{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T14:44:11Z","timestamp":1775745851364,"version":"3.50.1"},"reference-count":57,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2023,2,1]],"date-time":"2023-02-01T00:00:00Z","timestamp":1675209600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61862042"],"award-info":[{"award-number":["61862042"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Mathematics and Computers in Simulation"],"published-print":{"date-parts":[[2023,2]]},"DOI":"10.1016\/j.matcom.2022.07.030","type":"journal-article","created":{"date-parts":[[2022,8,8]],"date-time":"2022-08-08T17:32:15Z","timestamp":1659979935000},"page":"89-114","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":108,"special_numbering":"C","title":["A cluster of 1D quadratic chaotic map and its applications in image encryption"],"prefix":"10.1016","volume":"204","author":[{"given":"Lingfeng","family":"Liu","sequence":"first","affiliation":[]},{"given":"Jie","family":"Wang","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"issue":"12","key":"10.1016\/j.matcom.2022.07.030_b1","doi-asserted-by":"crossref","first-page":"3847","DOI":"10.1007\/s00521-017-2970-3","article-title":"A novel image encryption scheme based on orthogonal matrix, skew tent map, and XOR operation","volume":"30","author":"Ahmad","year":"2018","journal-title":"Neural Comput. Appl."},{"issue":"17","key":"10.1016\/j.matcom.2022.07.030_b2","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"10.1016\/j.matcom.2022.07.030_b3","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.optlaseng.2016.08.009","article-title":"A novel chaos-based image encryption algorithm using DNA sequence operations","volume":"88","author":"Chai","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"10.1016\/j.matcom.2022.07.030_b4","doi-asserted-by":"crossref","DOI":"10.1016\/j.chaos.2020.110131","article-title":"Reservoir computing based on quenched chaos","volume":"140","author":"Choi","year":"2020","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.matcom.2022.07.030_b5","doi-asserted-by":"crossref","DOI":"10.1155\/2020\/7647421","article-title":"An image encryption scheme using a 1D chaotic double section skew tent map","author":"Elmanfaloty","year":"2020","journal-title":"Complexity"},{"key":"10.1016\/j.matcom.2022.07.030_b6","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.optlastec.2019.01.039","article-title":"An image compression and encryption algorithm based on chaotic system and compressive sensing","volume":"115","author":"Gong","year":"2019","journal-title":"Opt. Laser Technol."},{"key":"10.1016\/j.matcom.2022.07.030_b7","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1007\/978-3-662-48410-4_7","article-title":"The 0-1 test for chaos: A review","author":"Gottwald","year":"2016","journal-title":"Chaos Detect. Predict."},{"issue":"3","key":"10.1016\/j.matcom.2022.07.030_b8","doi-asserted-by":"crossref","first-page":"1123","DOI":"10.1007\/s11071-015-2392-7","article-title":"A novel chaos-based image encryption using DNA sequence operation and secure hash algorithm SHA-2","volume":"83","author":"Guesmi","year":"2016","journal-title":"Nonlinear Dynam."},{"key":"10.1016\/j.matcom.2022.07.030_b9","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.ijleo.2019.03.065","article-title":"A novel bit level multiphase algorithm for image encryption based on PWLCM chaotic map","volume":"184","author":"Hasheminejad","year":"2019","journal-title":"Optik"},{"key":"10.1016\/j.matcom.2022.07.030_b10","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.ins.2014.11.018","article-title":"2D sine logistic modulation map for image encryption","volume":"297","author":"Hua","year":"2015","journal-title":"Inform. Sci."},{"key":"10.1016\/j.matcom.2022.07.030_b11","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/j.ins.2020.09.032","article-title":"Cross-plane colour image encryption using a two-dimensional logistic tent modular map","volume":"546","author":"Hua","year":"2021","journal-title":"Inform. Sci."},{"key":"10.1016\/j.matcom.2022.07.030_b12","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.future.2020.02.029","article-title":"Color image encryption using non-dominated sorting genetic algorithm with local chaotic search based 5D chaotic map","volume":"107","author":"Kaur","year":"2020","journal-title":"Future Gener. Comput. Syst. - Int. J. Escience"},{"issue":"2","key":"10.1016\/j.matcom.2022.07.030_b13","doi-asserted-by":"crossref","first-page":"943","DOI":"10.1007\/s11045-018-0589-x","article-title":"Chaos based efficient selective image encryption","volume":"30","author":"Khan","year":"2019","journal-title":"Multidimens. Syst. Signal Process."