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Cited by 247Chaos-based Image/Signal EncryptionComputer Science and EngineeringCryptographic Implementations and Security

Cryptanalysis of a Chaotic Image Encryption Algorithm Based on Information Entropy

Open access
Li, Chengqing, Lin, Dongdong, Feng, Bingbing, Lu, Jinhu, Hao, Feng·2018·IEEE Access
DOI 10.1109/access.2018.2883690
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Abstract

Recently, a chaotic image encryption algorithm based on information entropy (IEAIE) was proposed. This paper scrutinizes the security properties of the algorithm and evaluates the validity of the used quantifiable security metrics. When the round number is only one, the equivalent secret key of every basic operation of IEAIE can be recovered with a differential attack separately. Some common insecurity problems in the field of chaotic image encryption are found in IEAIE, e.g., the short orbits of the digital chaotic system and the invalid sensitivity mechanism built on information entropy of the plain image. Even worse, each security metric is questionable, which undermines the security credibility of IEAIE. Hence, IEAIE can only serve as a counterexample for illustrating common pitfalls in designing secure communication method for image data.

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  • The information-entropy-based chaotic image-encryption algorithm [180] is very insecure against differential attack.

    “The analysis result shows that it is very insecure against differential attack.”

    From Chaos-Based Image Encryption: Review, Application, and Challenges (2023) · cites this paper as [181]

    The Abstract (p. 2) reports that a differential attack can recover the equivalent secret key of every basic operation when IEAIE has one round. In “Differential Cryptanalysis” (p. 8), the authors say they skip cryptanalysis of the full two-round version. The claim omits that limitation and presents the differential-attack result as applying to the algorithm generally. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • The security assessment metrics used in chaotic cryptography are far ineffective for security analysis.

    “Considering the quantitative test results of the four special schemes on the metrics, it is concluded that the metrics are far ineffective for security analysis”

    From When an attacker meets a cipher-image in 2018: A year in review (2019) · cites this paper as [1]

    The Conclusion (p. 8) says every security metric used to assess IEAIE is incapable of testifying to its real security performance. That supports the criticism of those metrics, but not the broader claim that security-assessment metrics used throughout chaotic cryptography are ineffective. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • The sensitivity mechanisms of PRNS on the plain-image built in [80,119,27,92] can be easily canceled by constructing special plain-images.

    “For example, the sensitivity mechanisms of PRNS on the plain-image built in [80,119,27,92] can be easily canceled by constructing some special plain-images, which has been reported in many cryptanalysis papers such as [1,117].”

    From When an attacker meets a cipher-image in 2018: A year in review (2019) · cites this paper as [1]

    In “B. Differential Cryptanalysis” (p. 8), the paper says it is very easy to construct plain-images that produce the same keystream in IEAIE, defeating that scheme’s plain-image-dependent mechanism. The cited paper examines IEAIE, identified as [27] in its Introduction (p. 2); our copy does not establish the same result for the other three schemes named in the citing sentence. (LLM, conf=0.86)

    Experimental — accuracy not yet measured

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Cites

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Research works printed but not linked: 31

