{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T18:32:54Z","timestamp":1770748374974,"version":"3.49.0"},"reference-count":90,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T00:00:00Z","timestamp":1582848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific research at King Khalid University","award":["R.G.P 2\/58\/40"],"award-info":[{"award-number":["R.G.P 2\/58\/40"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Chaos-based encryption schemes have attracted many researchers around the world in the digital image security domain. Digital images can be secured using existing chaotic maps, multiple chaotic maps, and several other hybrid dynamic systems that enhance the non-linearity of digital images. The combined property of confusion and diffusion was introduced by Claude Shannon which can be employed for digital image security. In this paper, we proposed a novel system that is computationally less expensive and provided a higher level of security. The system is based on a shuffling process with fractals key along with three-dimensional Lorenz chaotic map. The shuffling process added the confusion property and the pixels of the standard image is shuffled. Three-dimensional Lorenz chaotic map is used for a diffusion process which distorted all pixels of the image. In the statistical security test, means square error (MSE) evaluated error value was greater than the average value of 10000 for all standard images. The value of peak signal to noise (PSNR) was 7.69(dB) for the test image. Moreover, the calculated correlation coefficient values for each direction of the encrypted images was less than zero with a number of pixel change rate (NPCR) higher than 99%. During the security test, the entropy values were more than 7.9 for each grey channel which is almost equal to the ideal value of 8 for an 8-bit system. Numerous security tests and low computational complexity tests validate the security, robustness, and real-time implementation of the presented scheme.<\/jats:p>","DOI":"10.3390\/e22030274","type":"journal-article","created":{"date-parts":[[2020,2,28]],"date-time":"2020-02-28T09:30:36Z","timestamp":1582882236000},"page":"274","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":109,"title":["A Novel Hybrid Secure Image Encryption Based on Julia Set of Fractals and 3D Lorenz Chaotic Map"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5788-4228","authenticated-orcid":false,"given":"Fawad","family":"Masood","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, Institute of Space Technology, Islamabad Highway 1, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6289-8248","authenticated-orcid":false,"given":"Jawad","family":"Ahmad","sequence":"additional","affiliation":[{"name":"School of Computing, Edinburgh Napier University, Edinburgh EH10 5DT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2052-1121","authenticated-orcid":false,"given":"Syed Aziz","family":"Shah","sequence":"additional","affiliation":[{"name":"School of Computing and Mathematics, Manchester Metropolitan University, Manchester M15 6BH, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sajjad Shaukat","family":"Jamal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iqtadar","family":"Hussain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Statistics, Physics, Qatar University, Doha 2713, Qatar"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,28]]},"reference":[{"key":"ref_1","first-page":"18","article-title":"Efficiency analysis and security evaluation of image encryption schemes","volume":"23","author":"Ahmad","year":"2010","journal-title":"Computing"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Younas, M.B., and Ahmad, J. (2014, January 8\u20139). Comparative analysis of chaotic and non-chaotic image encryption schemes. Proceedings of the 2014 International Conference on Emerging Technologies (ICET), Islamabad, Pakistan.","DOI":"10.1109\/ICET.2014.7021021"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"26203","DOI":"10.1007\/s11042-019-07818-4","article-title":"A novel chaotic image encryption technique based on multiple discrete dynamical maps","volume":"78","author":"Khan","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s11831-018-9298-8","article-title":"A comprehensive review on image encryption techniques","volume":"27","author":"Kaur","year":"2018","journal-title":"Arch. Comput. Methods Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s00340-019-7142-y","article-title":"A new approach to digital content privacy using quantum spin and finite-state machine","volume":"125","author":"Waseem","year":"2019","journal-title":"Appl. Phys. B"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2720","DOI":"10.1007\/s10773-019-04162-z","article-title":"A Novel Digital Contents Privacy Scheme Based on Kramer\u2019s Arbitrary Spin","volume":"58","author":"Khan","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"15527","DOI":"10.1007\/s11042-018-6953-x","article-title":"Construction of new S-boxes based on triangle groups and its applications in copyright