{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T13:16:09Z","timestamp":1783948569082,"version":"3.55.0"},"reference-count":42,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,10,28]],"date-time":"2022-10-28T00:00:00Z","timestamp":1666915200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Technologies Research and Development Program of Liaoning Province in China","award":["2021JH1\/10400079"],"award-info":[{"award-number":["2021JH1\/10400079"]}]},{"name":"Key Technologies Research and Development Program of Liaoning Province in China","award":["2217002"],"award-info":[{"award-number":["2217002"]}]},{"name":"Key Technologies Research and Development Program of Liaoning Province in China","award":["62171114"],"award-info":[{"award-number":["62171114"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2021JH1\/10400079"],"award-info":[{"award-number":["2021JH1\/10400079"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2217002"],"award-info":[{"award-number":["2217002"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["62171114"],"award-info":[{"award-number":["62171114"]}]},{"name":"National Natural Science Foundation of China","award":["2021JH1\/10400079"],"award-info":[{"award-number":["2021JH1\/10400079"]}]},{"name":"National Natural Science Foundation of China","award":["2217002"],"award-info":[{"award-number":["2217002"]}]},{"name":"National Natural Science Foundation of China","award":["62171114"],"award-info":[{"award-number":["62171114"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Recently, an image encryption scheme based on a 2D hyperchaotic map is proposed. It adopts the permutation\u2013diffusion architecture and consists of three steps, which are permutation, forward diffusion, and backward diffusion. In this paper, we break this cipher with both the chosen-plaintext attack (CPA) and the chosen-ciphertext attack (CCA). According to our analysis, we found the two complex diffusion processes could be simplified into two simple diffusions and a modular addition operation. Based on this, the equivalent key can be obtained with CPA and CCA. Detailed theoretical derivations and the results of experiments confirmed the feasibility of our attack methods. When the image size was 256\u00d7256, the running time of the attacks was less than 2 hours on a laptop with a 2.59 GHz Intel Core i7 and 16 GB DDR3 memory. Other sizes of images were also tested, and some rules were found. In addition, the probability of other attacks has also been discussed, and some suggestions for improvements are given. The source codes are publicly available and can be found online.<\/jats:p>","DOI":"10.3390\/e24111551","type":"journal-article","created":{"date-parts":[[2022,10,30]],"date-time":"2022-10-30T04:57:34Z","timestamp":1667105854000},"page":"1551","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["Cryptanalysis of an Image Encryption Algorithm Based on a 2D Hyperchaotic Map"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9143-6130","authenticated-orcid":false,"given":"Chengrui","family":"Zhang","sequence":"first","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4745-8361","authenticated-orcid":false,"given":"Junxin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Software, Dalian University of Technology, Dalian 116621, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7863-1230","authenticated-orcid":false,"given":"Dongming","family":"Chen","sequence":"additional","affiliation":[{"name":"Software College, Northeastern University, Shenyang 110169, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,28]]},"reference":[{"key":"ref_1","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_2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1109\/TIFS.2015.2489178","article-title":"On the security of permutation-only image encryption schemes","volume":"11","author":"Jolfaei","year":"2015","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wang, W., Yu, X., Fang, B., Zhao, D.Y., Chen, Y., Wei, W., and Chen, J. (2022). Cross-modality LGE-CMR Segmentation using Image-to-Image Translation based Data Augmentation. IEEE\/ACM Trans. Comput. Biol. Bioinform.","DOI":"10.1109\/TCBB.2022.3140306"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"87844","DOI":"10.1109\/ACCESS.2022.3199738","article-title":"Encrypting Multiple Images With an Enhanced Chaotic Map","volume":"10","author":"Laiphrakpam","year":"2022","journal-title":"IEEE Access"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Alawida, M., Teh, J.S., Mehmood, A., and Shoufan, A. (J. King Saud-Univ.