A New Hybrid Image Encryption Model Based on Custom Logic Functions and Dynamic Chaotic Keys

Abstract

Any secure image encryption system needs to distort the statistical and visual structure of the image to prevent unauthorized access. Unlike traditional chaos-XOR methods, this paper presents a new hybrid image encryption model based on dynamic chaotic key generation, combined with two novel dedicated bit-level logic functions. The proposed model includes image pre-processing steps, such as flattening color channels and pixel shuffling, to break down the spatial structure. Bit-level nonlinear transformations are then applied using dedicated bit-level logic functions (FLF and FOF). The Bogdanov scheme was used as the chaotic key generator. The image encryption quality was evaluated against four state-of-the-art models using Entropy, NPCR, UACI, PSNR, and SSIM, along with visual analysis of histograms and correlation indices. The experimental results reported an average Entropy value of 7.95. NPCR rate and UACI values were 99.61% and 33.2% respectively. The correlation coefficient was 0.0046. The SSIM remained at 1.0, while the average encryption execution was 0.47 seconds. These results demonstrate that the proposed system can achieve a high level of visual security. This study represents a qualitative and quantitative contribution to the development of secure digital image processing methods.

Keywords

• Image Processing
• Bogdanov Scheme
• FLF
• FOF
• Chaotic Key

References

1. D. Altunkaya, F. Y. Okay, and S. Özdemir, “Encoding IoT Data: A Comprehensive Review of Image Transformation Techniques,” Sakarya University Journal of Computer and Information Sciences, vol. 8, no. 2. pp. 358–381, 2025. doi: 10.35377/saucis.1639203.
2. M. Rafiei, J. Raitoharju, and A. Iosifidis, “Computer Vision on X-Ray Data in Industrial Production and Security Applications: A Comprehensive Survey,” IEEE Access, vol. 11. Institute of Electrical and Electronics Engineers Inc., pp. 2445–2477, Jan. 02, 2023. doi: 10.1109/ACCESS.2023.3234187.
3. A. Khalil, A. Humeau-Heurtier, P. Abraham, and G. Mahé, “Microvascular blood flow with laser speckle contrast imaging: Analysis of static scatterers effect through modelling and simulation,” Proceedings - UKSim-AMSS 8th European Modelling Symposium on Computer Modelling and Simulation, EMS 2014, no. October, pp. 82–86, 2014, doi: 10.1109/EMS.2014.53.
4. X. Liao, Y. Yu, B. Li, Z. Li, and Z. Qin, “A New Payload Partition Strategy in Color Image Steganography,” IEEE Transactions on Circuits and Systems for Video Technology, vol. 30, no. 3, pp. 685–696, 2020, doi: 10.1109/TCSVT.2019.2896270.
5. X. Liao, Z. Qin, and L. Ding, “Data embedding in digital images using critical functions,” Signal Processing: Image Communication, vol. 58, pp. 146–156, 2017, doi: 10.1016/j.image.2017.07.006.
6. Ü. ÇAVUŞOĞLU and H. AL-SANABANİ, “The Performance Comparison of Lightweight Encryption Algorithms,” Sakarya University Journal of Computer and Information Sciences, vol. 2, no. 3, pp. 158–169, 2019, doi: 10.35377/saucis. 02.03.648493.
7. Y. Alghamdi and A. Munir, “Image Encryption Algorithms: A Survey of Design and Evaluation Metrics,” Journal of Cybersecurity and Privacy, vol. 4, no. 1. Multidisciplinary Digital Publishing Institute, pp. 126–152, Feb. 23, 2024. doi: 10.3390/jcp4010007.
8. C. Li, S. Li, G. Alvarez, G. Chen, and K. T. Lo, “Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations,” Physics Letters, Section A: General, Atomic and Solid State Physics, vol. 369, no. 1–2, pp. 23–30, 2007, doi: 10.1016/j.physleta.2007.04.023.