protection","volume":"78","author":"Rafiq","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Younas, I., and Khan, M. (2018). A new efficient digital image encryption based on inverse left almost semi group and Lorenz chaotic system. Entropy, 20.","DOI":"10.3390\/e20120913"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Munir, N., and Khan, M. (2018, January 4\u20135). A generalization of algebraic expression for nonlinear component of symmetric key algorithms of any characteristic p. Proceedings of the 2018 International Conference on Applied and Engineering Mathematics (ICAEM), Taxila, Pakistan.","DOI":"10.1109\/ICAEM.2018.8536308"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1109\/TCSVT.2019.2896270","article-title":"A new payload partition strategy in color image steganography","volume":"30","author":"Liao","year":"2019","journal-title":"IEEE Trans. Circuits and Syst. Video Tech."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.compeleceng.2017.08.020","article-title":"Medical JPEG image steganography based on preserving inter-block dependencies","volume":"67","author":"Liao","year":"2018","journal-title":"Comput. Electr. Eng."},{"key":"ref_12","unstructured":"Will, M., William, B., and Jawad, A. (2020). An authentication protocol based on chaos and zero knowledge proof. Nonlinear Dyn."},{"key":"ref_13","unstructured":"Belkhouche, F., and Qidwai, U. (2003, January 11). Binary image encoding using 1D chaotic maps. Proceedings of the Annual Technical Conference IEEE Region 5, New Orleans, LA, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"749","DOI":"10.1016\/j.chaos.2003.12.022","article-title":"A symmetric image encryption scheme based on 3D chaotic cat maps","volume":"21","author":"Chen","year":"2004","journal-title":"Chaos Solitons Fractal"},{"key":"ref_15","unstructured":"Habutsu, T., Nishio, Y., Sasase, I., and Mori, S. (1991, January 8\u201311). A secret key cryptosystem by iterating a chaotic map. Proceedings of the Workshop on the Theory and Application of Cryptographic Techniques, Brighton, UK."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2714","DOI":"10.1016\/j.sigpro.2010.03.022","article-title":"A novel image encryption algorithm based on self-adaptive wave transmission","volume":"90","author":"Liao","year":"2010","journal-title":"Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3613","DOI":"10.1142\/S021812740401151X","article-title":"A novel fast image encryption scheme based on 3D chaotic baker maps","volume":"14","author":"Mao","year":"2004","journal-title":"Int. J. Bifurcation Chaos"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.optlaseng.2017.11.005","article-title":"Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion","volume":"103","author":"Annaby","year":"2018","journal-title":"Opt. Lasers Eng."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.chaos.2008.01.028","article-title":"A novel image encryption scheme based on spatial chaos map","volume":"38","author":"Sun","year":"2008","journal-title":"Chaos Solitons Fractals"},{"key":"ref_20","unstructured":"Guo, J.I. (2000, January 28\u201331). A new chaotic key-based design for image encryption and decryption. Proceedings of the 2000 IEEE International Symposium on Circuits and Systems, Geneva, Switzerland."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2028","DOI":"10.1016\/j.mcm.2010.06.005","article-title":"Image encryption using DNA addition combining with chaotic maps","volume":"52","author":"Zhang","year":"2010","journal-title":"Math. Comput. Mod."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2775","DOI":"10.1016\/j.optcom.2011.02.039","article-title":"A novel image encryption method based on total shuffling scheme","volume":"284","author":"Zhang","year":"2011","journal-title":"Opt. Commun."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication theory of secrecy systems","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Karmeshu, J. (2003). Entropy Measures, Maximum Entropy Principle and Emerging Applications, Springer. [2003 ed.].","DOI":"10.1007\/978-3-540-36212-8"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Khan, M., Masood, F., Alghafis, A., Amin, M., and Batool Naqvi, S.I. (2019). A novel image encryption technique using hybrid method of discrete dynamical chaotic maps and Brownian motion. PLoS ONE, 14.","DOI":"10.1371\/journal.pone.0225031"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.chaos.2006.05.011","article-title":"A novel algorithm for image encryption based on mixture of chaotic maps","volume":"35","author":"Behnia","year":"2008","journal-title":"Chaos Solitons Fractals"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/j.chaos.2004.11.096","article-title":"A block cipher based on a suitable use of the chaotic standard map","volume":"26","author":"Lian","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"514","DOI":"10.1016\/j.asoc.2009.12.011","article-title":"A new chaos-based fast image encryption algorithm","volume":"11","author":"Wang","year":"2011","journal-title":"Appl. Softw. Comput."