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Improved Chaotic Image Encryption on Grayscale Colorspace Using Elliptic Curves and 3D Lorenz System
Corresponding Author(s) : Daurat Sinaga
Kinetik: Game Technology, Information System, Computer Network, Computing, Electronics, and Control,
Vol. 10, No. 3, August 2025
Abstract
Digital data, especially visual content, faces significant security challenges due to its susceptibility to eavesdropping, manipulation, and theft in the modern digital landscape. One effective solution to address these issues is through the use of encryption techniques, such as image encryption algorithms that ensure the confidentiality, integrity, and authenticity of digital visual content. This study addresses these concerns by introducing an advanced image encryption method that combines Elliptic Curve Cryptography (ECC) with the 3D Lorenz chaotic system to enhance both security and efficiency. The method employs pixel permutation, ECC-based encryption, and diffusion using pseudo-random numbers generated by the Lorenz 3D system, tested on grayscale images such as MRI, Lena, and Peppers with a resolution of 512x512 pixels. The results show superior performance, with an MSE of 3032 and a PSNR of 8.87 dB for the Rice image, as well as UACI and NPCR values of 33.34% and 99.64%, respectively, indicating strong resilience to pixel intensity changes. During testing, the approach demonstrated robustness, allowing only the correct key to decrypt images accurately, while incorrect or modified keys led to distorted outputs, ensuring encryption reliability. Future work could explore extending the method to color images, optimizing processing for larger datasets, and incorporating additional chaotic systems to further fortify encryption strength.
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References
K. N. Singh, O. P. Singh, and A. K. Singh, “ECiS: Encryption prior to compression for digital image security with reduced memory,” Comput Commun, vol. 193, pp. 410–417, Sep. 2022, doi: 10.1016/j.comcom.2022.07.049.
E. A. Sofyan, C. A. Sari, H. Rachmawanto, and R. D. Cahyo, “High-Quality Evaluation for Invisible Watermarking Based on Discrete Cosine Transform (DCT) and Singular Value Decomposition (SVD),” Advance Sustainable Science, Engineering and Technology (ASSET), vol. 6, no. 1, 2024, doi: 10.26877/asset.v6i1.17186.
W. D. Ferreira, C. B. R. Ferreira, G. da Cruz Júnior, and F. Soares, “A review of digital image forensics,” Computers & Electrical Engineering, vol. 85, p. 106685, Jul. 2020, doi: 10.1016/j.compeleceng.2020.106685.
E. R. Pramudya et al., “Optimation of image encryption using fractal Tromino and polynomial Chebyshev based on chaotic matrix,” TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 22, no. 6, p. 1529, Aug. 2024, doi: 10.12928/telkomnika.v22i6.26080.
C. A. Sari, P. Purwanto, E. H. Rachmawanto, and A. Syukur, “An integration of quantum systems using BB84 for enhanced security in aeroponic smart farming,” TELKOMNIKA (Telecommunication Computing Electronics and Control), vol. 22, no. 6, p. 1491, Dec. 2024, doi: 10.12928/telkomnika.v22i6.26450.
M. Abu-Faraj et al., “Protecting Digital Images Using Keys Enhanced by 2D Chaotic Logistic Maps,” Cryptography, vol. 7, no. 2, 2023, doi: 10.3390/cryptography7020020.
S. T. Ahmed, D. A. Hammood, R. F. Chisab, A. Al-Naji, and J. Chahl, “Medical Image Encryption: A Comprehensive Review,” Aug. 01, 2023, Multidisciplinary Digital Publishing Institute (MDPI). doi: 10.3390/computers12080160.
M. Habek, Y. Genc, N. Aytas, A. Akkoc, E. Afacan, and E. Yazgan, “Digital image encryption using elliptic curve cryptography: A review,” in 2022 International Congress on Human-Computer Interaction, Optimization and Robotic Applications (HORA), IEEE, 2022, pp. 1–8.
V. Sathananthavathi, K. Ganesh Kumar, and M. Sathish Kumar, “Secure visual communication with advanced cryptographic and ımage processing techniques,” Multimed Tools Appl, 2023, doi: 10.1007/s11042-023-17224-6.
M. T. Elkandoz and W. Alexan, “Image encryption based on a combination of multiple chaotic maps,” Multimed Tools Appl, vol. 81, no. 18, pp. 25497–25518, Jul. 2022, doi: 10.1007/s11042-022-12595-8.
A. Banik, D. S. Laiphrakpam, A. Agrawal, and R. Patgiri, “Secret image encryption based on chaotic system and elliptic curve cryptography,” Digit Signal Process, vol. 129, p. 103639, Sep. 2022, doi: 10.1016/j.dsp.2022.103639.