-Comput. Inf. Sci., 2022). A chaos-based block cipher based on an enhanced logistic map and simultaneous confusion-diffusion operations, J. King Saud-Univ.-Comput. Inf. Sci., in press.","DOI":"10.1016\/j.jksuci.2022.07.025"},{"key":"ref_6","unstructured":"Wang, Y., Liu, Z., Zhang, L.Y., Pareschi, F., Setti, G., and Chen, G. (2021). From Chaos to Pseudorandomness: A Case Study on the 2-D Coupled Map Lattice. IEEE Trans. Cybern., 1\u201311."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"113163","DOI":"10.1109\/ACCESS.2020.3002763","article-title":"A new hash function based on chaotic maps and deterministic finite state automata","volume":"8","author":"Alawida","year":"2020","journal-title":"IEEE Access"},{"key":"ref_8","first-page":"10","article-title":"Research on image encryption based on hyperchaotic system","volume":"5","author":"Huang","year":"2020","journal-title":"J. Netw. Intell."},{"key":"ref_9","first-page":"697","article-title":"A Secure and Robust Image Encryption Based on Chaotic Permutation Multiple Circular Shrinking and Expanding","volume":"7","author":"Suryanto","year":"2016","journal-title":"J. Inf. Hiding Multim. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Feng, W., Zhao, X., Zhang, J., Qin, Z., Zhang, J., and He, Y. (2022). Image encryption algorithm based on plane-level image filtering and discrete logarithmic transform. Mathematics, 10.","DOI":"10.3390\/math10152751"},{"key":"ref_11","first-page":"2702653","article-title":"Generation of dynamical S-boxes for block ciphers via extended logistic map","volume":"2020","year":"2020","journal-title":"Math. Probl. Eng."},{"key":"ref_12","first-page":"413","article-title":"Hyperchaotic encryption based on multi-scroll piecewise linear systems","volume":"270","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8660","DOI":"10.1109\/ACCESS.2018.2890116","article-title":"Image encryption using Josephus problem and filtering diffusion","volume":"7","author":"Hua","year":"2019","journal-title":"IEEE Access"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2000","DOI":"10.1109\/TII.2021.3088465","article-title":"Compressed sensing framework for heart sound acquisition in internet of medical things","volume":"18","author":"Chen","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"107753","DOI":"10.1016\/j.optlastec.2021.107753","article-title":"Chaotic color image encryption based on 4D chaotic maps and DNA sequence","volume":"148","author":"Wang","year":"2022","journal-title":"Opt. Laser Technol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Qian, K., Feng, W., Qin, Z., Zhang, J., Luo, X., and Zhu, Z. (2022). A novel image encryption scheme based on memristive chaotic system and combining bidirectional bit-level cyclic shift and dynamic DNA-level diffusion. Front. Phys., 718.","DOI":"10.3389\/fphy.2022.963795"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1016\/j.sigpro.2017.07.034","article-title":"Exploiting self-adaptive permutation\u2013diffusion and DNA random encoding for secure and efficient image encryption","volume":"142","author":"Chen","year":"2018","journal-title":"Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.ins.2020.02.012","article-title":"The fast image encryption algorithm based on lifting scheme and chaos","volume":"520","author":"Zhang","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.patrec.2009.11.008","article-title":"Image scrambling encryption algorithm of pixel bit based on chaos map","volume":"31","author":"Ye","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Alawida, M., Omolara, A.E., Abiodun, O.I., and Al-Rajab, M. (J. King Saud-Univ.-Comput. Inf. Sci., 2022). A deeper look into cybersecurity issues in the wake of Covid-19: A survey, J. King Saud-Univ.-Comput. Inf. Sci., in press.","DOI":"10.1016\/j.jksuci.2022.08.003"},{"key":"ref_21","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_22","doi-asserted-by":"crossref","first-page":"107286","DOI":"10.1016\/j.sigpro.2019.107286","article-title":"Cryptanalysis and improvement of medical image encryption using high-speed scrambling and pixel adaptive diffusion","volume":"167","author":"Chen","year":"2020","journal-title":"Signal Process."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.sigpro.2018.06.008","article-title":"Image encryption using 2D H\u00e9non-Sine map and DNA approach","volume":"153","author":"Wu","year":"2018","journal-title":"Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.ins.2020.02.024","article-title":"Cryptanalysis of a DNA-based image encryption scheme","volume":"520","author":"Chen","year":"2020","journal-title":"Inf. Sci."