},{"key":"10.1016\/j.matcom.2022.07.030_b14","article-title":"DNA and plaintext dependent chaotic visual selective image encryption","volume":"8","author":"Khan","year":"2020","journal-title":"IEEE Access"},{"key":"10.1016\/j.matcom.2022.07.030_b15","article-title":"Chaos and compressive sensing based novel image encryption scheme","volume":"58","author":"Khan","year":"2021","journal-title":"J. Inf. Secur. Appl."},{"issue":"4","key":"10.1016\/j.matcom.2022.07.030_b16","doi-asserted-by":"crossref","first-page":"629","DOI":"10.15388\/Informatica.2017.149","article-title":"An improved image encryption scheme based on a non-linear chaotic algorithm and substitution boxes","volume":"28","author":"Khan","year":"2017","journal-title":"Informatica"},{"issue":"16","key":"10.1016\/j.matcom.2022.07.030_b17","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.110.168703","article-title":"Correlation dimension of complex network","volume":"110","author":"Lacasa","year":"2013","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"10.1016\/j.matcom.2022.07.030_b18","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1049\/iet-ipr.2018.5900","article-title":"Novel image encryption algorithm based on improved logistic map","volume":"13","author":"Li","year":"2019","journal-title":"IET Image Process."},{"issue":"9","key":"10.1016\/j.matcom.2022.07.030_b19","doi-asserted-by":"crossref","first-page":"1497","DOI":"10.3390\/sym12091497","article-title":"A novel chaos-based color image encryption scheme using bit-level permutation","volume":"12","author":"Li","year":"2020","journal-title":"Symmetry"},{"key":"10.1016\/j.matcom.2022.07.030_b20","doi-asserted-by":"crossref","first-page":"83596","DOI":"10.1109\/ACCESS.2020.2991420","article-title":"Color image encryption algorithm based on DNA coding and double chaos system","volume":"8","author":"Liu","year":"2020","journal-title":"IEEE Access"},{"issue":"5","key":"10.1016\/j.matcom.2022.07.030_b21","doi-asserted-by":"crossref","DOI":"10.1142\/S0218127418500591","article-title":"Reducing the dynamical degradation by bi-coupling digital chaotic maps","volume":"28","author":"Liu","year":"2018","journal-title":"Int. J. Bifurcation Chaos"},{"issue":"1","key":"10.1016\/j.matcom.2022.07.030_b22","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1186\/s40064-016-1959-1","article-title":"A new image encryption algorithm based on logistic chaotic map with varying parameter","volume":"5","author":"Liu","year":"2016","journal-title":"SpringerPlus"},{"key":"10.1016\/j.matcom.2022.07.030_b23","doi-asserted-by":"crossref","first-page":"21445","DOI":"10.1007\/s11042-017-5594-9","article-title":"A new simple one-dimensional chaotic map and its application for image encryption","volume":"77","author":"Liu","year":"2017","journal-title":"Multimedia Tools Appl."},{"issue":"3","key":"10.1016\/j.matcom.2022.07.030_b24","doi-asserted-by":"crossref","first-page":"2917","DOI":"10.1007\/s11071-020-05654-y","article-title":"Cryptanalysis and enhancement of an image encryption scheme based on a 1-D coupled Sine map","volume":"100","author":"Liu","year":"2020","journal-title":"Nonlinear Dynam."},{"issue":"10","key":"10.1016\/j.matcom.2022.07.030_b25","doi-asserted-by":"crossref","first-page":"3320","DOI":"10.1016\/j.camwa.2010.03.017","article-title":"Color image encryption based on one-time keys and robust chaotic maps","volume":"59","author":"Liu","year":"2010","journal-title":"Comput. Math. Appl."},{"issue":"16\u201317","key":"10.1016\/j.matcom.2022.07.030_b26","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1016\/j.optcom.2011.04.001","article-title":"Color image encryption using spatial bit-level permutation and high-dimension chaotic system","volume":"284","author":"Liu","year":"2011","journal-title":"Opt. Commun."},{"key":"10.1016\/j.matcom.2022.07.030_b27","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic nonperiodic flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atmos. Sci."},{"key":"10.1016\/j.matcom.2022.07.030_b28","doi-asserted-by":"crossref","first-page":"646","DOI":"10.1016\/j.matcom.2020.07.007","article-title":"Color multiple image encryption scheme based on 3D-chaotic maps","volume":"178","author":"Malik","year":"2020","journal-title":"Math. Comput. Simulation"},{"issue":"1","key":"10.1016\/j.matcom.2022.07.030_b29","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1070\/RM9859","article-title":"Topological integrability, classical and quantum chaos, and the theory of dynamical systems in the physics of condensed matter","volume":"74","author":"Maltsev","year":"2019","journal-title":"Russian Math. Surveys"},{"key":"10.1016\/j.matcom.2022.07.030_b30","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1016\/j.matcom.2021.06.008","article-title":"Cryptanalysis