  1. [1][1] H. Li, K. Wang, X. Liu, Y. Sun, and S. Guo, 'A selective privacypreserving approach for multimedia data,' IEEE MultiMedia, vol. 24, no. 4, pp. 14-25, 2017. -
  2. [2][2] M. Du, K. Wang, Y. Chen, X. Wang, and Y. Sun, 'Big data privacy preserving in multi-access edge computing for heterogeneous internet of things,' IEEE Communications Magazine, vol. 56, no. 8, pp. 62-67, 2018. -
  3. [3][3] X. Zhang, S.-H. Seo, and C. Wang, 'A lightweight encryption method for privacy protection in surveillance videos,' IEEE Access, vol. 6, pp. 18 074-18 087, 2018. -
  4. [4][4] S. Chatterjee, S. Roy, A. K. Das, S. Chattopadhyay, N. Kumar, and A. V. Vasilakos, 'Secure biometric-based authentication scheme using chebyshev chaotic map for multi-server environment,' IEEE Transactions on Dependable and Secure Computing, vol. 15, no. 5, pp. 824-839, 2018. -
  5. [5][5] C. Li, D. Lin, and J. Lü, 'Cryptanalyzing an image-scrambling encryption algorithm of pixel bits,' IEEE MultiMedia, vol. 3, pp. 64-71, 2017. -
  6. [6][6] Z. Hua and Y. Zhou, 'Image encryption using 2D logistic-adjusted-sine map,' Information Sciences, vol. 339, pp. 237-253, 2016. -
  7. [7][7] Z. Hua, F. Jin, B. Xu, and H. Huang, '2D logistic-sine-coupling map for image encryption,' Signal Processing, vol. 149, pp. 148-161, 2018. -
  8. [8][8] Z. Lin, S. Yu, and J. Lü, 'A novel approach for constructing one-way hash function based on a message block controlled 8D hyperchaotic map,' International Journal of Bifurcation and Chaos, vol. 27, no. 07, p. 1750106, 2017. -
  9. [9][9] C. Zhu, 'A novel image encryption scheme based on improved hyperchaotic sequences,' Optics Communications, vol. 285, no. 1, pp. 29-37, 2012. -
  10. [10][10] Q. Shen and W. Liu, 'A novel digital image encryption algorithm based on orbit variation of phase diagram,' International Journal of Bifurcation and Chaos, vol. 27, no. 13, p. Article number 1750204, DEC 15 2017. -
  11. [11][11] A. Shakiba, M. R. Hooshmandasl, and M. A. Meybodi, 'Cryptanalysis of multiplicative coupled cryptosystems based on the chebyshev polynomials,' International Journal of Bifurcation and Chaos, vol. 26, no. 07, p. 1650112, 2016. -
  12. [12][12] M. H. Abd, F. R. Tahir, G. A. Al-Suhail, and V.-T. Pham, 'An adaptive observer synchronization using chaotic time-delay system for secure communication,' Nonlinear Dynamics, vol. 90, no. 4, pp. 2583-2598, 2017. -
  13. [13][13] L. Zhang, S. Zhu, and S. Tang, 'Privacy protection for telecare medicine information systems using a chaotic map-based three-factor authenticated key agreement scheme,' IEEE Journal of Biomedical and Health Informatics, vol. 21, no. 2, pp. 465-475, 2017. -
  14. [14][14] X. Ge, B. Lu, F. Liu, and D. Gong, 'An image encryption algorithm based on information hiding,' International Journal of Bifurcation and Chaos, vol. 26, no. 11, p. Article number 1650192, OCT 2016. -
  15. [15][15] J. Sun, X. Liao, X. Chen, and S. Guo, 'Privacy-aware image encryption based on logistic map and data hiding,' International Journal of Bifurcation and Chaos, vol. 27, no. 5, p. Article number 1750073, MAY 2017. -
  16. [16][16] C. Li, T. Xie, Q. Liu, and G. Cheng, 'Cryptanalyzing image encryption using chaotic logistic map,' Nonlinear Dynamics, vol. 78, no. 2, pp. 15451551, 2014. -
  17. [17][17] [C. Li, 'Cracking a hierarchical chaotic image encryption algorithm based on permutation,' Signal Processing, vol. 118, pp. 203-210, 2016.](http://dx.doi.org/10.1016/j.sigpro.2015.07.008) - · DOI · Paper page
  18. [18][18] S. Li, C. Li, G. Chen, and X. Mou, 'Cryptanalysis of the RCES/RSES image encryption scheme,' Journal of Systems and Software, vol. 81, no. 7, pp. 1130-1143, 2008. -
  19. [19][19] C. Li, D. Lin, J. Lü, and F. Hao, 'Cryptanalyzing an image encryption algorithm based on autoblocking and electrocardiography,' IEEE MultiMedia, vol. 25, no. 4, 2018. -
  20. [20][20] X. Ge, B. Lu, F. Liu, and X. Luo, 'Cryptanalyzing an image encryption algorithm with compound chaotic stream cipher based on perturbation,' Nonlinear Dynamics, vol. 90, no. 2, pp. 1141-1150, 2017. -
  21. [21][21] W.-S. Yap, R. C.-W. Phan, W.-C. Yau, and S.-H. Heng, 'Cryptanalysis of a new image alternate encryption algorithm based on chaotic map,' Nonlinear Dynamics, vol. 80, no. 3, pp. 1483-1491, 2015. -
  22. [22][22] Q. Wang, S. Yu, C. Li, J. Lü, X. Fang, C. Guyeux, and J. M. Bahi, 'Theoretical design and FPGA-based implementation of higher-dimensional digital chaotic systems,' IEEE Transactions on Circuits and Systems IRegular Papers, vol. 63, no. 3, pp. 401-412, 2016. -
  23. [23][23] Y. Liu, Y. Luo, S. Song, L. Cao, and J. Liu, 'Counteracting dynamical degradation of digital chaotic chebyshev map via perturbation,' International Journal of Bifurcation and Chaos, vol. 27, no. 3, p. art. no. 1750033, 2017. -
  24. [24][24] G. Alvarez and S. Li, 'Some basic cryptographic requirements for chaosbased cryptosystems,' International Journal of Bifurcation and Chaos, vol. 16, no. 8, pp. 2129-2151, AUG 2006. -
  25. [25][25] F. Özkaynak, 'Brief review on application of nonlinear dynamics in image encryption,' Nonlinear Dynamics, vol. 92, no. 2, pp. 305-313, 2018. -
  26. [26][26] C. Zhu and K. Sun, 'Cryptanalyzing and improving a novel color image encryption algorithm using RT-enhanced chaotic tent maps,' IEEE Access, vol. 6, pp. 18 759-18 770, 2018. -
  27. [27][27] G. Ye, C. Pan, X. Huang, Z. Zhao, and J. He, 'A chaotic image encryption algorithm based on information entropy,' International Journal of Bifurcation and Chaos, vol. 28, no. 1, p. art. no. 1850010, 2018. -
  28. [29][29] [C. Li, B. Feng, S. Li, J. Kurths, and G. Chen, 'Dynamic analysis of chaotic maps as complex networks in the digital domain, arXiv:1410.7694,' 2017.](http://arxiv.org/abs/1410.7694) - · arXiv
  29. [31][31] M. Madiman, A. W. Marcus, and P. Tetali, 'Entropy and set cardinality inequalities for partition-determined functions,' Random Structures & Algorithms, vol. 40, no. 4, pp. 399-424, 2011. -
  30. [32][32] E. Y. Xie, C. Li, S. Yu, and J. Lü, 'On the cryptanalysis of Fridrich's chaotic image encryption scheme,' Signal Processing, vol. 132, pp. 150154, 2017. -
  31. [33][33] T. Xiang, S. Guo, and X. Li, 'Perceptual visual security index based on edge and texture similarities,' IEEE Transactions on Information Forensics and Security, vol. 11, no. 5, pp. 951-963, 2016. <!-- image --> IEEEAccess IEEEAccesS <!-- image --> <!-- image --> CHENGQING LI (M'07-SM'13) received his M.Sc. degree in Applied Mathematics from Zhejiang University, China in 2005 and his Ph.D. degree in Electronic Engineering from City University of Hong Kong in 2008. Thereafter, he worked as a Postdoctoral Fellow at The Hong Kong Polytechnic University till September 2010. Then, he worked at the College of Information Engineering, Xiangtan University, China. From April 2013 to July 2014, he worked at the University of Konstanz, Germany, under the support of the Alexander von Humboldt Foundation. Currently, he is working at School of Computer Science and Electronic Engineering, Hunan University as a full professor. Prof. Li focuses on security analysis of multimedia encryption schemes and privacy protection schemes. He has published about fifty papers on the subject in the past 13 years, receiving more than 2500 citations with h-index 28. <!-- image --> DONGDONG LIN received his M.Sc. degree and B.Sc. degree both in computer science at the College of Information Engineering, Xiangtan University, China in 2015 and 2018, respectively. Currently, he is visiting at School of Computer Science and Electronic Engineering, Hunan University, China. His research interests include cryptanalysis and image privacy protection. <!-- image --> <!-- image --> BINGBING FENG received his M.Sc. degree and B.Sc. degree both in computer science at the College of Information Engineering, Xiangtan University in 2015 and 2018, respectively. His research interests include complex networks and nonlinear dynamics. JINHU LÜ (M'03-SM'06-F'13) received the Ph.D degree in applied mathematics from the Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China in 2002. Currently, he is a Professor in the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He was a Professor in the RMIT University, Australia and a Visiting Fellow in the Princeton University, USA. He is the author of three research monographs and more than 110 SCI journal papers published in the fields of complex networks and complex systems, nonlinear circuits and systems, receiving more than 8000 SCI citations with h-index 42. He is an ISI Highly Cited Researcher in Engineering. <!-- image --> FENG HAO is a Professor of Security Engineering at the Department of Computer Science, University of Warwick. He received his PhD in Computer Security from the Computer Lab, University of Cambridge in 2007. He worked in security industry for several years before joining the faculty at Newcastle University as a lecturer in 2010 and was promoted to the readership in 2014. His research interests include applied cryptography, security engineering and efficient computing.