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"145459","DOI":"10.1109\/ACCESS.2021.3123571","article-title":"Cryptanalysis and improvement of the image encryption scheme based on Feistel network and dynamic DNA encoding","volume":"9","author":"Feng","year":"2021","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"209471","DOI":"10.1109\/ACCESS.2020.3038006","article-title":"Cryptanalzing a novel hyper-chaotic image encryption scheme based on pixel-level filtering and DNA-level diffusion","volume":"8","author":"Feng","year":"2020","journal-title":"IEEE Access"},{"key":"ref_27","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. Simul."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6571","DOI":"10.1007\/s11042-021-11810-2","article-title":"Cryptanalysis and Improvement of Novel Image Encryption Technique Using Hybrid Method of Discrete Dynamical Chaotic Maps and Brownian Motion","volume":"81","author":"Munir","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_29","first-page":"1050","article-title":"Security Analysis and Improvement of An Image Encryption Scheme Based on Chaotic Tent Map","volume":"9","author":"Wu","year":"2018","journal-title":"J. Inf. Hiding Multim. Signal Process."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"16679","DOI":"10.1007\/s11042-022-11973-6","article-title":"Cryptanalysis and enhancement of image encryption scheme based on word-oriented feed back shift register","volume":"81","author":"Arora","year":"2022","journal-title":"Multimed. Tools Appl."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.ijleo.2018.12.103","article-title":"Cryptanalysis of the integrated chaotic systems based image encryption algorithm","volume":"186","author":"Feng","year":"2019","journal-title":"Optik"},{"key":"ref_32","first-page":"102844","article-title":"A novel image encryption scheme based on non-adjacent parallelable permutation and dynamic DNA-level two-way diffusion","volume":"61","author":"Li","year":"2021","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1142\/S0218127410026563","article-title":"Cryptanalysis of Fridrich\u2019s chaotic image encryption","volume":"20","author":"Solak","year":"2010","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.ins.2017.11.021","article-title":"Improved known-plaintext attack to permutation-only multimedia ciphers","volume":"430","author":"Zhang","year":"2018","journal-title":"Inf. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1163","DOI":"10.1109\/TCYB.2017.2682561","article-title":"On the security of a class of diffusion mechanisms for image encryption","volume":"48","author":"Zhang","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1750155","DOI":"10.1142\/S0218127417501553","article-title":"Security analysis of some diffusion mechanisms used in chaotic ciphers","volume":"27","author":"Zhang","year":"2017","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"4747","DOI":"10.1109\/TCSVT.2021.3054508","article-title":"Re-evaluation of the security of a family of image diffusion mechanisms","volume":"31","author":"Chen","year":"2021","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2494","DOI":"10.1109\/TCSVT.2020.3021908","article-title":"Cryptanalysis of image ciphers with permutation-substitution network and chaos","volume":"31","author":"Chen","year":"2020","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2372","DOI":"10.1109\/TMM.2020.3011315","article-title":"Universal chosen-ciphertext attack for a family of image encryption schemes","volume":"23","author":"Chen","year":"2020","journal-title":"IEEE Trans. Multimed."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"107252","DOI":"10.1016\/j.optlastec.2021.107252","article-title":"Image encryption algorithm based on 2D hyperchaotic map","volume":"142","author":"Gao","year":"2021","journal-title":"Opt. Laser Technol."},{"key":"ref_41","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":"Inf. Sci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"2557","DOI":"10.1109\/TIE.2017.2736515","article-title":"Sine-transform-based chaotic system with FPGA implementation","volume":"65","author":"Hua","year":"2017","journal-title":"IEEE Trans. Ind. Electron."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1551\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:05:16Z","timestamp":1760144716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1551"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,28]]},"references-count":42,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["e24111551"],"URL":"https:\/\/doi.org\/10.3390\/e24111551","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,28]]}}}