{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T06:01:49Z","timestamp":1769148109994,"version":"3.49.0"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,10,4]],"date-time":"2018-10-04T00:00:00Z","timestamp":1538611200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Research Center of the Center for Female Scientific and Medical Colleges"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2018,10,4]]},"abstract":"<jats:p>In the literature, different algebraic techniques have been applied on Galois field <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>G<\/mml:mi><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">8<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math> to construct substitution boxes. In this paper, instead of Galois field <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>G<\/mml:mi><mml:mi>F<\/mml:mi><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">8<\/mml:mn><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>, we use a cyclic group <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">255<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> in the formation of proposed substitution box. The construction proposed S-box involves three simple steps. In the first step, we introduce a special type of transformation <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>T<\/mml:mi><\/mml:mrow><\/mml:math> of order 255 to generate <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">255<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. Next, we adjoin <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mn fontstyle=\"italic\">0<\/mml:mn><\/mml:mrow><\/mml:math> to <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mrow><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">255<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> and write the elements of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:msub><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">255<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>\u222a<\/mml:mo><mml:mfenced open=\"{\" close=\"}\" separators=\"|\"><mml:mrow><mml:mn fontstyle=\"italic\">0<\/mml:mn><\/mml:mrow><\/mml:mfenced><\/mml:math> in <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mn fontstyle=\"italic\">16<\/mml:mn><mml:mo>\u00d7<\/mml:mo><mml:mn fontstyle=\"italic\">16<\/mml:mn><\/mml:math> matrix to destroy the initial sequence <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mn fontstyle=\"italic\">0,1<\/mml:mn><mml:mo>,<\/mml:mo><mml:mn fontstyle=\"italic\">2<\/mml:mn><mml:mo>,<\/mml:mo><mml:mo>\u2026<\/mml:mo><mml:mo>,<\/mml:mo><mml:mn fontstyle=\"italic\">255<\/mml:mn><\/mml:math>. In the <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mrow><mml:msup><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">n<\/mml:mi><mml:mi mathvariant=\"normal\">d<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math> step, the randomness in the data is increased by applying certain permutations of the symmetric group <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:msub><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">16<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math> on rows and columns of the matrix. In the last step we consider the symmetric group <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:msub><mml:mrow><mml:mi>S<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn fontstyle=\"italic\">256<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>, and positions of the elements of the matrix obtained in step 2 are changed by its certain permutations to construct the suggested S-box. The strength of our S-box to work against cryptanalysis is checked through various tests. The results are then compared with the famous S-boxes. The comparison shows that the ability of our S-box to create confusion is better than most of the famous S-boxes.<\/jats:p>","DOI":"10.1155\/2018\/4987021","type":"journal-article","created":{"date-parts":[[2018,10,4]],"date-time":"2018-10-04T19:40:28Z","timestamp":1538682028000},"page":"1-9","source":"Crossref","is-referenced-by-count":18,"title":["A Novel Technique for the Construction of Safe Substitution Boxes Based on Cyclic and Symmetric Groups"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1898-4082","authenticated-orcid":true,"given":"Abdul","family":"Razaq","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Education Lahore, Jauharabad Campus, Pakistan"}]},{"given":"Hanan A.","family":"Al-Olayan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Saud University, Saudi Arabia"}]},{"given":"Atta","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University Islamabad, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0704-2230","authenticated-orcid":true,"given":"Arshad","family":"Riaz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Education Lahore, Jauharabad Campus, Pakistan"}]},{"given":"Adil","family":"Waheed","sequence":"additional","affiliation":[{"name":"Department of Information Technology, University of Education Lahore, Jauharabad Campus, Pakistan"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1949.tb00928.x"},{"key":"2","year":"2011"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00630563"},{"key":"4","year":"2009"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48285-7"},{"key":"6","year":"2002"},{"key":"8","volume":"2017","year":"2017","journal-title":"Security and Communication Networks"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.17485\/ijst\/2015\/v8i28\/71759"},{"issue":"2","key":"11","first-page":"111","volume":"48","year":"2011","journal-title":"Proceedings of the Pakistan Academy of Sciences"},{"issue":"25-28","key":"12","first-page":"1263","volume":"5","year":"2010","journal-title":"International Journal of Contemporary Mathematical Sciences"},{"key":"14","year":"1998"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2015.01.003"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.022"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.04.023"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0904-x"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3046-0"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3409-1"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-1887-y"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-88757-9"},{"key":"20","first-page":"523","volume-title":"On the design of S-boxes","year":"1986"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1049\/ip-e.1988.0044"},{"key":"22","first-page":"1","journal-title":"Neural Computing and Applications"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.3390\/e20070525"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.5560\/zna.2012-0022"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/4987021.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/4987021.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/4987021.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,10,4]],"date-time":"2018-10-04T19:40:32Z","timestamp":1538682032000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2018\/4987021\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,4]]},"references-count":24,"alternative-id":["4987021","4987021"],"URL":"https:\/\/doi.org\/10.1155\/2018\/4987021","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"value":"1939-0114","type":"print"},{"value":"1939-0122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,4]]}}}