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Authors
Li, C., Lin, D., Feng, B., Lu, J., & Hao, F.
Affiliations
  • Hunan University (CN)
  • Xiangtan University (CN)
  • University of Warwick (GB)
ORCID
Venue
IEEE Access
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Published
2018
Volume
6
Pages
75834-75842
ISSN
2169-3536 (ISSN-L)
DOI
10.1109/access.2018.2883690
OpenAlex
W2794632346
Cited by
247
References
2
Citations by year
2026: 8 · 2025: 16 · 2024: 23 · 2023: 21 · 2022: 36 · 2021: 35 · 2020: 49 · 2019: 55 · 2018: 4
FWCI
17.89
Type
journal article
Language
en
Open access
Licence
ieeexplore.ieee.org/Xplorehelp/downloads/license-information/OAPA.html (vor)
Locations
  • IEEE Access (publishedVersion)
  • Warwick Research Archive Portal (University of Warwick) (acceptedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
National Natural Science Foundation of China (61772447, 61532020, U1736113)
Topics
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
  • Physical Sciences › Computer Science › Artificial Intelligence › Computer Science and Engineering
  • Physical Sciences › Computer Science › Artificial Intelligence › Cryptographic Implementations and Security
Keywords
chaotic image encryption, cryptanalysis, Shannon entropy, differential attack, key recovery, security metrics, image security

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