Image Cryptography Process Using Arnold’s Cat Map And Henon Map Algorithms

Moch Azhar Al Ghifari; Bayu Surarso; Aris Sugiharto

doi:10.52436/1.jutif.2026.7.3.5354

Authors

Moch Azhar Al Ghifari Master Program of Information System, Postgraduate School, Universitas Diponegoro, Indonesia
Bayu Surarso Department of Mathematics, Universitas Diponegoro, Indonesia
Aris Sugiharto Department of Computer Engineering, Universitas Diponegoro, Indonesia

DOI:

https://doi.org/10.52436/1.jutif.2026.7.3.5354

Keywords:

Arnold’s Cat Map, Henon Map, image encryption, chaotic systems, security validation, evaluation of encryption quality

Abstract

The security of digital image data is a crucial aspect in various fields, such as communications, medicine, and the military. The inherent characteristics of digital images—namely high pixel correlation and large data size—render conventional encryption methods less optimal. This study aims to evaluate the encryption quality of images using the Arnold’s Cat Map (ACM) and Henon Map algorithms, both individually and in combination (ACM-Henon and Henon-ACM). ACM is utilized to rearrange pixel positions to create a confusion effect, while the Henon Map is employed to randomly alter pixel values (diffusion). The implementation is carried out using the Python programming language within the Visual Studio Code development environment. Encryption quality is assessed using parameters such as Avalanche Effect (AE), Unified Average Changing Intensity (UACI), Number of Pixels Change Rate (NPCR), and correlation coefficient. Experimental results show that the combined chaos-based methods significantly enhance security compared to the individual algorithms, particularly by analyzing the impact of algorithm order on encryption quality. The best performance was achieved by the Henon→ACM combination, producing NPCR ≈ 99.44%, UACI ≈ 19.93%, entropy ≈ 7.9874, and AE ≈ 50.12%, indicating strong randomness and resistance to differential attacks.

This research demonstrates that combining confusion and diffusion mechanisms yields more secure cipher images than using either method alone. The main contribution of this study lies in providing a systematic comparative evaluation of single and combined chaos-based encryption schemes, including order-sensitive analysis across different image characteristics, rather than proposing a new encryption algorithm. However, the encryption performance is influenced by image size, parameter selection, and iteration count, which may limit consistency across different image characteristics. Future work may explore adaptive parameter optimization and improved diffusion mechanisms for higher UACI values.

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References

H. Zhang, X. Feng, J. Sun, and P. Yan, “Chaotic Image Security Techniques and Developments: A Review,” Mathematics, vol. 13, pp. 1–28, Jun. 2025, doi: 10.3390/math13121976.

M. Jiang and H. Yang, “Image Encryption Using a New Hybrid Chaotic Map and Spiral Transformation,” Entropy, vol. 25, pp. 1–18, Nov. 2023, doi: 10.3390/e25111516.

L. Li, “A novel chaotic map application in image encryption algorithm,” Expert Syst Appl, vol. 252, May 2024, doi: 10.1016/j.eswa.2024.124316.

Y. Yang, J. Gao, and H. Imani, “Design, analysis, circuit implementation, and synchronization of a new chaotic system with application to information encryption,” AIP Adv, vol. 13, Jul. 2023, doi: 10.1063/5.0161382.

P. S. Sneha, S. Sankar, and A. S. Kumar, “A chaotic colour image encryption scheme combining Walsh–Hadamard transform and Arnold–Tent maps,” J Ambient Intell Humaniz Comput, vol. 11, no. 3, pp. 1289–1308, Mar. 2020, doi: 10.1007/s12652-019-01385-0.

A. Dinu and M. Frunzete, “Image Encryption Using Chaotic Maps: Development, Application, and Analysis,” vol. 13, pp. 1–16, Aug. 2025, doi: 10.3390/math13162588.

D. E. Mfungo, X. Fu, Y. Xian, and X. Wang, “A Novel Image Encryption Scheme Using Chaotic Maps and Fuzzy Numbers for Secure Transmission of Information,” Applied Sciences (Switzerland), vol. 13, no. 12, Jun. 2023, doi: 10.3390/app13127113.

A. Arham and N. Lestari, “Secure medical image watermarking based on reversible data hiding with Arnold’s cat map,” International Journal of Advances in Intelligent Informatics, vol. 9, no. 3, pp. 445–456, Nov. 2023, doi: 10.26555/ijain.v9i3.1029.

V. Rathore and A. K. Pal, “An image encryption scheme in bit plane content using Henon map based generated edge map,” Multimed Tools Appl, vol. 80, no. 14, pp. 22275–22300, Jun. 2021, doi: 10.1007/s11042-021-10719-0.