of hybrid secure image encryption based on Julia set fractals and three-dimensional Lorenz chaotic map","volume":"190","author":"Munir","year":"2021","journal-title":"Math. Comput. Simulation"},{"issue":"6","key":"10.1016\/j.matcom.2022.07.030_b31","doi-asserted-by":"crossref","DOI":"10.1063\/1.5099261","article-title":"Image encryption based on the pseudo-orbits from 1D chaotic map","volume":"29","author":"Nepomuceno","year":"2019","journal-title":"Chaos"},{"issue":"3","key":"10.1016\/j.matcom.2022.07.030_b32","doi-asserted-by":"crossref","first-page":"2805","DOI":"10.1007\/s11071-021-06235-3","article-title":"Utilizing true periodic orbits in chaos-based cryptography","volume":"103","author":"Ozturk","year":"2021","journal-title":"Nonlinear Dynam."},{"issue":"3","key":"10.1016\/j.matcom.2022.07.030_b33","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1080\/02564602.2019.1595751","article-title":"Secure, lossless, and noise-resistive image encryption using chaos, hyper-chaos, and DNA sequence operation","volume":"37","author":"Patro","year":"2020","journal-title":"IETE Tech. Rev."},{"issue":"6","key":"10.1016\/j.matcom.2022.07.030_b34","doi-asserted-by":"crossref","first-page":"3513","DOI":"10.1073\/pnas.94.8.3513","article-title":"Not all (possibly) \u2018random\u2019 sequences are created equal","volume":"94","author":"Pincus","year":"1997","journal-title":"Proc. Natl. Acad. Sci."},{"issue":"3","key":"10.1016\/j.matcom.2022.07.030_b35","doi-asserted-by":"crossref","first-page":"341","DOI":"10.3390\/e23030341","article-title":"A new algorithm for digital image encryption based on chaos theory","volume":"23","author":"Pourasad","year":"2021","journal-title":"Entropy"},{"issue":"1","key":"10.1016\/j.matcom.2022.07.030_b36","first-page":"1","article-title":"Dynamical analysis and adaptive fuzzy control for the fractional-order financial risk chaotic system","volume":"2020","author":"Sambas","year":"2020","journal-title":"Adv. Difference Equ."},{"issue":"2","key":"10.1016\/j.matcom.2022.07.030_b37","doi-asserted-by":"crossref","first-page":"788","DOI":"10.3390\/app11020788","article-title":"Mathematical model and FPGA realization of a multi-stable chaotic dynamical system with a closed butterfly-like curve of equilibrium points","volume":"11","author":"Sambas","year":"2021","journal-title":"Appl. Sci."},{"key":"10.1016\/j.matcom.2022.07.030_b38","doi-asserted-by":"crossref","DOI":"10.1109\/ACCESS.2020.3011724","article-title":"A 3-D multi-stable system with a peanut-shaped equilibrium curve: Circuit design, FPGA realization, and an application to image encryption","volume":"8","author":"Sambas","year":"2020","journal-title":"IEEE Access"},{"issue":"4","key":"10.1016\/j.matcom.2022.07.030_b39","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1016\/j.dcan.2020.02.001","article-title":"Securing color image transmission using compression-encryption model with dynamic key generator and efficient symmetric key distribution","volume":"6","author":"Setyaningsih","year":"2020","journal-title":"Digit. Commun. Netw."},{"issue":"24","key":"10.1016\/j.matcom.2022.07.030_b40","doi-asserted-by":"crossref","first-page":"34773","DOI":"10.1007\/s11042-019-08071-5","article-title":"A novel randomized one-dimensional chaotic Chebyshev mapping for chosen plaintext attack secure image encryption with a novel chaotic breadth first traversal","volume":"78","author":"Shakiba","year":"2019","journal-title":"Multimedia Tools Appl."},{"issue":"18","key":"10.1016\/j.matcom.2022.07.030_b41","doi-asserted-by":"crossref","first-page":"3329","DOI":"10.1016\/j.ijleo.2012.11.002","article-title":"An image encryption scheme based on new spatiotemporal chaos","volume":"124","author":"Song","year":"2013","journal-title":"Optik - Int. J. Light Electron Opt."},{"key":"10.1016\/j.matcom.2022.07.030_b42","series-title":"Chaos and Time Series Analysis","author":"Sprott","year":"2003"},{"issue":"SI","key":"10.1016\/j.matcom.2022.07.030_b43","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.ecocom.2016.12.009","article-title":"Hopf and torus bifurcations, torus destruction and chaos in population biology","volume":"30","author":"Stollenwerk","year":"2017","journal-title":"Ecol. Complex."},{"issue":"17","key":"10.1016\/j.matcom.2022.07.030_b44","doi-asserted-by":"crossref","first-page":"24765","DOI":"10.1007\/s11042-019-7602-8","article-title":"A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption","volume":"78","author":"Tang","year":"2019","journal-title":"Multimedia Tools Appl."