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2645","DOI":"10.1016\/j.physleta.2007.12.026","article-title":"A fast image encryption scheme based on chaotic standard map","volume":"372","author":"Wong","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Khan, M., Masood, F., and Alghafis, A. (2019). Secure image encryption scheme based on fractals key with Fibonacci series and discrete dynamical system. Neur. Comput. Appl., 1\u201321.","DOI":"10.1007\/s00521-019-04667-y"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Agarwal, S. (2018). Secure image transmission using fractal and 2D-chaotic map. J. Imaging, 4.","DOI":"10.3390\/jimaging4010017"},{"key":"ref_32","first-page":"104","article-title":"Color Image Encryption Using Hybrid Method of Fractal-Based Key and Private XOR Key","volume":"13","author":"Minas","year":"2018","journal-title":"Kirkuk Univ. J. Sci. Stud."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"31","DOI":"10.9790\/0661-16513135","article-title":"Image encryption techniques using fractal geometry: A comparative study","volume":"16","author":"Gupta","year":"2014","journal-title":"IOSR J. Comput. Eng."},{"key":"ref_34","unstructured":"Mandelbrot, B.B. (1982). The Fractal Geometry of Nature, Henry Holt and Company."},{"key":"ref_35","unstructured":"Crownover, R.M. (1995). Introduction to Fractals and Chaos, Jones & Bartlett Pub. [1st ed.]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"742","DOI":"10.1049\/iet-ipr.2013.0570","article-title":"A fractal-based image encryption system","volume":"8","author":"Radwan","year":"2014","journal-title":"IET Image Process."},{"key":"ref_37","first-page":"224","article-title":"Analysis of the fractal structures for the infor2mation encrypting process","volume":"4","year":"2012","journal-title":"Int. J. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Kumar, S. (2006, January 23\u201325). Public key cryptographic system using Mandelbrot sets. Proceedings of the MILCOM 2006-2006 IEEE Military Communications Conference, Washington, DC, USA.","DOI":"10.1109\/MILCOM.2006.302396"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1049\/iet-ipr.2014.0224","article-title":"Image compression and encryption scheme using fractal dictionary and Julia set","volume":"9","author":"Sun","year":"2015","journal-title":"IET Image Process"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2017\/7367518","article-title":"Two-phase image encryption scheme based on FFCT and fractals","volume":"2017","author":"Mikhail","year":"2017","journal-title":"Secur. Commun. Netw."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Ahmad, J., Larijani, H., Emmanuel, R., and Mannion, M. (2018, January 19\u201321). Secure occupancy monitoring system for IoT using lightweight intertwining logistic map. Proceedings of the 2018 10th Computer Science and Electronic Engineering (CEEC), Colchester, UK.","DOI":"10.1109\/CEEC.2018.8674208"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Ahmad, J., Larijani, H., Emmanuel, R., Mannion, M., Javed, A., and Ahmadinia, A. (2018, January 16\u201318). An intelligent real-time occupancy monitoring system with enhanced encryption and privacy. Proceedings of the 2018 IEEE 17th International Conference on Cognitive Informatics & Cognitive Computing (ICCI* CC), Berkeley, CA, USA.","DOI":"10.1109\/ICCI-CC.2018.8482047"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Khan, J.S., ur Rehman, A., Ahmad, J., and Habib, Z. (2015, January 18). A new chaos-based secure image encryption scheme using multiple substitution boxes. Proceedings of the 2015 Conference on Information Assurance and Cyber Security (CIACS), Rawalpindi, Pakistan.","DOI":"10.1109\/CIACS.2015.7395561"},{"key":"ref_44","unstructured":"Stallings, W. (2007). Cryptography and Network Security, McGraw-Hill, Inc.. [4th ed.]."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1080\/0161-118991863745","article-title":"On the derivation of a \u201cchaotic\u201d encryption algorithm","volume":"13","author":"Matthews","year":"1989","journal-title":"Cryptologia"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/S0375-9601(98)00086-3","article-title":"Cryptography with chaos","volume":"240","author":"Baptista","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Hilborn, R.C. (2000). Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, Oxford University Press Inc.. [2nd ed.].","DOI":"10.1093\/acprof:oso\/9780198507239.001.0001"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Alexan, W., Hamza, A., and Medhat, H. (2019, January 2\u20134). An aes double\u2013layer based message security scheme. Proceedings of the 2019 International Conference on Innovative Trends in Computer Engineering, Aswan, Egypt.","DOI":"10.1109\/ITCE.2019.8646461"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Elkandoz, M.T., Alexan, W., and Hussein, H.H. (2019, January 19\u201321). 