{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T09:16:53Z","timestamp":1772183813195,"version":"3.50.1"},"reference-count":69,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,11,3]],"date-time":"2018-11-03T00:00:00Z","timestamp":1541203200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61472451"],"award-info":[{"award-number":["61472451"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Open Project of Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing","award":["2016CSOBDP0103"],"award-info":[{"award-number":["2016CSOBDP0103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper presents an improved cryptanalysis of a chaos-based image encryption scheme, which integrated permutation, diffusion, and linear transformation process. It was found that the equivalent key streams and all the unknown parameters of the cryptosystem can be recovered by our chosen-plaintext attack algorithm. Both a theoretical analysis and an experimental validation are given in detail. Based on the analysis of the defects in the original cryptosystem, an improved color image encryption scheme was further developed. By using an image content\u2013related approach in generating diffusion arrays and the process of interweaving diffusion and confusion, the security of the cryptosystem was enhanced. The experimental results and security analysis demonstrate the security superiority of the improved cryptosystem.<\/jats:p>","DOI":"10.3390\/e20110843","type":"journal-article","created":{"date-parts":[[2018,11,5]],"date-time":"2018-11-05T10:43:45Z","timestamp":1541414625000},"page":"843","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":70,"title":["Improved Cryptanalysis and Enhancements of an Image Encryption Scheme Using Combined 1D Chaotic Maps"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9662-0532","authenticated-orcid":false,"given":"Congxu","family":"Zhu","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Central South University, Changsha 410083, China"},{"name":"School of Computer Science and Technology, Guangzhou University, Guangzhou 510006, China"},{"name":"School of Computer and Science, Liaocheng University, Liaocheng 252059, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guojun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kehui","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,11,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1142\/S0218127406015970","article-title":"Some basic cryptographic requirements for chaos-based cryptosystems","volume":"16","author":"Alvarez","year":"2006","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0378-4371(95)00294-4","article-title":"Generalized kolmogorov entropy in the dynamics of the multifractal generation","volume":"223","author":"Zanette","year":"1996","journal-title":"Phys. A Stat. Mech. Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1016\/0167-2789(83)90127-6","article-title":"Symbolic dynamics of noisy chaos","volume":"7","author":"Crutchfield","year":"1983","journal-title":"Phys. D"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1063\/1.1530990","article-title":"Regularities unseen, randomness observed: Levels of entropy convergence","volume":"13","author":"Crutchfield","year":"2003","journal-title":"Chaos"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1142\/S021812749800098X","article-title":"Symmetric ciphers based on two-dimensional chaotic maps","volume":"8","author":"Fridrich","year":"1998","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.cnsns.2013.06.031","article-title":"An image encryption scheme based on rotation matrix bit-level permutation and block diffusion","volume":"19","author":"Zhang","year":"2014","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"472","DOI":"10.1016\/j.optlaseng.2012.11.001","article-title":"Double optical image encryption using discrete chirikov standard map and chaos-based fractional random transform","volume":"51","author":"Zhang","year":"2013","journal-title":"Opt. Lasers Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Gan, Z.H., Chai, X.L., Han, D.J., and Chen, Y.R. (2018). A chaotic image encryption algorithm based on 3-D bit-plane permutation. Neural Comput. Appl., 1\u201320.","DOI":"10.1007\/s00521-018-3541-y"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1359","DOI":"10.1007\/s11071-016-3119-0","article-title":"An efficient chaotic image cipher with dynamic lookup table driven bit-level permutation strategy","volume":"87","author":"Hu","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1007\/s11071-015-2465-7","article-title":"Chaotic image encryption algorithm using wave-line permutation and block diffusion","volume":"83","author":"Ye","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.optlaseng.2016.04.023","article-title":"Novel permutation measures for image encryption algorithms","volume":"85","author":"AbdElHaleem","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.optlaseng.2016.10.020","article-title":"A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation","volume":"90","author":"Li","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.image.2012.12.009","article-title":"A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations","volume":"28","author":"Zhang","year":"2013","journal-title":"Signal Process. Image Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1007\/s11071-015-2590-3","article-title":"An effective and fast image encryption algorithm based on chaos and interweaving of ranks","volume":"84","author":"Wang","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.optlaseng.2016.10.012","article-title":"A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion","volume":"91","author":"Xu","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1016\/j.sigpro.2017.10.004","article-title":"Medical image encryption using high-speed scrambling and pixel adaptive diffusion","volume":"144","author":"Hua","year":"2018","journal-title":"Signal Process."