},{"issue":"3","key":"10.1016\/j.matcom.2022.07.030_b45","doi-asserted-by":"crossref","first-page":"457","DOI":"10.3390\/math10030457","article-title":"A novel chaos-based image encryption using magic square scrambling and octree diffusing","volume":"10","author":"Wang","year":"2022","journal-title":"Mathematics"},{"key":"10.1016\/j.matcom.2022.07.030_b46","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.future.2020.04.002","article-title":"A logistic mapping-based encryption scheme for wireless body area networks","volume":"110","author":"Wang","year":"2020","journal-title":"Future Gener. Comput. Syst. - Int. J. Escience"},{"key":"10.1016\/j.matcom.2022.07.030_b47","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2020.07.051","article-title":"Spatiotemporal chaos in improved cross coupled map lattice and its application in a bit-level image encryption scheme","volume":"544","author":"Wang","year":"2021","journal-title":"Inform. Sci."},{"key":"10.1016\/j.matcom.2022.07.030_b48","article-title":"An iteration-time combination method to reduce the dynamic degradation of digital chaotic maps","volume":"11","author":"Wu","year":"2020","journal-title":"Complexity"},{"key":"10.1016\/j.matcom.2022.07.030_b49","doi-asserted-by":"crossref","DOI":"10.1016\/j.optlaseng.2020.106202","article-title":"Image encryption based on chaotic sub-block scrambling and chaotic digit selection diffusion","volume":"134","author":"Xian","year":"2020","journal-title":"Opt. Lasers Eng."},{"issue":"06","key":"10.1016\/j.matcom.2022.07.030_b50","first-page":"1797","article-title":"Algorithm of image encryption in wavelet domain based on cross chaotic map","volume":"35","author":"Yan","year":"2018","journal-title":"Appl. Res. Comput."},{"key":"10.1016\/j.matcom.2022.07.030_b51","doi-asserted-by":"crossref","first-page":"745","DOI":"10.1007\/s11071-018-4391-y","article-title":"An efficient pixel-level chaotic image encryption algorithm","volume":"94","author":"Ye","year":"2018","journal-title":"Nonlinear Dynam."},{"issue":"24","key":"10.1016\/j.matcom.2022.07.030_b52","doi-asserted-by":"crossref","first-page":"17157","DOI":"10.1007\/s11042-015-2982-x","article-title":"An image encryption scheme based on DNA coding and permutation of hyper-image","volume":"75","author":"Zhang","year":"2016","journal-title":"Multimedia Tools Appl."},{"key":"10.1016\/j.matcom.2022.07.030_b53","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1016\/j.matcom.2021.06.012","article-title":"A novel image encryption algorithm based on SPWLCM and DNA coding","volume":"190","author":"Zhang","year":"2021","journal-title":"Math. Comput. Simulation"},{"issue":"29","key":"10.1016\/j.matcom.2022.07.030_b54","doi-asserted-by":"crossref","first-page":"20753","DOI":"10.1007\/s11042-020-08835-4","article-title":"Multiple-image encryption algorithm based on bit planes and chaos","volume":"79","author":"Zhang","year":"2020","journal-title":"Multimedia Tools Appl."},{"key":"10.1016\/j.matcom.2022.07.030_b55","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1016\/j.matcom.2021.02.009","article-title":"A three-dimensional bit-level image encryption algorithm with Rubik\u2019s cube method","volume":"185","author":"Zhu","year":"2021","journal-title":"Math. Comput. Simulation"},{"key":"10.1016\/j.matcom.2022.07.030_b56","article-title":"Plaintext-related image encryption algorithm based on block structure and five-dimensional chaotic map","volume":"7","author":"Zhu","year":"2019","journal-title":"IEEE Access"},{"key":"10.1016\/j.matcom.2022.07.030_b57","doi-asserted-by":"crossref","first-page":"67095","DOI":"10.1109\/ACCESS.2018.2874336","article-title":"A novel image compression-encryption scheme based on chaos and compression sensing","volume":"6","author":"Zhu","year":"2018","journal-title":"IEEE Access"}],"container-title":["Mathematics and Computers in Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475422003329?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0378475422003329?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T08:27:50Z","timestamp":1759912070000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0378475422003329"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2]]},"references-count":57,"alternative-id":["S0378475422003329"],"URL":"https:\/\/doi.org\/10.1016\/j.matcom.2022.07.030","relation":{},"ISSN":["0378-4754"],"issn-type":[{"value":"0378-4754","type":"print"}],"subject":[],"published":{"date-parts":[[2023,2]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A cluster of 1D quadratic chaotic map and its applications in image encryption","name":"articletitle","label":"Article Title"},{"value":"Mathematics and Computers in Simulation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.matcom.2022.07.030","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.","name":"copyright","label":"Copyright"}]}}