3D Image Steganography Using Sine Logistic Map and 2D Hyperchaotic Map. Proceedings of the 2019 International Conference on Electrical and Computing Technologies and Applications (ICECTA), Ras Al Khaimah, United Arab Emirates.","DOI":"10.1109\/ICECTA48151.2019.8959700"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1007\/s11277-019-06594-6","article-title":"A novel image encryption technique based on generalized advanced encryption standard based on field of any characteristic","volume":"109","author":"Khan","year":"2019","journal-title":"Wirel. Per. Commun."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3091","DOI":"10.1007\/s10773-019-04188-3","article-title":"Application based construction and optimization of substitution boxes over 2D mixed chaotic maps","volume":"58","author":"Ali","year":"2019","journal-title":"Int. J. Theor. Phys."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1007\/s11071-015-2173-3","article-title":"A novel image encryption scheme based on multiple chaotic S-boxes","volume":"82","author":"Khan","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"13951","DOI":"10.1007\/s11042-015-2973-y","article-title":"A secure image encryption scheme based on chaotic maps and affine transformation","volume":"75","author":"Ahmad","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1007\/s11071-015-2281-0","article-title":"Chaos-based diffusion for highly autocorrelated data in encryption algorithms","volume":"82","author":"Ahmad","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1007\/s00521-016-2405-6","article-title":"A compression sensing and noise-tolerant image encryption scheme based on chaotic maps and orthogonal matrices","volume":"28","author":"Ahmad","year":"2017","journal-title":"Neur. Comput. Appl."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1007\/s11042-012-1292-9","article-title":"A simple, sensitive and secure image encryption algorithm based on hyper-chaotic system with only one round diffusion process","volume":"71","author":"Norouzi","year":"2014","journal-title":"Multimed. Tools Appl."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"901","DOI":"10.1007\/s11277-015-2667-9","article-title":"An experimental comparison of chaotic and non-chaotic image encryption schemes","volume":"84","author":"Ahmad","year":"2015","journal-title":"Wirel. Per. Commun."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11042-019-07881-x","article-title":"A novel image encryption scheme based on Arnold scrambling and Lucas series","volume":"78","author":"Batool","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_59","first-page":"41904","article-title":"Image encryption using four-dimensional hyper chaotic Lorenz system","volume":"87","author":"Kumar","year":"2016","journal-title":"Elixir Elec. Eng."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"e2632","DOI":"10.1002\/jnm.2632","article-title":"Cognitive health care system and its application in pill-rolling assessment","volume":"32","author":"Shah","year":"2019","journal-title":"Int. J. Numer. Mod. Electr. Netw. Dev. Fields"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MAES.2019.2933971","article-title":"RF sensing technologies for assisted daily living in healthcare: A comprehensive review","volume":"34","author":"Shah","year":"2019","journal-title":"IEEE Aerosp. Electr. Syst. Mag."},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Shah, S.A., and Fioranelli, F. (2019, January 23\u201327). Human Activity Recognition: Preliminary Results for Dataset Portability using FMCW Radar. Proceedings of the 2019 International Radar Conference, Toulon, France.","DOI":"10.1109\/RADAR41533.2019.171307"},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Tahir, A., Ahmad, J., Shah, S.A., Morison, G., Skelton, D.A., Larijani, H., Abbasi, Q.H., Imran, M.A., and Gibson, R.M. (2019). WiFreeze: Multiresolution scalograms for freezing of gait detection in Parkinson\u2019s leveraging 5G spectrum with deep learning. Electronics, 8.","DOI":"10.3390\/electronics8121433"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1007\/s00521-019-04037-8","article-title":"Diagnosis of the Hypopnea syndrome in the early stage","volume":"32","author":"Yang","year":"2020","journal-title":"Neur. Comput. Appl."},{"key":"ref_65","first-page":"261","article-title":"Superior Julia set","volume":"8","author":"Rani","year":"2004","journal-title":"Res. Math. Edu."},{"key":"ref_66","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":"ref_67","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1016\/j.chaos.2009.03.084","article-title":"Color image encryption based on coupled nonlinear chaotic map","volume":"42","author":"Mazloom","year":"2009","journal-title":"Chaos Solitons Fractals"},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"1202","DOI":"10.1016\/j.sigpro.2011.11.004","article-title":"A fast color image encryption algorithm based on coupled two-dimensional piecewise chaotic map","volume":"92","author":"Seyedzadeh","year":"2012","journal-title":"Signal Process."},{"key":"ref_69","first-page":"1091","article-title":"An Improved Image Encryption Algorithm based on Chaotic System","volume":"4","author":"Liu","year":"2009","journal-title":"Jcp"},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"4653","DOI":"10.1016\/j.cnsns.2012.05.033","article-title":"An image encryption scheme based on quantum logistic map","volume":"17","author":"Akhshani","year":"2012","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1016\/j.sigpro.2011.10.023","article-title":"A novel color image encryption algorithm based on chaos","volume":"92","author":"Wang","year":"2012","journal-title":"Signal Process."