Image Cryptography Based on Chebyshev Polynomials and Transposition- Substitution Transformations

Donia Fadil Chalob; Russul Hussein Hasan; Zainab Mohammed Essa

doi:10.32628/IJSRSET2411450

Authors

Donia Fadil Chalob Computer Science Department, Mustansiriyah University, Baghdad, Iraq Author
Russul Hussein Hasan University of Baghdad, Baghdad, Iraq Author
Zainab Mohammed Essa Computer Science Department, Mustansiriyah University, Baghdad, Iraq Author

DOI:

https://doi.org/10.32628/IJSRSET2411450

Keywords:

Multimedia Encryption, Chebyshev Map, Block Scrambling, Real Time Image Cipher, Non-Linear Transformation

Abstract

The confirming of security and confidentiality of multimedia data is a serious challenge through the growing dependence on digital communication. This paper offers a new image cryptography based on the Chebyshev chaos polynomials map, via employing the randomness characteristic of chaos concept to improve security. The suggested method includes block shuffling, dynamic offset chaos key production, inter-layer XOR, and block 90 degree rotations to disorder the correlations intrinsic in image. The method is aimed for efficiency and scalability, accomplishing complexity order for n-pixels over specific cipher rounds. The experiment outcomes depict great resistant to cryptanalysis attacks, containing statistical, differential and brute-force attacks, due to its big key space size and sensitivity to initial values. This algorithm be responsible for a forceful and flexible solution for acquiring secure images, appropriate for high resolution data and real time applications.

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References

S. A. Mehdi, “Image encryption algorithm based on a novel 4D chaotic system”, International Journal of Information Security and Privacy, Vol. 15, No. 4, pp. 118-131, 2021. DOI: https://doi.org/10.4018/IJISP.2021100107

A. Onwutalobi, “Overview of Cryptography”, SSRN Electronic Journal, pp. 1-10, 2011. DOI: https://doi.org/10.2139/ssrn.2741776

N. N. Jasem and S. A. Mehdi, “Multiple Random Keys for Image Encryption Based on Sensitivity of a New 6D Chaotic System,” Int. J. Intell. Eng. Syst., vol. 16, no. 5, pp. 576–585, 2023, doi: 10.22266/ijies2023.1031.49. DOI: https://doi.org/10.22266/ijies2023.1031.49

D. F. Chalob, R. H. Hasan, F. N. Abbas, Image Encryption based on Chaotic Blocks Shuffling and RC4. Baghdad Sci.J [Internet]. [cited 2025 Jan. 6]; 22(7). Available from: https://www.bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9781.

D. F. Chalob, R. H. Hasan, and R. F. Yaser, "Image Cryptography Based on Confusion and Diffusion Using 6D Hyper Chaotic System and Fibonacci Q-Matrix," International Journal of Intelligent Engineering and Systems, vol. 17, no. 4, pp. 944-956, 2024, doi: 10.22266/ijies2024.0831.71. DOI: https://doi.org/10.22266/ijies2024.0831.71

A. Kanso and M. Ghebleh, "A novel image encryption algorithm based on a 3D chaotic map," Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 8, pp. 2943–2959, Aug. 2012. DOI: 10.1016/j.cnsns.2011.11.035. DOI: https://doi.org/10.1016/j.cnsns.2011.11.030

B. Stoyanov and K. Kordov, "Image Encryption Using Chebyshev Map and Rotation Eq.," Entropy, vol. 17, no. 4, pp. 2117–2139, Apr. 2015. doi: 10.3390/e17042117. DOI: https://doi.org/10.3390/e17042117

H. Zhu, X. Zhang, H. Yu, C. Zhao, and Z. Zhu, "A novel image encryption scheme using the composite discrete chaotic system," Entropy, vol. 18, no. 8, p. 276, 2016, doi: 10.3390/e18080276. DOI: https://doi.org/10.3390/e18080276

H. Linqing, S. Cai, M. Xiao, and X. Xiong, "A Simple Chaotic Map-Based Image Encryption System Using Both Plaintext Related Permutation and Diffusion," Entropy, vol. 20, no. 7, p. 535, Jul. 2018, doi: 10.3390/e20070535. DOI: https://doi.org/10.3390/e20070535

