{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T11:29:51Z","timestamp":1776166191224,"version":"3.50.1"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,11,1]],"date-time":"2026-11-01T00:00:00Z","timestamp":1793491200000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["ORF-2026-323"],"award-info":[{"award-number":["ORF-2026-323"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2026,11]]},"DOI":"10.1016\/j.cam.2026.117633","type":"journal-article","created":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:15:17Z","timestamp":1774311317000},"page":"117633","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Enhanced S-box design using hybrid sinusoidal rational exponential map with optimization technique"],"prefix":"10.1016","volume":"486","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-4773-280X","authenticated-orcid":false,"given":"Furqan","family":"Ahmad","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5715-9299","authenticated-orcid":false,"given":"Muhammad Kamran","family":"Jamil","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0005-2305-0179","authenticated-orcid":false,"given":"Zubair","family":"Hafeez","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4492-1082","authenticated-orcid":false,"given":"Adel Fahad","family":"Alrasheedi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0007-0473-1571","authenticated-orcid":false,"given":"Muhammad","family":"Junaid Murtaza","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"6","key":"10.1016\/j.cam.2026.117633_bib0001","doi-asserted-by":"crossref","first-page":"2322","DOI":"10.1109\/TCSI.2018.2888688","article-title":"Dynamic analysis of digital chaotic maps via state-mapping networks","volume":"66","author":"Li","year":"2019","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"issue":"24","key":"10.1016\/j.cam.2026.117633_bib0002","doi-asserted-by":"crossref","first-page":"5019","DOI":"10.3390\/electronics13245019","article-title":"A lightweight keystream generator based on expanded chaos with a counter for secure IoT","volume":"13","author":"Lee","year":"2024","journal-title":"Electronics"},{"key":"10.1016\/j.cam.2026.117633_bib0003","doi-asserted-by":"crossref","first-page":"14103","DOI":"10.1007\/s11071-025-10934-6","article-title":"A review of chaotification techniques for discrete-time systems","volume":"113","author":"Moysis","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.cam.2026.117633_bib0004","series-title":"Multi-objective ant colony optimization: review","author":"Awadallah","year":"2024"},{"issue":"5","key":"10.1016\/j.cam.2026.117633_bib0005","doi-asserted-by":"crossref","DOI":"10.1016\/j.heliyon.2023.e15902","article-title":"Secure communication through reliable S-box design: a proposed approach using coset graphs and matrix operations","volume":"9","author":"Razaq","year":"2023","journal-title":"Heliyon"},{"key":"10.1016\/j.cam.2026.117633_bib0006","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2017.02.031","article-title":"Delay introducing method to improve the dynamical degradation of a digital chaotic map","volume":"396","author":"Liu","year":"2017","journal-title":"Inf. Sci."},{"key":"10.1016\/j.cam.2026.117633_bib0007","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2023.122030","article-title":"Region of interest-based medical image encryption technique based on chaotic S-boxes","volume":"238","author":"Jamal","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.cam.2026.117633_bib0008","doi-asserted-by":"crossref","first-page":"14081","DOI":"10.1109\/ACCESS.2019.2893538","article-title":"2D Logistic-modulated sine-coupling-logistic chaotic map for image encryption","volume":"7","author":"Zhu","year":"2019","journal-title":"IEEE Access"},{"issue":"41","key":"10.1016\/j.cam.2026.117633_bib0009","doi-asserted-by":"crossref","first-page":"30329","DOI":"10.1007\/s11042-020-09595-x","article-title":"An improved digital logistic map and its application in image encryption","volume":"79","author":"Xiang","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"10.1016\/j.cam.2026.117633_bib0010","doi-asserted-by":"crossref","first-page":"653","DOI":"10.1007\/s11071-021-07198-1","article-title":"Uniform non-degeneracy discrete chaotic system and its application in image encryption","volume":"108","author":"Liu","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.cam.2026.117633_bib0011","article-title":"Proposed hybrid encryption algorithm for robust 3D image communication over wireless channels","volume":"273","author":"Mai","year":"2023","journal-title":"Optik"},{"key":"10.1016\/j.cam.2026.117633_bib0012","doi-asserted-by":"crossref","first-page":"2841","DOI":"10.1007\/s11071-022-07956-9","article-title":"A new S-box three-layer optimization method and its application","volume":"111","author":"Su","year":"2023","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.cam.2026.117633_bib0013","series-title":"A novel S-box generator using frobenius automorphism and its applications in image encryption","first-page":"1","author":"Ali","year":"2024"},{"key":"10.1016\/j.cam.2026.117633_bib0014","series-title":"New color image encryption technique based on three-dimensional logistic map and Grey Wolf Optimization-based generated substitution boxes","author":"Khan","year":"2023"},{"key":"10.1016\/j.cam.2026.117633_bib0015","series-title":"Kookaburra optimization algorithm: a new bio-inspired metaheuristic algorithm for solving optimization problems","first-page":"9","author":"Dehghani","year":"2024"},{"key":"10.1016\/j.cam.2026.117633_bib0016","series-title":"A survey on several new popular swarm intelligence optimization algorithms","first-page":"1","author":"Wei","year":"2023"},{"key":"10.1016\/j.cam.2026.117633_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.eswa.2023.122779","article-title":"Substitution