{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T17:27:57Z","timestamp":1781803677001,"version":"3.54.5"},"reference-count":31,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T00:00:00Z","timestamp":1536883200000},"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":["Symmetry"],"abstract":"<jats:p>This article performs the cryptanalysis of an image encryption algorithm using an S-box generated by chaos. The algorithm has the advantages of simple structure, high encryption efficiency, and good encryption performance. However, an attentive investigation reveals that it has some undiscovered security flaws. The image cryptosystem is totally breakable under proposed chosen-plaintext attack, and only two chosen plain-images are required. An array equivalent to the S-box is constructed by an elaborately designed chosen-plaintext image, and the cipher-image is deciphered without having to know the S-box itself. Both mathematical deduction and experimental results validate the feasibility of the attacking scheme. Furthermore, an improved encryption scheme is proposed, in which a feedback mechanism is introduced, a bidirectional diffusion scheme is designed, and values of the ciphertext are associated with more parameters in each diffusion process. Testing results and security analysis verify that the improved cryptographic system can achieve a higher security level and has a better performance than some of the latest encryption algorithms.<\/jats:p>","DOI":"10.3390\/sym10090399","type":"journal-article","created":{"date-parts":[[2018,9,14]],"date-time":"2018-09-14T10:57:59Z","timestamp":1536922679000},"page":"399","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":79,"title":["Cryptanalysis and Improvement on an Image Encryption Algorithm Design Using a Novel Chaos Based S-Box"],"prefix":"10.3390","volume":"10","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":"Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guojun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Technology, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kehui","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Physics and Electronics, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,14]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","unstructured":"Bashir, Z., Watrobski, J., Rashid, T., Zafar, S., and Salabun, W. (2017). Chaotic dynamical state variables selection procedure based image encryption scheme. Symmetry, 9.","DOI":"10.3390\/sym9120312"},{"key":"ref_3","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_4","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_5","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_6","doi-asserted-by":"crossref","first-page":"1391","DOI":"10.1007\/s11042-016-4288-z","article-title":"Chaos based adaptive double-image encryption scheme using hash function and s-boxes","volume":"77","author":"Liu","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_7","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_8","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s11071-013-1086-2","article-title":"A novel image encryption algorithm based on dynamic s-boxes constructed by chaos","volume":"75","author":"Wang","year":"2014","journal-title":"Nonlinear Dyn."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"7739","DOI":"10.1007\/s11042-015-2691-5","article-title":"Image encryption algorithm based on hyper-chaotic system and dynamic s-box","volume":"75","author":"Liu","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1007\/s00521-015-1887-y","article-title":"Construction of s-box based on chaotic boolean functions and its application in image encryption","volume":"27","author":"Khan","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1007\/s11071-016-3099-0","article-title":"A novel approach for strong s-box generation algorithm design based on chaotic scaled zhongtang system","volume":"87","author":"Cavusoglu","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s11071-016-3046-0","article-title":"Efficient cryptosystem approaches: S-boxes and permutation-substitution-based encryption","volume":"87","author":"Belazi","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4363","DOI":"10.1007\/s11042-015-2479-7","article-title":"Image encryption algorithm based on chaotic system and dynamic s-boxes composed of DNA sequences","volume":"75","author":"Liu","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1007\/s11071-016-2934-7","article-title":"An image encryption scheme using dynamic s-boxes","volume":"86","author":"Devaraj","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.chaos.2016.12.018","article-title":"Secure image encryption algorithm design using a novel chaos based s-box","volume":"95","author":"Cavusoglu","year":"2017","journal-title":"Chaos Solitons Fractals"},{"key":"ref_16","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_17","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_18","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1007\/s11071-015-1956-x","article-title":"Cryptanalysis of a new image alternate encryption algorithm based on chaotic map","volume":"80","author":"Yap","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"120503","DOI":"10.7498\/aps.61.120503","article-title":"Cryptanalysis and improvement of a class of hyperchaos based image encryption algorithms","volume":"61","author":"Zhu","year":"2012","journal-title":"Acta Phys. Sin."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"15641","DOI":"10.1007\/s11042-016-3861-9","article-title":"Cryptanalysis and improvement of an image encryption algorithm based on hyper-chaotic system and dynamic s-box","volume":"76","author":"Zhang","year":"2017","journal-title":"Multimed. Tools Appl."},{"key":"ref_21","first-page":"6429","article-title":"A novel color image encryption scheme using rectangular transform-enhanced chaotic tent maps","volume":"5","author":"Wu","year":"2017","journal-title":"IEEE Access"},{"key":"ref_22","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_23","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.compeleceng.2017.07.026","article-title":"An encryption algorithm based on combined chaos in body area networks","volume":"65","author":"Wang","year":"2018","journal-title":"Comput. Electr. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ahmad, M., Al Solami, E., Wang, X.Y., Doja, M., Beg, M., and Alzaidi, A. (2018). Cryptanalysis of an Image Encryption Algorithm Based on Combined Chaos for a Ban System, and Improved Scheme using SHA-512 and Hyperchaos. Symmetry, 10.","DOI":"10.3390\/sym10070266"},{"key":"ref_25","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":"2005","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_26","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_27","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_28","doi-asserted-by":"crossref","unstructured":"Curiac, D.I., Iercan, D., Dranga, O., Dragan, F., and Banias, O. Chaos-Based Cryptography: End of the Road? In Proceedings of the International Conference on Emerging Security Information, System and Technologies, Valencia, Spain, 14\u201320 October 2007; pp.","DOI":"10.1109\/SECUREWARE.2007.4385313"},{"key":"ref_29","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_30","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. Depend. Secur. Comput."},{"key":"ref_31","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":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/9\/399\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:20:27Z","timestamp":1760196027000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/10\/9\/399"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,14]]},"references-count":31,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2018,9]]}},"alternative-id":["sym10090399"],"URL":"https:\/\/doi.org\/10.3390\/sym10090399","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,14]]}}}