TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Cryptanalysis of permutation-based image encryption algorithms

* , , , , ,

* Corresponding author · click or hover a name for details

pp. 4157–4167Vol. 29Issue 10-BOctober 2026DOI: 10.47974/JDMSC-3040 Crossmark XML
Received:
01 Apr 2026
Published Online:
31 Oct 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-3040
Pages:
4157–4167

Abstract

Image encryption algorithms based on permutation-based algorithms are being common since they are simple and fast to compute but their security is a major issue when subjected to a high level of cryptanalysis. This paper provides a detailed discussion of the permutation-only schemes, in terms of their mathematical representation, and structural weaknesses. The systematized research questions are the patterns of vulnerabilities caused by deterministic pixel rearrangements, which do not possess diffusion qualities. The cryptanalytic methods such as known-plaintext attacks (KPA) and chosen-plaintext attacks (CPA) are discussed in order to illustrate the effectiveness of retrieval of permutation keys using little computing power. In addition, optimization techniques are suggested to expedite key reconstruction with heuristic and reduction of search space techniques. Through experimental analysis, it is demonstrated that permutation only schemes are highly vulnerable, recovering key with more than 90% accuracy and with a lesser level of computation. The results indicate that to achieve robustness, it is important to incorporate diffusion processes, which can be helpful in creating secure image encryption systems.

Keywords

Subject Classifications

68M2568U10

References

[1] M. Li, K. Zhou, H. Ren, and H. Fan, “Cryptanalysis of permutation–diffusion-based lightweight chaotic image encryption scheme using CPA,” Applied Sciences, vol. 9, no. 3, Art. no. 494 (2019), doi: 10.3390/app9030494.

[2] C.-C. Chang, S. Xu, K. Gao, and C.-C. Chang, “Cryptanalysis of dual-stage permutation encryption using large-kernel convolutional neural network and known plaintext attack,” Cryptography, vol. 8, no. 3, Art. no. 41 (2024), doi: 10.3390/cryptography8030041.

[3] Y. Zhao, Q. Shi, and Q. Ding, “Cryptanalysis of an image encryption algorithm using DNA coding and chaos,” Entropy, vol. 27, no. 1, Art. no. 40 (2025), doi: 10.3390/e27010040.

[4] S. Zhu, C. Zhu, and H. Yan, “Cryptanalyzing and improving an image encryption algorithm based on chaotic dual scrambling of pixel position and bit,” Entropy, vol. 25, no. 3, Art. no. 400 (2023), doi: 10.3390/e25030400.

[5] M. Jiang and H. Yang, “Image encryption algorithm using multi-level permutation and improved Logistic–Chebyshev coupled map,” Information, vol. 14, no. 8, Art. no. 456 (2023), doi: 10.3390/info14080456.

[6] Y. Dou and M. Li, “Cryptanalysis of a new color image encryption using combination of the 1D chaotic map,” Applied Sciences, vol. 10, no. 6, Art. no. 2187 (2020), doi: 10.3390/app10062187.

[7] L. Jyotsna and L. P. Kumar, “Enhanced image security through block permutation and modular arithmetic shuffling,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 29, no. 3, pp. 1313–1333 (2026), doi: 10.47974/JDMSC-2617.

[8] H. Fan, H. Lu, C. Zhang, M. Li, and Y. Liu, “Cryptanalysis of an image encryption algorithm based on random walk and hyperchaotic systems,” Entropy, vol. 24, no. 1, Art. no. 40 (2022), doi: 10.3390/e24010040.

[9] C.-Y. Lin and J.-L. Wu, “Cryptanalysis and improvement of a chaotic map-based image encryption system using both plaintext related permutation and diffusion,” Entropy, vol. 22, no. 5, Art. no. 589 (2020), doi: 10.3390/e22050589.

[10] F. Movahedi, A. Karimi, and Z. Samiei, “Euler-Sombor index of chemical graphs and its applications,” Journal of Information and Optimization Sciences, vol. 47, no. 4, pp. 1515–1524 (2026), doi: 10.47974/JIOS-1975.

[11] M. Ahmad, E. Al Solami, X.-Y. Wang, M. N. Doja, M. M. S. Beg, and A. A. Alzaidi, “Cryptanalysis of an image encryption algorithm based on combined chaos for a BAN system, and improved scheme using SHA-512 and hyperchaos,” Symmetry, vol. 10, no. 7, Art. no. 266 (2018), doi: 10.3390/sym10070266.

[12] X. Zhang and X. Wang, “Multiple-image encryption algorithm based on the 3D permutation model and chaotic system,” Symmetry, vol. 10, no. 11, Art. no. 660 (2018), doi: 10.3390/sym10110660.

[13] C. İnce, K. İnce, and D. Hanbay, “A multilayer nonlinear permutation framework and its demonstration in lightweight image encryption,” Entropy, vol. 26, no. 10, Art. no. 885 (2024), doi: 10.3390/e26100885.

[14] C. Zhu, G. Wang, and K. Sun, “Improved cryptanalysis and enhancements of an image encryption scheme using combined 1D chaotic maps,” Entropy, vol. 20, no. 11, Art. no. 843 (2018), doi: 10.3390/e20110843.

[15] R. C. Poonia, R. Almakki, A. K. J. Saudagar, A. Altameem, and M. Albathan, “An optimization approach for real-time object detection in IoT devices through edge computing and deep learning,” Journal of Information and Optimization Sciences, vol. 45, no. 5, pp. 1465–1475 (2024), doi: 10.47974/JIOS-1768.

Views: 11Downloads: 5Citations: 0