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/j.sigpro.2018.04.014","article-title":"A compression-diffusion-permutation strategy for securing image","volume":"150","author":"Huang","year":"2018","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1016\/j.sigpro.2017.08.020","article-title":"A novel bit-level image encryption algorithm based on 2D-LICM hyperchaotic map","volume":"143","author":"Cao","year":"2018","journal-title":"Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1159","DOI":"10.1007\/s11042-015-3088-1","article-title":"An image encryption algorithm based on bit level brownian motion and new chaotic systems","volume":"76","author":"Chai","year":"2017","journal-title":"Multimed. Tools Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.sigpro.2018.03.010","article-title":"2D Logistic-Sine-coupling map for image encryption","volume":"149","author":"Hua","year":"2018","journal-title":"Signal Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.ins.2016.01.017","article-title":"Image encryption using 2D Logistic-adjusted-Sine map","volume":"339","author":"Hua","year":"2016","journal-title":"Inf. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1049\/el.2017.4426","article-title":"Efficient image encryption method based on improved lorenz chaotic system","volume":"54","author":"Kaur","year":"2018","journal-title":"Electron. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"10217","DOI":"10.1007\/s11042-017-5406-2","article-title":"A digital image encryption algorithm based on bit-planes and an improved logistic map","volume":"77","author":"Liu","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/j.optcom.2011.08.079","article-title":"A novel image encryption scheme based on improved hyperchaotic sequences","volume":"285","author":"Zhu","year":"2012","journal-title":"Opt. Commun."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"6647","DOI":"10.1007\/s11042-017-4577-1","article-title":"A plaintext-related image encryption algorithm based on chaos","volume":"77","author":"Zhang","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2015","DOI":"10.1002\/sec.1458","article-title":"A secure image encryption algorithm based on chaotic maps and SHA-3","volume":"9","author":"Ye","year":"2016","journal-title":"Secur. Commun. Netw."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.asoc.2015.08.008","article-title":"A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps","volume":"37","author":"Wu","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.optlaseng.2017.06.015","article-title":"Image encryption algorithm based on multiple mixed hash functions and cyclic shift","volume":"107","author":"Wang","year":"2017","journal-title":"Opt. Lasers Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"15561","DOI":"10.1007\/s11042-016-3858-4","article-title":"A fast chaos-based image encryption scheme with a novel plain image-related swapping block permutation and block diffusion","volume":"76","author":"Chai","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_30","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":"ref_31","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 Dyn."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"234","DOI":"10.1016\/j.sigpro.2016.12.008","article-title":"Chaotic image cryptosystem using DNA deletion and DNA insertion","volume":"134","author":"Hu","year":"2017","journal-title":"Signal Process."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"6229","DOI":"10.1007\/s11042-016-3311-8","article-title":"A novel and effective image encryption algorithm based on chaos and DNA encoding","volume":"76","author":"Wang","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"6243","DOI":"10.1007\/s11042-017-4534-z","article-title":"A novel color image encryption scheme using DNA permutation based on the lorenz system","volume":"77","author":"Wang","year":"2017","journal-title":"Multimed. Tools Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.optlaseng.2015.03.022","article-title":"A novel chaotic image encryption scheme using DNA sequence operations","volume":"73","author":"Wang","year":"2015","journal-title":"Opt. Lasers Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"100504","DOI":"10.1088\/1674-1056\/26\/10\/100504","article-title":"A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations","volume":"26","author":"Zhang","year":"2017","journal-title":"Chin. Phys. B"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2191","DOI":"10.1007\/s11042-017-4370-1","article-title":"A fast and efficient approach to color-image encryption based on compressive sensing and fractional fourier transform","volume":"77","author":"Zhang","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1007\/s11071-014-1729-y","article-title":"A fast image algorithm based on rows and columns switch","volume":"79","author":"Wang","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.jvcir.2015.09.014","article-title":"A fast encryption algorithm of color image based on four-dimensional chaotic system","volume":"33","author":"Tong","year":"2015","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1049\/iet-ipr.2016.0040","article-title":"Chaos-based fast colour image encryption scheme with true random number keys from environmental noise","volume":"11","author":"Liu","year":"2017","journal-title":"IET Image Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.optlaseng.2016.03.019","article-title":"A fast image encryption algorithm based on chaotic map","volume":"84","author":"Liu","year":"2016","journal-title":"Opt. Lasers Eng."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Bibi, N., Farwa, S., Muhammad, N., Jahngir, A., and Usman, M. (2018). A novel encryption scheme for high-contrast image data in the fresnelet domain. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0208305"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1007\/s13319-017-0135-x","article-title":"A novel image encryption based on algebraic s-box and arnold transform","volume":"8","author":"Farwa","year":"2017","journal-title":"3D Res."},{"key":"ref_44","first-page":"360","article-title":"An image encryption technique based on chaotic s-box and arnold transform","volume":"8","author":"Farwa","year":"2017","journal-title":"Int. J. Adv. Comput. Sci. Appl."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.1016\/j.patcog.2005.01.002","article-title":"Efficient encryption of wavelet-based coded color images","volume":"38","author":"Martin","year":"2005","journal-title":"Pattern Recognit."