box generator with enhanced cryptographic properties and minimal computation time","volume":"241","author":"Haider","year":"2024","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.cam.2026.117633_bib0018","series-title":"Towards accurate keyspace analysis of chaos-based image ciphers","first-page":"1","author":"Abba","year":"2024"},{"key":"10.1016\/j.cam.2026.117633_bib0019","series-title":"A method for designing substitution boxes based on chaos with high nonlinearity","first-page":"1","author":"Artuger","year":"2024"},{"key":"10.1016\/j.cam.2026.117633_bib0020","article-title":"An S-box multi-objective optimization algorithm based on composite chaos and rolling boolean","volume":"191","author":"Cheng","year":"2024","journal-title":"Res. Square"},{"key":"10.1016\/j.cam.2026.117633_bib0021","article-title":"Enhancing logistic chaotic map for improved cryptographic security in random number generation","volume":"80","author":"Alawida","year":"2024","journal-title":"J. Inf. Security Appl."},{"key":"10.1016\/j.cam.2026.117633_bib0022","doi-asserted-by":"crossref","first-page":"135880","DOI":"10.1109\/ACCESS.2023.3337443","article-title":"A robust S-box design using cyclic groups and image encryption","volume":"11","author":"Ali","year":"2023","journal-title":"IEEE Access"},{"key":"10.1016\/j.cam.2026.117633_bib0023","series-title":"A novel post-processing approach for improving minimum nonlinearity in S-boxes: a case study based on 2D hyperchaotic schaffer transformation map","first-page":"1688","author":"n","year":"2025"},{"issue":"24","key":"10.1016\/j.cam.2026.117633_bib0024","doi-asserted-by":"crossref","first-page":"34001","DOI":"10.1007\/s11071-025-11815-8","article-title":"S-Box generation through enhanced hybrid chaotic maps and tabu-optimized technique","volume":"113","author":"Naz","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"10.1016\/j.cam.2026.117633_bib0025","article-title":"An efficient 2D hyperchaos and DNA encoding-based S-box generation method using chaotic evolutionary improvement algorithm for nonlinearity","volume":"191","author":"n","year":"2025","journal-title":"Chaos, Solitons Fractals"},{"issue":"1","key":"10.1016\/j.cam.2026.117633_bib0026","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-025-02102-y","article-title":"Secure medical image encryption with hyperelliptic curve-based S-boxes","volume":"15","author":"Alali","year":"2025","journal-title":"Sci. Rep."},{"key":"10.1016\/j.cam.2026.117633_bib0027","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/j.aej.2025.03.109","article-title":"Secure S-box construction with 1D chaotic maps and finite field theory for block cipher encryption","volume":"125","author":"Jamal","year":"2025","journal-title":"Alexand. Eng. J."},{"issue":"1","key":"10.1016\/j.cam.2026.117633_bib0028","article-title":"Lightweight image encryption scheme for IoT environment and machine learning-driven robust S-box selection","volume":"88","author":"que","year":"2025","journal-title":"Telecommun. Syst."},{"key":"10.1016\/j.cam.2026.117633_bib0029","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.ijleo.2018.12.178","article-title":"An image encryption algorithm based on modified logistic chaotic map","volume":"181","author":"Han","year":"2019","journal-title":"Optik"},{"key":"10.1016\/j.cam.2026.117633_bib0030","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.ins.2021.04.013","article-title":"A privacy image encryption algorithm based on piecewise coupled map lattice with multi dynamic coupling coefficient","volume":"569","author":"Wang","year":"2021","journal-title":"Inf. Sci."},{"key":"10.1016\/j.cam.2026.117633_bib0031","series-title":"A novel perturbation method to reduce the dynamical degradation of digital chaotic maps","first-page":"1","author":"Liu","year":"2021"},{"key":"10.1016\/j.cam.2026.117633_bib0032","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.ins.2018.12.048","article-title":"Cosine-transform-based chaotic system for image encryption","volume":"480","author":"Hua","year":"2019","journal-title":"Inf. Sci."},{"key":"10.1016\/j.cam.2026.117633_bib0033","doi-asserted-by":"crossref","DOI":"10.1016\/j.jvcir.2022.103467","article-title":"A novel unsupervised multiple feature hashing for image retrieval and indexing (MFHIRI)","volume":"84","author":"Sharma","year":"2022","journal-title":"J. Vis. Commun. Image Represent"},{"issue":"3","key":"10.1016\/j.cam.2026.117633_bib0034","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1016\/j.camwa.2010.05.010","article-title":"A wavelet-based tool for studying non-periodicity","volume":"60","author":"Benitez","year":"2010","journal-title":"Comput. Math. Appl."},{"issue":"5","key":"10.1016\/j.cam.2026.117633_bib0035","doi-asserted-by":"crossref","DOI":"10.1142\/S0129183119500335","article-title":"Exploiting ergodicity of the logistic map using deep-zoom to improve security of chaos-based cryptosystems","volume":"30","author":"Machicao","year":"2019","journal-title":"Int. J. Mod. Phys. C"}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726002761?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726002761?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T10:11:14Z","timestamp":1776161474000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726002761"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,11]]},"references-count":35,"alternative-id":["S0377042726002761"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117633","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2026,11]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Enhanced S-box design using hybrid sinusoidal rational exponential map with optimization technique","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117633","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"117633"}}