{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:43:24Z","timestamp":1760208204175,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2017,1,7]],"date-time":"2017-01-07T00:00:00Z","timestamp":1483747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The improved version of the author\u2019s previously declared asymmetric cipher protocol based on matrix power function (MPF) is presented. Proposed modification avoids discrete logarithm attack (DLA) which could be applied to the previously declared protocol. This attack allows us to transform the initial system of MPF equations to so-called matrix multivariate quadratic (MMQ) system of equations, which is a system representing a subclass of multivariate quadratic (MQ) systems of equations. We are making a conjecture that avoidance of DLA in protocol, presented here, should increase its security, since an attempt to solve the initial system of MPF equations would appear to be no less complex than solving the system of MMQ equations. No algorithms are known to solve such a system of equations. Security parameters and their secure values are defined. Security analysis against chosen plaintext attack (CPA) and chosen ciphertext attack (CCA) is presented. Measures taken to prevent DLA attack increase the security of this protocol with respect to the previously declated protocol.<\/jats:p>","DOI":"10.3390\/sym9010009","type":"journal-article","created":{"date-parts":[[2017,1,9]],"date-time":"2017-01-09T11:03:23Z","timestamp":1483959803000},"page":"9","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security"],"prefix":"10.3390","volume":"9","author":[{"given":"Eligijus","family":"Sakalauskas","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Natural Sciences, Department of Applied Mathematics, Kaunas University of Technology, Studentu str. 50-324, Kaunas LT - 51368, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8661-3021","authenticated-orcid":false,"given":"Aleksejus","family":"Mihalkovich","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Natural Sciences, Department of Applied Mathematics, Kaunas University of Technology, Studentu str. 50-324, Kaunas LT - 51368, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9114-9497","authenticated-orcid":false,"given":"Algimantas","family":"Ven\u010dkauskas","sequence":"additional","affiliation":[{"name":"Faculty of Informatics, Department of Computer Science, Kaunas University of Technology, Studentu str. 50-213, Kaunas LT - 51368, Lithuania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"283","DOI":"10.15388\/Informatica.2014.15","article-title":"New asymmetric cipher of non-commuting cryptography class based on matrix power function","volume":"25","author":"Sakalauskas","year":"2014","journal-title":"Informatica"},{"key":"ref_2","first-page":"2655","article-title":"Matrix power function and its application to block cipher s-box construction","volume":"8","author":"Sakalauskas","year":"2012","journal-title":"Int. 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Proceedings of the GV-Global Virtual Conference, \u017dilina, Slovakia."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/1\/9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:25:42Z","timestamp":1760207142000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/9\/1\/9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1,7]]},"references-count":16,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1]]}},"alternative-id":["sym9010009"],"URL":"https:\/\/doi.org\/10.3390\/sym9010009","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2017,1,7]]}}}