9. C. Li, Y. Liu, L. Y. Zhang, and M. Z. Q. Chen, “Breaking a chaotic image encryption algorithm based on modulo addition and xor operation,” International Journal of Bifurcation and Chaos, vol. 23, no. 4, p. 48, 2013, doi: 10.1142/S0218127413500752.
10. A. Shafique, J. Ahmed, M. U. Rehman, and M. M. Hazzazi, “Noise-Resistant Image Encryption Scheme for Medical Images in the Chaos and Wavelet Domain,” IEEE Access, vol. 9, pp. 59108–59130, 2021, doi: 10.1109/ACCESS.2021.3071535.
11. A. Tiwari, P. Diwan, T. D. Diwan, M. Miroslav, and S. P. Samal, “A compressed image encryption algorithm leveraging optimized 3D chaotic maps for secure image communication,” Scientific Reports 2025 15:1, vol. 15, no. 1, pp. 1–16, Apr. 2025, doi: 10.1038/s41598-025-95995-8.
12. W. Zhou, Y. Lu, R. Wang, Q. Wang, and J. Zheng, “A Novel Image Encryption Based on Style Transfer,” in ISKE 2023 - 18th International Conference on Intelligent Systems and Knowledge Engineering, 2023, pp. 119–127. doi: 10.1109/ISKE60036.2023.10481503.
13. M. Kumar, A. Aggarwal, and A. Garg, “A Review on Various Digital Image Encryption Techniques and Security Criteria,” International Journal of Computer Applications, vol. 96, no. 13, pp. 975–8887, 2014.
14. U. Zia et al., “Survey on image encryption techniques using chaotic maps in spatial, transform and spatiotemporal domains,” International Journal of Information Security, vol. 21, no. 4, pp. 917–935, Aug. 2022, doi: 10.1007/s10207-022-00588-5.
15. O. F. Mohammad, M. Shafry, M. Rahim, S. Rafeeq, M. Zeebaree, and F. Y. H. Ahmed, “A Survey and Analysis of the Image Encryption Methods,” 2017. Accessed: Jul. 20, 2025. [Online]. Available: https://www.academia.edu/download/57642736/Dec2017ijaerv12n23_35.pdf
16. S. Tunçer and C. Karakuzu, “Performance Analysis of Chaotic Neural Network and Chaotic Cat Map Based Image Encryption,” Sakarya University Journal of Computer and Information Sciences, vol. 5, no. 1, pp. 37–47, Apr. 2022, doi: 10.35377/saucis...1002582.
17. J. Wang, X. Song, H. Wang, and A. A. Abd El-Latif, “Applicable image security based on new hyperchaotic system,” Symmetry, vol. 13, no. 12, 2021, doi: 10.3390/sym13122290.
18. S. Patel and T. Veeramalai, “Image Encryption Using a Spectrally Efficient Halton Logistics Tent (HaLT) Map and DNA Encoding for Secured Image Communication,” Entropy, vol. 24, no. 6, 2022, doi: 10.3390/e24060803.
19. M. Hanif et al., “A Novel Grayscale Image Encryption Scheme Based on the Block-Level Swapping of Pixels and the Chaotic System,” Sensors, vol. 22, no. 16, 2022, doi: 10.3390/s22166243.
20. Z. Yuan, H. Li, Y. Miao, W. Hu, and X. Zhu, “Digital-Analog Hybrid Scheme and Its Application to Chaotic Random Number Generators,” International Journal of Bifurcation and Chaos, vol. 27, no. 14, Dec. 2017, doi: 10.1142/S0218127417502108.
21. Y. Pourasad, R. Ranjbarzadeh, and A. Mardani, “A New Algorithm for Digital Image Encryption Based on Chaos Theory,” Entropy 2021, Vol. 23, Page 341, vol. 23, no. 3, p. 341, Mar. 2021, doi: 10.3390/E23030341.
22. A. G. Mohamed et al., “Chaos Fractal Digital Image Encryption Transmission in Underwater Optical Wireless Communication System,” IEEE Access, vol. 12, pp. 117541–117559, 2024, doi: 10.1109/ACCESS.2024.3446836.
23. O. M. Al Hazaimeh, M. F. Al Jamal, A. K. Alomari, M. J. Bawaneh, and N. Tahat, “Image encryption using anti-synchronisation and Bogdanov transformation map,” International Journal of Computing Science and Mathematics, vol. 15, no. 1, p. 43, 2022, doi: 10.1504/IJCSM.2022.122144.
24. H. Jiexian, Y. Khizar, Z. A. Ali, R. Hasan, and M. S. Pathan, “On the dynamic reconfigurable implementations of MISTY1 and KASUMI block ciphers,” PLoS ONE, vol. 18, no. 9, September, p. e0291429, Sep. 2023, doi: 10.1371/journal.pone.0291429.
25. C. Li, Y. Liu, T. Xie, and M. Z. Q. Chen, “Breaking a novel image encryption scheme based on improved hyperchaotic sequences,” Nonlinear Dynamics, vol. 73, no. 3, pp. 2083–2089, Aug. 2013, doi: 10.1007/s11071-013-0924-6.
26. L. Liu, S. Hao, J. Lin, Z. Wang, X. Hu, and S. Miao, “Image block encryption algorithm based on chaotic maps,” IET Signal Processing, vol. 12, no. 1, pp. 22–30, Feb. 2018, doi: 10.1049/iet-spr.2016.0584.
27. K. Yildiz, A. Buldu, and H. Saritas, “Elliptic curve coding technique application for digital signature,” Security and Communication Networks, vol. 9, no. 17, pp. 4242–4254, Nov. 2016, doi: 10.1002/sec.1601.
28. C. E. Shannon, “A Mathematical Theory of Communication,” Bell System Technical Journal, vol. 27, no. 3, pp. 379–423, 1948, doi: 10.1002/j.1538-7305.1948.tb01338.x.
29. B. Schneier, APPLIED CRYPTOGRAPHY: Protocols, Algorithms, and Source Code in C, 20th Anniversary Edition. Wiley, 2015. doi: 10.1002/9781119183471.
30. C. E. Shannon, “Communication Theory of Secrecy Systems,” Bell System Technical Journal, vol. 28, no. 4, pp. 656–715, 1949, doi: 10.1002/j.1538-7305.1949.tb00928.x.