{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:10Z","timestamp":1760241670286,"version":"build-2065373602"},"reference-count":8,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,7,19]],"date-time":"2018-07-19T00:00:00Z","timestamp":1531958400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["MTM2016-77213-R"],"award-info":[{"award-number":["MTM2016-77213-R"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cryptography"],"abstract":"<jats:p>In 2008, Doliskani et al. proposed an ElGamal-style encryption scheme using the symmetric group Sn as mathematical platform. In 2012, an improvement of the cryptosystem\u2019s memory requirements was suggested by Othman. The proposal by Doliskani et al. in particular requires the discrete logarithm problem in Sn, using its natural representation, to be hard. Making use of the Chinese Remainder Theorem, we describe an efficient method to solve this discrete logarithm problem, yielding a polynomial time secret key recovery attack against Doliskani et al.\u2019s proposal.<\/jats:p>","DOI":"10.3390\/cryptography2030016","type":"journal-article","created":{"date-parts":[[2018,7,20]],"date-time":"2018-07-20T02:10:11Z","timestamp":1532052611000},"page":"16","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Cryptanalysis of a Proposal Based on the Discrete Logarithm Problem Inside Sn"],"prefix":"10.3390","volume":"2","author":[{"given":"Mar\u00eda Isabel","family":"Gonz\u00e1lez Vasco","sequence":"first","affiliation":[{"name":"MACIMTE, Universidad Rey Juan Carlos, 28933 M\u00f3stoles, Madrid, Spain"}]},{"given":"Angela","family":"Robinson","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA"}]},{"given":"Rainer","family":"Steinwandt","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431, USA"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,19]]},"reference":[{"key":"ref_1","first-page":"226","article-title":"A Cryptosystem Based on the Symmetric Group Sn","volume":"8","author":"Doliskani","year":"2008","journal-title":"IJCSNS Int. J. Comput. Sci. Netw. Secur."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","article-title":"A public key cryptosystem and a signature scheme based on discrete logarithms","volume":"31","author":"Gamal","year":"1985","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Jones, G.A., and Jones, J.M. (1998). Elementary Number Theory, Springer.","DOI":"10.1007\/978-1-4471-0613-5"},{"key":"ref_4","unstructured":"Bogomolny, A. (2018, May 01). Chinese Remainder Theorem from Interactive Mathematics Miscellany and Puzzles. Available online: http:\/\/www.cut-the-knot.org\/blue\/chinese.shtml."},{"key":"ref_5","unstructured":"Von zur Gathen, J., and Gerhard, J. (1999). Chapter The Euclidean Algorithm. Modern Computer Algebra, The Press Syndicate of the University of Cambridge."},{"key":"ref_6","first-page":"92","article-title":"\u00dcber die Maximalordnung der Permutationen gegebenen Grades","volume":"5","author":"Landau","year":"1903","journal-title":"Arch. Math. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"269","DOI":"10.5802\/afst.612","article-title":"Majoration explicite de l\u2019ordre Maximum d\u2019un \u00c9l\u00e9ment du groupe sym\u00e9trique","volume":"6","author":"Massias","year":"1984","journal-title":"Ann. Fac. Sci. Toulouse Math."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1090\/S0025-5718-1989-0979940-4","article-title":"Effective Bounds for the Maximal Order of an Element in the Symmetric Group","volume":"53","author":"Massias","year":"1989","journal-title":"Math. Comput."}],"container-title":["Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2410-387X\/2\/3\/16\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:13:00Z","timestamp":1760195580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2410-387X\/2\/3\/16"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,19]]},"references-count":8,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["cryptography2030016"],"URL":"https:\/\/doi.org\/10.3390\/cryptography2030016","relation":{},"ISSN":["2410-387X"],"issn-type":[{"type":"electronic","value":"2410-387X"}],"subject":[],"published":{"date-parts":[[2018,7,19]]}}}