in the framework of Kolmogorov complexity. We prove the lower bound on either key entropy or key size for these models and study the relations between these normalized security notions.<\/jats:p>","DOI":"10.3390\/e19030100","type":"journal-article","created":{"date-parts":[[2017,3,7]],"date-time":"2017-03-07T11:12:32Z","timestamp":1488885152000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Normalized Unconditional \u03f5-Security of Private-Key Encryption"],"prefix":"10.3390","volume":"19","author":[{"given":"Lvqing","family":"Bi","sequence":"first","affiliation":[{"name":"School of Electronics and Communication Engineering, Yulin Normal University, Yulin 537000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2283-9459","authenticated-orcid":false,"given":"Songsong","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8591-2313","authenticated-orcid":false,"given":"Bo","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mechanical and Electrical Engineering, Guizhou Normal University, Guiyang 550025, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. 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Proceedings of the International Conference on Information Theoretic Security (ICITS), Springer."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1145\/321356.321363","article-title":"On the length of programs for computing finite binary sequences","volume":"13","author":"Chaitin","year":"1966","journal-title":"J. ACM"},{"key":"ref_10","first-page":"1","article-title":"Three approaches to the quantitative definition of information","volume":"1","author":"Kolmogorov","year":"1965","journal-title":"Probl. Inf. Transm."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0019-9958(64)90223-2","article-title":"A formal theory of inductive inference, part I","volume":"7","author":"Solomonoff","year":"1964","journal-title":"Inf. Control"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley.","DOI":"10.1002\/047174882X"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Li, M., and Vit\u00e1nyi, P.M.B. (2008). An Introduction to Kolmogorov Complexity and Its Applications, Springer. [3rd ed.].","DOI":"10.1007\/978-0-387-49820-1"},{"key":"ref_14","unstructured":"Antunes, L., Laplante, S., Pinto, A., and Salvador, L. (2009). Information Theoretic Security, Springer."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kaced, T. (August, January 31). Almost-perfect secret sharing. Proceedings of the 2011 IEEE International Symposium on Information Theory Proceedings (ISIT), Saint Petersburg, Russia.","DOI":"10.1109\/ISIT.2011.6033816"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1135","DOI":"10.3390\/e17031135","article-title":"Comparing security notions of secret sharing schemes","volume":"17","author":"Dai","year":"2015","journal-title":"Entropy"},{"key":"ref_17","unstructured":"Gr\u00fcnwald, P., and Vit\u00e1nyi, P. (2008). Shannon Information and Kolmogorov Complexity. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"595","DOI":"10.3390\/e13030595","article-title":"Entropy measures vs. kolmogorov complexity","volume":"13","author":"Teixeira","year":"2011","journal-title":"Entropy"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:29:52Z","timestamp":1760207392000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/3\/100"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,7]]},"references-count":18,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,3]]}},"alternative-id":["e19030100"],"URL":"https:\/\/doi.org\/10.3390\/e19030100","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2017,3,7]]}}}