{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:29:30Z","timestamp":1753885770875,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:p> We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and correction algorithms of golden cryptography previously known only for recurrences of a special form. They are based on proving the checking relations (inequalities satisfied by the ciphertext) under the condition that the analog of the golden Q-matrix has the strong Perron\u2013Frobenius property. These algorithms are proved to be especially efficient when the characteristic polynomial of the recurrence is a Pisot polynomial. Finally, we outline algorithms for generating recurrences that satisfy our conditions. <\/jats:p>","DOI":"10.1142\/s179383092250094x","type":"journal-article","created":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T15:08:03Z","timestamp":1650380883000},"source":"Crossref","is-referenced-by-count":1,"title":["Linear recurrent cryptography: Golden-like cryptography for higher order linear recurrences"],"prefix":"10.1142","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8264-3701","authenticated-orcid":false,"given":"Sergiy","family":"Koshkin","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Houston-Downtown, One Main Street, Houston, TX 77002, USA"}]},{"given":"Daniel","family":"Rodriguez","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Houston-Downtown, One Main Street, Houston, TX 77002, USA"}]}],"member":"219","published-online":{"date-parts":[[2022,5,5]]},"reference":[{"issue":"3","key":"S179383092250094XBIB001","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s00605-008-0011-0","volume":"155","author":"Akiyama S.","year":"2008","journal-title":"Monatsh. Math."},{"key":"S179383092250094XBIB002","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-51502-7","volume-title":"Recurrent Sequences","author":"Andrica D.","year":"2020"},{"key":"S179383092250094XBIB003","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/S0024-3795(96)00290-X","volume":"260","author":"Augot D.","year":"1997","journal-title":"Linear Algebra Appl."},{"issue":"1","key":"S179383092250094XBIB004","doi-asserted-by":"crossref","first-page":"49","DOI":"10.12732\/ijpam.v107i1.5","volume":"107","author":"Bani-Ahmad F.","year":"2016","journal-title":"Int. J. Pure Appl. Math."},{"issue":"1","key":"S179383092250094XBIB005","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1142\/S1793830914500086","volume":"6","author":"Basu M.","year":"2014","journal-title":"Discrete Math. Algorithms Appl."},{"issue":"5","key":"S179383092250094XBIB006","doi-asserted-by":"crossref","first-page":"2517","DOI":"10.1016\/j.chaos.2008.09.030","volume":"41","author":"Basu M.","year":"2009","journal-title":"Chaos Solitons Fractals"},{"issue":"214","key":"S179383092250094XBIB007","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1090\/S0025-5718-96-00693-X","volume":"65","author":"Boyd D.","year":"1996","journal-title":"Math. Comput."},{"issue":"3","key":"S179383092250094XBIB008","first-page":"448","volume":"7","author":"del Rey A.","year":"2008","journal-title":"Int. J. Netw. Secur."},{"issue":"3","key":"S179383092250094XBIB009","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1080\/10586458.2014.992080","volume":"24","author":"Dubickas A.","year":"2015","journal-title":"Exp. Math."},{"issue":"3","key":"S179383092250094XBIB010","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/j.chaos.2011.01.003","volume":"44","author":"Fiorenza A.","year":"2011","journal-title":"Chaos Solitons Fractals"},{"issue":"6","key":"S179383092250094XBIB011","doi-asserted-by":"crossref","first-page":"1307","DOI":"10.1142\/S1793042121500378","volume":"17","author":"Hare K.","year":"2021","journal-title":"Int. J. Number Theory"},{"volume-title":"Linear Algebra","year":"1971","author":"Hoffman K.","key":"S179383092250094XBIB012"},{"key":"S179383092250094XBIB013","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.chaos.2017.10.015","volume":"105","author":"Koshkin S.","year":"2017","journal-title":"Chaos Solitons Fractals"},{"volume-title":"Theory of Matrices","year":"1969","author":"Lancaster P.","key":"S179383092250094XBIB014"},{"volume-title":"Nonnegative Matrices","year":"1988","author":"Minc H.","key":"S179383092250094XBIB015"},{"issue":"3","key":"S179383092250094XBIB016","first-page":"131","volume":"2","author":"Mishra M.","year":"2012","journal-title":"Int. J. Cryptogr. Inf. Secur."},{"issue":"8","key":"S179383092250094XBIB017","first-page":"1","volume":"12","author":"Mohamed M.","year":"2014","journal-title":"Int. J. Comput. Sci. Inf. Secur."},{"issue":"5","key":"S179383092250094XBIB018","first-page":"1633","volume":"49","author":"Nej M.","year":"2019","journal-title":"Rocky Mountain J. Math."},{"key":"S179383092250094XBIB019","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.laa.2005.06.037","volume":"412","author":"Noutsos D.","year":"2006","journal-title":"Linear Algebra Appl."},{"key":"S179383092250094XBIB020","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/S0024-3795(02)00414-7","volume":"353","author":"Schneider H.","year":"2002","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"S179383092250094XBIB021","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.chaos.2005.12.054","volume":"32","author":"Stakhov A.","year":"2006","journal-title":"Chaos Solitons Fractals"},{"key":"S179383092250094XBIB022","doi-asserted-by":"crossref","first-page":"1138","DOI":"10.1016\/j.chaos.2006.03.069","volume":"32","author":"Stakhov A.","year":"2007","journal-title":"Chaos Solitons Fractals"},{"issue":"5","key":"S179383092250094XBIB023","first-page":"203","volume":"7","author":"Sudha K.","year":"2007","journal-title":"Int. J. Comput. Sci. Netw. Secur."},{"key":"S179383092250094XBIB024","first-page":"65","volume-title":"Proc. IEEE Conf. Open Systems","author":"Tahghighi M.","year":"2011"},{"key":"S179383092250094XBIB025","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05156-2","volume-title":"Matrix Iterative Analysis","author":"Varga R.","year":"2000"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383092250094X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,24]],"date-time":"2023-03-24T10:13:42Z","timestamp":1679652822000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S179383092250094X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5,5]]},"references-count":25,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["10.1142\/S179383092250094X"],"URL":"https:\/\/doi.org\/10.1142\/s179383092250094x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2022,5,5]]},"article-number":"2250094"}}