R. Ramasamy, V. Ranganathan, S. Kadry, R. Damaševičius, and T. Blažauskas, "An Image Encryption Scheme Based on Block Scrambling, Modified Zigzag Transformation and Key Generation Using Enhanced Logistic—Tent Map," Entropy, vol. 21, no. 7, pp. 656, Jul. 2019, doi: 10.3390/e21070656. DOI: https://doi.org/10.3390/e21070656

Yang, C.; Pan, P.; Ding, Q. Image Encryption Scheme Based on Mixed Chaotic Bernoulli Measurement Matrix Block Compressive Sensing. Entropy 2022, 24, 273. doi.org/10.3390/e24020273. DOI: https://doi.org/10.3390/e24020273

Alghamdi, Y.; Munir, A.; Ahmad, J. A Lightweight Image Encryption Algorithm Based on Chaotic Map and Random Substitution. Entropy 2022, 24, 1344.doi.org/10.3390/e24101344. DOI: https://doi.org/10.3390/e24101344

Jiang, M.; Yang, H. Imag Encryption Using a New Hybrid Chaotic Map and Spiral Transformation. Entropy 2023, 25, 1516. doi.org/10.3390/e25111516. DOI: https://doi.org/10.3390/e25111516

R. S. Mohammed, K. K. Jabbar, and H. A. Hilal, "Image encryption under spatial domain based on modify 2D LSCM chaotic map via dynamic substitution-permutation network," Int. J. Electr. Comput. Eng., vol. 11, no. 4, pp. 3070-3083, Aug. 2021, doi: 10.11591/ijece.v11i4.pp3070-3083. DOI: https://doi.org/10.11591/ijece.v11i4.pp3070-3083

Jiang, M.; Yang, H. Image Encryption Algorithm Using Multi-Level Permutation and Improved Logistic–Chebyshev Coupled Map. Information 2023, 14, 456. doi.org/10.3390/info14080456. DOI: https://doi.org/10.3390/info14080456

H. Fadel, R. S. Hameed, J. N. Hasoon, S. A. Mostafa, and B. A. Khalaf, "A light-weight ESalsa20 ciphering based on 1D logistic and Chebyshev chaotic maps," Solid State Technology, vol. 63, no. 1, pp. 1078-1093, 2020.

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, p. 589, May 2020, doi: 10.3390/e22050589. DOI: https://doi.org/10.3390/e22050589

Zhu, S.; Deng, X.; Zhang, W.; Zhu, C. Image Encryption Scheme Based on Newly Designed Chaotic Map and Parallel DNA Coding. Mathematics 2023, 11, 231. doi.org/10.3390/math11010231. DOI: https://doi.org/10.3390/math11010231

Moya-Albor, E.; Romero-Arellano, A.; Brieva, J.; Gomez-Coronel, S.L. Color Image Encryption Algorithm Based on a Chaotic Model Using the Modular Discrete Derivative and Langton’s Ant. Mathematics 2023, 11, 2396. doi.org/10.3390/math11102396. DOI: https://doi.org/10.3390/math11102396

Zhang, B.; Liu, L. Chaos-Based Image Encryption: Review, Application, and Challenges. Mathematics 2023, 11, 2585. doi.org/10.3390/math11112585. DOI: https://doi.org/10.3390/math11112585

Huang, S.; Deng, G.; Liu, L.; Li, X. Technique for Enhancing the Chaotic Characteristics of Chaotic Maps Using Delayed Coupling and Its Application in Image Encryption. Mathematics 2023, 11, 3295. doi.org/10.3390/math11153295. DOI: https://doi.org/10.3390/math11153295

Zhou, Z.; Xu, X.; Jiang, Z.; Sun, K. Multiple-Image Encryption Scheme Based on an N-Dimensional Chaotic Modular Model and Overlapping Block Permutation–Diffusion Using Newly Deﬁned Operation. Mathematics 2023, 11, 3373. doi.org/10.3390/math11153373. DOI: https://doi.org/10.3390/math11153373