{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T14:03:28Z","timestamp":1769004208963,"version":"3.49.0"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2017]]},"abstract":"The substitution box is a basic tool to convert the plaintext into an enciphered format. In this paper, we use coset diagram for the action of P<\/mml:mi>S<\/mml:mi>L<\/mml:mi>(<\/mml:mo>2<\/mml:mn>,<\/mml:mo>Z<\/mml:mi>)<\/mml:mo><\/mml:math> on projective line over the finite field G<\/mml:mi>F<\/mml:mi>2<\/mml:mn><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math> to construct proposed S-box. The vertices of the cost diagram are elements of G<\/mml:mi>F<\/mml:mi>2<\/mml:mn><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math> which can be represented by powers of \u03b1<\/mml:mi><\/mml:mrow><\/mml:math>, where \u03b1<\/mml:mi><\/mml:mrow><\/mml:math> is the root of irreducible polynomial p<\/mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:mfenced>=<\/mml:mo>x<\/mml:mi><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup>+<\/mml:mo>x<\/mml:mi><\/mml:mrow>4<\/mml:mn><\/mml:mrow><\/mml:msup>+<\/mml:mo>1<\/mml:mn><\/mml:math> over Z<\/mml:mi><\/mml:mrow>2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>. Let G<\/mml:mi>F<\/mml:mi><\/mml:mrow>\u204e<\/mml:mo><\/mml:mrow><\/mml:msup>2<\/mml:mn><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math> denote the elements of G<\/mml:mi>F<\/mml:mi>2<\/mml:mn><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math> which are of the form of even powers of \u03b1<\/mml:mi><\/mml:mrow><\/mml:math>. In the first step, we construct a 16<\/mml:mn>\u00d7<\/mml:mo>16<\/mml:mn><\/mml:math> matrix with the elements of G<\/mml:mi>F<\/mml:mi><\/mml:mrow>\u204e<\/mml:mo><\/mml:mrow><\/mml:msup>2<\/mml:mn><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math> in a specific order, determined by the coset diagram. Next, we consider h<\/mml:mi>:<\/mml:mo>G<\/mml:mi>F<\/mml:mi><\/mml:mrow>\u204e<\/mml:mo><\/mml:mrow><\/mml:msup>2<\/mml:mn><\/mml:mrow>9<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced>\u27f6<\/mml:mo>G<\/mml:mi>F<\/mml:mi>2<\/mml:mn><\/mml:mrow>8<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math> defined by h<\/mml:mi>\u03b1<\/mml:mi><\/mml:mrow>2<\/mml:mn>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced>=<\/mml:mo>\u03c9<\/mml:mi><\/mml:mrow>n<\/mml:mi><\/mml:mrow><\/mml:msup><\/mml:math> to destroy the structure of G<\/mml:mi>F<\/mml:mi>2<\/mml:mn><\/mml:mrow>8<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:mfenced><\/mml:math>. In the last step, we apply a bijective map g<\/mml:mi><\/mml:mrow><\/mml:math> on each element of the matrix to evolve proposed S-box. The ability of the proposed S-box is examined by different available algebraic and statistical analyses. The results are then compared with the familiar S-boxes. We get encouraging statistics of the proposed box after comparison.<\/jats:p>","DOI":"10.1155\/2017\/5101934","type":"journal-article","created":{"date-parts":[[2017,11,20]],"date-time":"2017-11-20T18:31:04Z","timestamp":1511202664000},"page":"1-16","source":"Crossref","is-referenced-by-count":51,"title":["A Novel Construction of Substitution Box Involving Coset Diagram and a Bijective Map"],"prefix":"10.1155","volume":"2017","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, Jauharabad, Pakistan"}]},{"given":"Awais","family":"Yousaf","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan"}]},{"given":"Umer","family":"Shuaib","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University Faisalabad, Faisalabad, Pakistan"}]},{"given":"Nasir","family":"Siddiqui","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, University of Engineering and Technology, Taxila, Punjab, Pakistan"}]},{"given":"Atta","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"}]},{"given":"Adil","family":"Waheed","sequence":"additional","affiliation":[{"name":"Department of Information Technology, University of Education Lahore, Jauharabad Campus, Jauharabad, Pakistan"}]}],"member":"311","reference":[{"key":"19","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1949.tb00928.x"},{"key":"7","year":"2002"},{"key":"5","first-page":"1","volume-title":"encyclopaedia of design theory","year":"2013"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1080\/00927879708825955"},{"key":"16","volume":"89","year":"2015"},{"issue":"48","key":"17","first-page":"77","volume":"2","year":"1993","journal-title":"Journal of the London Mathematical Society"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1216\/JCA-2010-2-4-501"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1049\/ip-e.1988.0044"},{"issue":"2","key":"24","first-page":"137","volume":"9","year":"2001","journal-title":"Turkish Journal of Electrical Engineering & Computer Sciences"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/BF00630563"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.5560\/zna.2012-0022"},{"key":"9","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":"13","first-page":"1263","volume":"5","year":"2010","journal-title":"International Journal of Contemporary Mathematical Sciences"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2015.01.003"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.022"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.04.023"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-0904-x"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3046-0"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-017-3409-1"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s00521-015-1887-y"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2017\/5101934.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2017\/5101934.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2017\/5101934.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,11,20]],"date-time":"2017-11-20T18:31:06Z","timestamp":1511202666000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2017\/5101934\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"references-count":21,"alternative-id":["5101934","5101934"],"URL":"https:\/\/doi.org\/10.1155\/2017\/5101934","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"value":"1939-0114","type":"print"},{"value":"1939-0122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017]]}}}