C. A. Sari et al., “A Chaotic Image Encryption Based on Random Noise and Arnold Cat Maps,” in 2024 International Seminar on Application for Technology of Information and Communication (iSemantic), 2024, pp. 347–352. doi: 10.1109/iSemantic63362.2024.10762216.
C. A. Sari, M. H. Dzaki, E. H. Rachmawanto, R. R. Ali, and M. Doheir, “High PSNR Using Fibonacci Sequences in Classical Cryptography and Steganography Using LSB,” International Journal of Intelligent Engineering and Systems, vol. 16, no. 4, pp. 568–580, 2023, doi: 10.22266/ijies2023.0831.46.
S. Yin, J. Liu, and L. Teng, “Improved Elliptic Curve Cryptography with Homomorphic Encryption for Medical Image Encryption.,” Int. J. Netw. Secur., vol. 22, no. 3, pp. 419–424, 2020.
P. Parida, C. Pradhan, X.-Z. Gao, D. S. Roy, and R. K. Barik, “Image Encryption and Authentication With Elliptic Curve Cryptography and Multidimensional Chaotic Maps,” IEEE Access, vol. 9, pp. 76191–76204, 2021, doi: 10.1109/ACCESS.2021.3072075.
G. Ye, M. Liu, and M. Wu, “Double image encryption algorithm based on compressive sensing and elliptic curve,” Alexandria Engineering Journal, vol. 61, no. 9, pp. 6785–6795, Sep. 2022, doi: 10.1016/j.aej.2021.12.023.
K. Wang, X. Wu, H. Wang, H. Kan, and J. Kurths, “New color image cryptosystem via SHA-512 and hybrid domain,” Multimed Tools Appl, vol. 80, no. 12, pp. 18875–18899, 2021, doi: 10.1007/s11042-021-10511-0.
S. Zhou, P. He, and N. Kasabov, “A dynamic DNA color image encryption method based on SHA-512,” Entropy, vol. 22, no. 10, pp. 1–23, Oct. 2020, doi: 10.3390/e22101091.
P. N. Lone, D. Singh, V. Stoffová, D. C. Mishra, U. H. Mir, and N. Kumar, “Cryptanalysis and Improved Image Encryption Scheme Using Elliptic Curve and Affine Hill Cipher,” Mathematics, vol. 10, no. 20, Oct. 2022, doi: 10.3390/math10203878.
S. Ullah, J. Zheng, N. Din, M. T. Hussain, F. Ullah, and M. Yousaf, “Elliptic Curve Cryptography; Applications, challenges, recent advances, and future trends: A comprehensive survey,” Comput Sci Rev, vol. 47, p. 100530, 2023, doi: https://doi.org/10.1016/j.cosrev.2022.100530.
A. V. Lucca, G. A. M. Sborz, V. R. Q. Leithardt, M. Beko, C. A. Zeferino, and W. D. Parreira, “A review of techniques for implementing elliptic curve point multiplication on hardware,” Mar. 01, 2021, MDPI AG. doi: 10.3390/jsan10010003.
M. Gabr et al., “Application of DNA Coding, the Lorenz Differential Equations and a Variation of the Logistic Map in a Multi-Stage Cryptosystem,” Symmetry (Basel), vol. 14, no. 12, Dec. 2022, doi: 10.3390/sym14122559.
M. Naim, A. Ali Pacha, and C. Serief, “A novel satellite image encryption algorithm based on hyperchaotic systems and Josephus problem,” Advances in Space Research, vol. 67, no. 7, pp. 2077–2103, Apr. 2021, doi: 10.1016/j.asr.2021.01.018.
W. Alexan, N. Alexan, and M. Gabr, “Multiple-Layer Image Encryption Utilizing Fractional-Order Chen Hyperchaotic Map and Cryptographically Secure PRNGs,” Fractal and Fractional, vol. 7, no. 4, Apr. 2023, doi: 10.3390/fractalfract7040287.
D. Chicco, M. J. Warrens, and G. Jurman, “The coefficient of determination R-squared is more informative than SMAPE, MAE, MAPE, MSE and RMSE in regression analysis evaluation,” PeerJ Comput Sci, vol. 7, p. e623, Jul. 2021, doi: 10.7717/peerj-cs.623.
U. Sara, M. Akter, and M. S. Uddin, “Image Quality Assessment through FSIM, SSIM, MSE and PSNR—A Comparative Study,” Journal of Computer and Communications, vol. 07, no. 03, pp. 8–18, 2019, doi: 10.4236/jcc.2019.73002.
A. A. Arab, M. J. B. Rostami, and B. Ghavami, “An image encryption algorithm using the combination of chaotic maps,” Optik (Stuttg), vol. 261, p. 169122, 2022, doi: https://doi.org/10.1016/j.ijleo.2022.169122.