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"2986","DOI":"10.1016\/j.sigpro.2013.03.031","article-title":"A new approach to chaotic image encryption based on quantum chaotic system, exploiting color spaces","volume":"93","author":"Li","year":"2013","journal-title":"Signal Process."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"4033","DOI":"10.1016\/j.optcom.2012.06.039","article-title":"A novel chaotic image encryption algorithm based on water wave motion and water drop diffusion models","volume":"285","author":"Wang","year":"2012","journal-title":"Opt. Commun."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/j.ins.2013.11.027","article-title":"Design of image cipher using latin squares","volume":"264","author":"Wu","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_75","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1007\/s00521-014-1800-0","article-title":"An efficient chaotic image encryption scheme","volume":"26","author":"Khan","year":"2015","journal-title":"Neur. Comput. Appl."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"2123","DOI":"10.1016\/j.optcom.2009.02.044","article-title":"Multi chaotic systems-based pixel shuffle for image encryption","volume":"282","author":"Huang","year":"2009","journal-title":"Opt. Commun."},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.chaos.2007.07.083","article-title":"OCML-based colour image encryption","volume":"40","author":"Rhouma","year":"2009","journal-title":"Chaos Soliton Fractals"},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.advengsoft.2012.03.001","article-title":"Novel approach for fast compressed hybrid color image cryptosystem","volume":"49","author":"Gupta","year":"2012","journal-title":"Adv. Eng. Softw."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"1671","DOI":"10.1016\/j.ijleo.2013.09.040","article-title":"Color image encryption using skew tent map and hyper chaotic system of 6th-order CNN","volume":"125","author":"Kadir","year":"2014","journal-title":"Optik"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"1457","DOI":"10.1016\/j.asoc.2012.01.016","article-title":"Image encryption using DNA complementary rule and chaotic maps","volume":"12","author":"Liu","year":"2012","journal-title":"Appl. Softw. Comput."},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/j.jss.2011.08.017","article-title":"A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system","volume":"85","author":"Wei","year":"2012","journal-title":"J. Syst. Softw."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"1240","DOI":"10.1016\/j.compeleceng.2012.02.007","article-title":"A RGB image encryption algorithm based on DNA encoding and chaos map","volume":"38","author":"Liu","year":"2012","journal-title":"Comput. Electr. Eng."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.sigpro.2016.03.021","article-title":"A novel image encryption scheme based on substitution-permutation network and chaos","volume":"128","author":"Belazi","year":"2016","journal-title":"Signal Process."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1080\/19393555.2016.1212954","article-title":"A novel sensitive image encryption algorithm based on the Zaslavsky chaotic map","volume":"25","author":"Hamza","year":"2016","journal-title":"Inf. Secur. J. A Glob. Perspect."},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s11042-012-1331-6","article-title":"An image encryption algorithm based on hyper-chaos and DNA sequence","volume":"72","author":"Huang","year":"2014","journal-title":"Multimed. Tools Appl."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.optlaseng.2014.08.005","article-title":"A novel chaotic block image encryption algorithm based on dynamic random growth technique","volume":"66","author":"Wang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1007\/s00521-016-2511-5","article-title":"A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation","volume":"29","author":"Khan","year":"2018","journal-title":"Neur. Comput. Appl."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"3877","DOI":"10.3390\/e17063877","article-title":"A colour image encryption scheme using permutation-substitution based on chaos","volume":"17","author":"Wang","year":"2015","journal-title":"Entropy"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1007\/s13319-015-0068-1","article-title":"A novel image encryption algorithm based on the two-dimensional logistic map and the latin square image cipher","volume":"6","author":"Machkour","year":"2015","journal-title":"3D Res."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"2771","DOI":"10.1007\/s11277-014-1667-5","article-title":"A noisy channel tolerant image encryption scheme","volume":"77","author":"Ahmed","year":"2014","journal-title":"Wirel. Per. 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