{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T13:46:39Z","timestamp":1784123199314,"version":"3.55.0"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,21]],"date-time":"2023-02-21T00:00:00Z","timestamp":1676937600000},"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":["62271157"],"award-info":[{"award-number":["62271157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2022A1515010005"],"award-info":[{"award-number":["2022A1515010005"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["62271157"],"award-info":[{"award-number":["62271157"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2022A1515010005"],"award-info":[{"award-number":["2022A1515010005"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper analyzes the security of an image encryption algorithm based on a two-dimensional hyperchaotic map. This encryption algorithm generated chaotic sequences through a combination of two one-dimensional chaotic maps and used them as the permutation and diffusion key. Then, the image was encrypted by using the structure of row\u2013column permutation, forward-diffusion, and backward-diffusion. The proposer claimed that the above algorithm was secure. However, it was found through cryptanalysis that the algorithm cannot withstand the chosen plaintext attack. Although the forward-diffusion and backward-diffusion of the original algorithm use two different diffusion keys and there is a ciphertext feedback mechanism, the analysis of the diffusion by iterative optimization showed that it can be equivalent to global diffusion. In addition, the generation of chaotic sequences in the encryption process is independent of the plaintext image, so the equivalent diffusion and permutation key stream can be obtained by adjusting the individual pixel values of the chosen plaintexts. Aiming at the security loopholes in the encryption algorithm, the theoretical and experimental results are presented to support the efficiency of the proposed attack and suggestions for improvement are given. Finally, compared with the performance analysis of the existing cracking algorithm, our cryptanalysis greatly improved the cracking efficiency without increasing the complexity of the data.<\/jats:p>","DOI":"10.3390\/e25030395","type":"journal-article","created":{"date-parts":[[2023,2,22]],"date-time":"2023-02-22T02:57:38Z","timestamp":1677034658000},"page":"395","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Cryptanalysis of an Image Encryption Algorithm Based on Two-Dimensional Hyperchaotic Map"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1503-3254","authenticated-orcid":false,"given":"Qinmao","family":"Jiang","sequence":"first","affiliation":[{"name":"College of Automation, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1192-6955","authenticated-orcid":false,"given":"Simin","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Automation, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4063-5401","authenticated-orcid":false,"given":"Qianxue","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Automation, Guangdong University of Technology, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,21]]},"reference":[{"key":"ref_1","first-page":"735","article-title":"Some progresses of chaotic cipher and its applications in multimedia secure communications","volume":"38","author":"Yu","year":"2016","journal-title":"J. Electron. Inf. Technol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s11071-016-3030-8","article-title":"An image encryption scheme based on chaotic tent map","volume":"87","author":"Li","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_3","first-page":"102931","article-title":"4D mixed chaotic system and its application to RGB image encryption using substitution-diffusion","volume":"61","author":"Shah","year":"2021","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3794","DOI":"10.1109\/TCSI.2021.3091404","article-title":"Constructing Higher-Dimensional Digital Chaotic Systems via Loop-State Contraction Algorithm","volume":"68","author":"Wang","year":"2021","journal-title":"IEEE Trans. Circuits Syst. Regul. Pap."},{"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":"42","DOI":"10.4018\/IJISP.2018070104","article-title":"A literature review on image encryption techniques","volume":"12","author":"Geetha","year":"2018","journal-title":"Int. J. Inf. Secur. Priv. (IJISP)"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/s00521-017-2993-9","article-title":"A novel image encryption scheme based on DNA sequence operations and chaotic systems","volume":"31","author":"Chai","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1016\/j.image.2016.12.007","article-title":"An image encryption algorithm based on the memristive hyperchaotic system, cellular automata and DNA sequence operations","volume":"52","author":"Chai","year":"2017","journal-title":"Signal Process. Image Commun."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Zhu, S., and Zhu, C. (2022). Secure image encryption algorithm based on hyperchaos and dynamic DNA coding. Entropy, 22.","DOI":"10.3390\/e22070772"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"106393","DOI":"10.1016\/j.optlaseng.2020.106393","article-title":"Chaotic image encryption algorithm based on hybrid multi-objective particle swarm optimization and DNA sequence","volume":"137","author":"Wang","year":"2021","journal-title":"Opt. Lasers Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s11071-016-3046-0","article-title":"Efficient cryptosystem approaches: S-boxes and permutation\u2013substitution-based encryption","volume":"87","author":"Belazi","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhu, S., Wang, G., and Zhu, C. (2019). A secure and fast image encryption scheme based on double chaotic S-boxes. Entropy, 21.","DOI":"10.3390\/e21080790"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3041","DOI":"10.1007\/s11071-019-05413-8","article-title":"An image encryption scheme based on a new hybrid chaotic map and optimized substitution box","volume":"99","author":"Farah","year":"2020","journal-title":"Nonlinear Dyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"060507","DOI":"10.1088\/1674-1056\/abdea3","article-title":"An image encryption algorithm based on improved baker transformation and chaotic S-box","volume":"30","author":"Wang","year":"2021","journal-title":"Chin. Phys. B"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/j.optcom.2014.12.084","article-title":"Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform","volume":"343","author":"Zhou","year":"2015","journal-title":"Opt. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1016\/j.optlastec.2016.02.018","article-title":"Image compression\u2013encryption scheme based on hyper-chaotic system and 2D compressive sensing","volume":"82","author":"Zhou","year":"2016","journal-title":"Opt. Laser Technol."},{"key":"ref_17","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":"ref_18","doi-asserted-by":"crossref","first-page":"29243","DOI":"10.1007\/s11042-020-09542-w","article-title":"A novel hyper-chaotic image encryption scheme based on quantum genetic algorithm and compressive sensing","volume":"79","author":"Cheng","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"5573","DOI":"10.1007\/s11042-019-08273-x","article-title":"A novel image encryption algorithm based on bit-plane matrix rotation and hyper chaotic systems","volume":"79","author":"Xu","year":"2020","journal-title":"Multimed. Tools Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"7111","DOI":"10.1007\/s00521-018-3541-y","article-title":"A chaotic image encryption algorithm based on 3-D bit-plane permutation","volume":"31","author":"Gan","year":"2019","journal-title":"Neural Comput. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"105995","DOI":"10.1016\/j.optlaseng.2019.105995","article-title":"An image encryption algorithm based on a hidden attractor chaos system and the Knuth\u2013Durstenfeld algorithm","volume":"128","author":"Wang","year":"2020","journal-title":"Opt. Lasers Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"106202","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."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Wu, Z., Pan, P., Sun, C., and Zhao, B. (2021). Plaintext-related dynamic key chaotic image encryption algorithm. Entropy, 23.","DOI":"10.3390\/e23091159"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"32841","DOI":"10.1007\/s11042-021-11218-y","article-title":"A novel image encryption algorithm using PWLCM map-based CML chaotic system and dynamic DNA encryption","volume":"80","author":"Tian","year":"2021","journal-title":"Multimed. Tools Appl."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9721675","DOI":"10.1155\/2020\/9721675","article-title":"Image encryption scheme based on a generalized arnold map and RSA algorithm","volume":"2020","author":"Jiao","year":"2020","journal-title":"Secur. Commun. Netw."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lin, H., Wang, C., Xu, C., Zhang, X., and Iu, H.H. (2022). A memristive synapse control method to generate diversified multi-structure chaotic attractors. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.","DOI":"10.1109\/TCAD.2022.3186516"},{"key":"ref_27","first-page":"311","article-title":"Generating n-Scroll Chaotic Attractors From A Memristor-based Magnetized Hopfield Neural Network","volume":"70","author":"Lin","year":"2022","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"8839","DOI":"10.1109\/TII.2022.3155599","article-title":"Brain-like initial-boosted hyperchaos and application in biomedical image encryption","volume":"18","author":"Lin","year":"2022","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1007\/s11071-022-07630-0","article-title":"Hyperchaotic memristive ring neural network and application in medical image encryption","volume":"110","author":"Lin","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1140\/epjp\/i2019-12797-4","article-title":"Cryptanalysis of an image encryption cryptosystem based on binary bit planes extraction and multiple chaotic maps","volume":"134","author":"Wen","year":"2019","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Hu, Y., Yu, S., and Zhang, Z. (2020). On the Cryptanalysis of a Bit-Level Image Chaotic Encryption Algorithm. Math. Probl. Eng., 2020.","DOI":"10.1155\/2020\/5747082"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1007\/s11071-016-3311-2","article-title":"Cryptanalysis of a chaotic image cipher using Latin square-based confusion and diffusion","volume":"88","author":"Hu","year":"2017","journal-title":"Nonlinear Dyn."},{"key":"ref_33","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_34","doi-asserted-by":"crossref","unstructured":"Fan, H., Lu, H., Zhang, C., Li, M., and Liu, Y. (2021). Cryptanalysis of an Image Encryption Algorithm Based on Random Walk and Hyperchaotic Systems. Entropy, 24.","DOI":"10.3390\/e24010040"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Wen, H., Yu, S., and L\u00fc, J. (2019). Breaking an image encryption algorithm based on DNA encoding and spatiotemporal chaos. Entropy, 21.","DOI":"10.3390\/e21030246"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"75834","DOI":"10.1109\/ACCESS.2018.2883690","article-title":"Cryptanalysis of a chaotic image encryption algorithm based on information entropy","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_37","first-page":"102566","article-title":"Cryptanalysis of an image block encryption algorithm based on chaotic maps","volume":"54","author":"Ma","year":"2020","journal-title":"J. Inf. Secur. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"103424","DOI":"10.1016\/j.jvcir.2021.103424","article-title":"Security measurement of a medical communication scheme based on chaos and DNA coding","volume":"83","author":"Chen","year":"2022","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_39","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_40","doi-asserted-by":"crossref","unstructured":"Zhang, C., Chen, J., and Chen, D. (2022). Cryptanalysis of An Image Encryption Algorithm Based on a 2D Hyperchaotic Map. Entropy, 24.","DOI":"10.3390\/e24111551"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/395\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:38:15Z","timestamp":1760121495000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/3\/395"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,21]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["e25030395"],"URL":"https:\/\/doi.org\/10.3390\/e25030395","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,21]]}}}