{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:22:51Z","timestamp":1760242971369,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2015,3,10]],"date-time":"2015-03-10T00:00:00Z","timestamp":1425945600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Different security notions of secret sharing schemes have been proposed by different information measures. Entropies, such as Shannon entropy and min entropy, are frequently used in the setting security notions for secret sharing schemes. Different to the entropies, Kolmogorov complexity was also defined and used in study the security of individual instances for secret sharing schemes. This paper is concerned with these security notions for secret sharing schemes defined by the variational measures, including Shannon entropy, guessing probability, min entropy and Kolmogorov complexity.<\/jats:p>","DOI":"10.3390\/e17031135","type":"journal-article","created":{"date-parts":[[2015,3,10]],"date-time":"2015-03-10T10:59:09Z","timestamp":1425985149000},"page":"1135-1145","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Comparing Security Notions of Secret Sharing Schemes"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2283-9459","authenticated-orcid":false,"given":"Songsong","family":"Dai","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donghui","family":"Guo","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,3,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Blakley, G.R. (1979, January 4\u20137). Safeguarding cryptographic keys, New York, NY, USA.","DOI":"10.1109\/MARK.1979.8817296"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1145\/359168.359176","article-title":"How to share a secret","volume":"22","author":"Shamir","year":"1979","journal-title":"Commun. ACM."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/S0020-0190(97)00194-4","article-title":"On secret sharing schemes","volume":"65","author":"Blundo","year":"1998","journal-title":"Inf. Process. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1109\/TIT.1983.1056621","article-title":"On secret sharing systems","volume":"29","author":"Karnin","year":"1983","journal-title":"IEEE Trans. Inf. Theory."},{"key":"ref_5","unstructured":"Iwamoto, M., and Ohta, K. (August, January 31). Security notions for information theoretically secure encryptions, St. Petersburg, Russia."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Iwamoto, M., and Shikata, J. (2013, January 28\u201330). Information theoretic security for encryption based on conditional R\u00e9nyi entropies, Singapore, Singapore.","DOI":"10.1007\/978-3-319-04268-8_7"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Iwamoto, M., and Shikata, J. (Secret sharing schemes based on min-entropies, 2014). Secret sharing schemes based on min-entropies, arXiv:1401.5896.","DOI":"10.1109\/ISIT.2014.6874863"},{"key":"ref_8","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_9","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_10","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_11","doi-asserted-by":"crossref","unstructured":"Cover, T.M., and Thomas, J.A. (2006). Elements of Information Theory, Wiley.","DOI":"10.1002\/047174882X"},{"key":"ref_12","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_13","unstructured":"Gr\u00fcnwald, P., and Vit\u00e1nyi, P. (Shannon information and Kolmogorov complexity, 2008). Shannon information and Kolmogorov complexity, arXiv:cs\/0410002v1."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1007\/s00224-009-9177-7","article-title":"Comparing notions of computational entropy","volume":"45","author":"Pinto","year":"2009","journal-title":"Theory Comput. Syst."},{"key":"ref_15","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"},{"key":"ref_16","unstructured":"Antunes, L., Laplante, S., Pinto, A, and Salvador, L. (2009). Information Theoretic Security, Springer."},{"key":"ref_17","unstructured":"Kaced, T. (August, January 31). Almost-perfect secret sharing, St. Petersburg, Russia."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jiang, S. (2013). On Unconditional \u220a-Security of Private Key Encryption. Comput. J.","DOI":"10.1093\/comjnl\/bxt097"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Alimomeni, M., and Safavi-Naini, R. (2012, January 15\u201317). Guessing secrecy, Montreal, QC, Canada.","DOI":"10.1007\/978-3-642-32284-6_1"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF00198463","article-title":"On the size of shares for secret sharing schemes","volume":"6","author":"Capocelli","year":"1993","journal-title":"J. Cryptol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/18.272461","article-title":"Decomposition constructions for secret sharing Schemes","volume":"40","author":"Stinson","year":"1994","journal-title":"IEEE Trans. Inf. 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