{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,14]],"date-time":"2026-06-14T02:35:53Z","timestamp":1781404553575,"version":"3.54.1"},"reference-count":29,"publisher":"Wiley","license":[{"start":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T00:00:00Z","timestamp":1543708800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["18J23484"],"award-info":[{"award-number":["18J23484"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Security and Communication Networks"],"published-print":{"date-parts":[[2018,12,2]]},"abstract":"<jats:p>Elliptic curves (ECs) are considered as one of the highly secure structures against modern computational attacks. In this paper, we present an efficient method based on an ordered isomorphic EC for the generation of a large number of distinct, mutually uncorrelated, and cryptographically strong injective S-boxes. The proposed scheme is characterized in terms of time complexity and the number of the distinct S-boxes. Furthermore, rigorous analysis and comparison of the newly developed method with some of the existing methods are conducted. Experimental results reveal that the newly developed scheme can efficiently generate a large number of distinct, uncorrelated, and secure S-boxes when compared with some of the well-known existing schemes.<\/jats:p>","DOI":"10.1155\/2018\/3421725","type":"journal-article","created":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T18:33:11Z","timestamp":1543775591000},"page":"1-9","source":"Crossref","is-referenced-by-count":48,"title":["An Injective S-Box Design Scheme over an Ordered Isomorphic Elliptic Curve and Its Characterization"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7941-3419","authenticated-orcid":true,"given":"Naveed Ahmed","family":"Azam","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1373-7701","authenticated-orcid":true,"given":"Umar","family":"Hayat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4431-3186","authenticated-orcid":true,"given":"Ikram","family":"Ullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1949.tb00928.x"},{"key":"2","year":"1999"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-58108-1_24"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-46877-3_35"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/5790189"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.compeleceng.2012.11.019"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2012.01.009"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.aej.2015.01.003"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1002\/sec.1110"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/s13319-015-0043-x"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-39799-X_31"},{"key":"16","year":"1994"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1080\/00207721.2017.1364446"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-016-3756-0"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-48910-X_20"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1007\/s11277-018-5698-1"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2018.10.011"},{"key":"23","year":"1809"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.2307\/1971363"},{"key":"26","series-title":"Discrete Mathematics and its Applications","year":"2008"},{"issue":"2","key":"27","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.chaos.2004.04.023","volume":"23","year":"2005","journal-title":"Chaos, Solitons and Fractals"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2006.08.003"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1080\/01611190802653228"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04722-4"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.17485\/ijst\/2015\/v8i28\/71759"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.022"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2010.07.019"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127415501278"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172769"}],"container-title":["Security and Communication Networks"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/3421725.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/3421725.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/scn\/2018\/3421725.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T18:33:16Z","timestamp":1543775596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/scn\/2018\/3421725\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,2]]},"references-count":29,"alternative-id":["3421725","3421725"],"URL":"https:\/\/doi.org\/10.1155\/2018\/3421725","relation":{},"ISSN":["1939-0114","1939-0122"],"issn-type":[{"value":"1939-0114","type":"print"},{"value":"1939-0122","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,2]]}}}