},{"key":"ref_46","first-page":"126","article-title":"Wavelet based fast technique for images encryption","volume":"25","author":"Shahed","year":"2007","journal-title":"Basrah J. Sci."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1016\/j.chaos.2005.08.110","article-title":"A new chaotic algorithm for image encryption","volume":"29","author":"Gao","year":"2006","journal-title":"Chaos Solitons Fractals"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Guariglia, E. (2016). Entropy and fractal antennas. Entropy, 18.","DOI":"10.3390\/e18030084"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Guariglia, E. (2018). Harmonic sierpinski gasket and applications. Entropy, 20.","DOI":"10.3390\/e20090714"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1109\/MMUL.2017.3051512","article-title":"Cryptanalyzing an image-scrambling encryption algorithm of pixel bits","volume":"24","author":"Li","year":"2017","journal-title":"IEEE Multimed."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1007\/s11071-013-0924-6","article-title":"Breaking a novel image encryption scheme based on improved hyperchaotic sequences","volume":"73","author":"Li","year":"2013","journal-title":"Nonlinear Dyn."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1016\/j.dsp.2013.10.020","article-title":"Cryptanalysis of an image encryption algorithm using chebyshev generator","volume":"25","author":"Wang","year":"2014","journal-title":"Digit. Signal Prog."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.sigpro.2017.06.014","article-title":"Cryptanalysis and enhancements of image encryption based on three-dimensional bit matrix permutation","volume":"142","author":"Wu","year":"2018","journal-title":"Signal Process."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"18759","DOI":"10.1109\/ACCESS.2018.2817600","article-title":"Cryptanalyzing and improving a novel color image encryption algorithm using rt-enhanced chaotic tent maps","volume":"6","author":"Zhu","year":"2018","journal-title":"IEEE Access"},{"key":"ref_55","first-page":"6429","article-title":"A novel colour image encryption scheme using rectangular transform-enhanced chaotic tent maps","volume":"5","author":"Wu","year":"2017","journal-title":"IEEE Access"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.sigpro.2015.06.008","article-title":"Image encryption based on three-dimensional bit matrix permutation","volume":"118","author":"Zhang","year":"2016","journal-title":"Signal Process."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Sun, K.H., He, S.B., Yin, L.Z., and Duo, L.K. (2012). Application of fuzzyen algorithm to the analysis of complexity of chaotic sequence. Acta Phys. Sin., 130507.","DOI":"10.7498\/aps.61.130507"},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"010501","DOI":"10.7498\/aps.62.010501","article-title":"Complexity analysis of chaotic pseudo-random sequences based on spectral entropy algorithm","volume":"62","author":"Sun","year":"2013","journal-title":"Acta Phys. Sin."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"He, S.B., Sun, K.H., and Zhu, C.X. (2013). Complexity analyses of multi-wing chaotic systems. Chin. Phys. B, 220\u2013225.","DOI":"10.1088\/1674-1056\/22\/5\/050506"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.sigpro.2017.03.011","article-title":"A new color image encryption using combination of the 1d chaotic map","volume":"138","author":"Pak","year":"2017","journal-title":"Signal Process."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1016\/j.sigpro.2017.11.005","article-title":"Cryptanalysis and enhancements of image encryption using combination of the 1d chaotic map","volume":"144","author":"Wang","year":"2018","journal-title":"Signal Process."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1007\/s11071-018-4332-9","article-title":"Cryptanalysis and improvement in an image encryption scheme using combination of the 1d chaotic map","volume":"93","author":"Chen","year":"2018","journal-title":"Nonlinear Dyn."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"3119","DOI":"10.1142\/S0218127405014052","article-title":"On the dynamical degradation of digital piecewise linear chaotic maps","volume":"15","author":"Li","year":"2015","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/j.physleta.2004.09.028","article-title":"Baptista-type chaotic cryptosystems: Problems and countermeasures","volume":"332","author":"Li","year":"2004","journal-title":"Phys. Lett. A"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"940276","DOI":"10.1155\/2012\/940276","article-title":"Chaotic trajectory design for monitoring an arbitrary number of specified locations using points of interest","volume":"2012","author":"Curiac","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Curiac, D.I., Iercan, D., Dragan, F., and Banias, O. (2007, January 14\u201320). Chaos-based cryptography: End of the road?. In Proceedings of the International Conference on Emerging Security Information, System and Technologies, Valencia, Spain.","DOI":"10.1109\/SECUREWARE.2007.4385313"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"6121","DOI":"10.1007\/s00500-017-2676-6","article-title":"A trajectory privacy-preserving scheme based on query exchange in mobile social networks","volume":"22","author":"Zhang","year":"2018","journal-title":"Soft Comput."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1109\/TDSC.2015.2469655","article-title":"Dependable structural health monitoring using wireless sensor networks","volume":"14","author":"Bhuiyan","year":"2017","journal-title":"IEEE Trans. Dependable Secur."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"31541","DOI":"10.1109\/ACCESS.2018.2845468","article-title":"PRMS: A personalized mobile search over encrypted outsourced data","volume":"6","author":"Zhang","year":"2018","journal-title":"IEEE Access"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/843\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:27:50Z","timestamp":1760196470000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/20\/11\/843"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,11,3]]},"references-count":69,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["e20110843"],"URL":"https:\/\/doi.org\/10.3390\/e20110843","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,11,3]]}}}