K. V. Sudheesh, S. B. Santhosha, and K. Puttegowda, “Henon Maps based selective image encryption approach for enhanced control and security,” Journal of Integrated Science and Technology, vol. 13, no. 2, 2025, doi: 10.62110/sciencein.jist.2025.v13.1034.

A. A. P. Ratna et al., “Chaos-based image encryption using Arnold’s cat map confusion and Henon map diffusion,” Advances in Science, Technology and Engineering Systems, vol. 6, no. 1, pp. 316–326, 2021, doi: 10.25046/aj060136.

Q. K. Abed and W. A. M. Al-Jawher, “Optimized Color Image Encryption Using Arnold Transform, URUK Chaotic Map and GWO Algorithm,” Journal Port Science Research, vol. 7, no. 3, Jul. 2024, doi: 10.36371/port.2024.3.3.

A. Musthofa, D. Rosal, and I. M. Setiadi, “Layered Image Encryption Method Based on Combination of Logistic Map, Henon Map, and Sine Map to Enhance Digital Image Security,” Journal of Applied Informatics and Computing (JAIC), vol. 9, no. 4, pp. 1280–1289, Aug. 2025, doi: 10.30871/jaic.v9i4.9569.

Siti Nurul Hatikah Mohammad and Arif Mandangan, “Colour Image Encryption and Decryption using Arnold’s Cat Map and Henon Map,” International Journal of Advanced Research in Computational Thinking and Data Science, vol. 1, no. 1, pp. 41–52, Apr. 2025, doi: 10.37934/ctds.1.1.4152a.

M. Es-Sabry, N. El Akkad, M. Merras, A. Saaidi, and K. Satori, “A new color image encryption algorithm using multiple chaotic maps with the intersecting planes method,” Sci Afr, vol. 16, Jul. 2022, doi: 10.1016/j.sciaf.2022.e01217.

U. Zia et al., “Survey on image encryption techniques using chaotic maps in spatial, transform and spatiotemporal domains,” Int J Inf Secur, vol. 21, no. 4, pp. 917–935, Aug. 2022, doi: 10.1007/s10207-022-00588-5.

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,” Sci Rep, vol. 15, no. 1, Dec. 2025, doi: 10.1038/s41598-025-95995-8.

S. Kanwal, S. Inam, S. Al-Otaibi, J. Akbar, N. Siddiqui, and M. Ashiq, “An efficient image encryption algorithm using 3D-cyclic chebyshev map and elliptic curve,” Sci Rep, vol. 14, no. 1, Dec. 2024, doi: 10.1038/s41598-024-77955-w.

W. Lu, C. Jin, J. Wang, X. Liu, J. Liu, and Z. Zhai, “A novel image encryption scheme using 3D chaotic maps with Josephus permutation and dynamic diffusion,” Journal of King Saud University - Computer and Information Sciences, vol. 37, no. 8, Oct. 2025, doi: 10.1007/s44443-025-00284-z.

M. Mohammed Ibrahim and R. Venkatesan, “Image encryption using novel chaotic map and cellular automata dynamics,” RAIRO - Theoretical Informatics and Applications, vol. 59, p. 2, 2025, doi: 10.1051/ita/2025001.

K. M. Hosny, Y. M. Elnabawy, R. A. Salama, and A. M. Elshewey, “Multiple image encryption algorithm using channel randomization and multiple chaotic maps,” Sci Rep, vol. 14, no. 1, Dec. 2024, doi: 10.1038/s41598-024-79282-6.

M. A. Alkhonaini, E. Gemeay, F. M. Zeki Mahmood, M. Ayari, F. A. Alenizi, and S. Lee, “A new encryption algorithm for image data based on two-way chaotic maps and iterative cellular automata,” Sci Rep, vol. 14, no. 1, Dec. 2024, doi: 10.1038/s41598-024-64741-x.

R. Vinoth Raj, V. Vinoth Kumar, R. Murugan, and K. Yazhini, “5D chaotic map-based image encryption trade-off analysis on various stages of encryption,” EURASIP J Adv Signal Process, vol. 2025, no. 1, Dec. 2025, doi: 10.1186/s13634-025-01255-2.

S. Subathra and V. Thanikaiselvan, “Image adaptive encryption using EfficientNet B3 feature guided multi scroll chaotic map with modulo controlled pseudo parallel processing,” Sci Rep, vol. 15, no. 1, Dec. 2025, doi: 10.1038/s41598-025-27080-z.

A. Y. Darani, Y. K. Yengejeh, H. Pakmanesh, and G. Navarro, “Image encryption algorithm based on a new 3D chaotic system using cellular automata,” Chaos Solitons Fractals, vol. 179, Feb. 2024, doi: 10.1016/j.chaos.2023.114396.

M. Aliyu, O. F. Nonso, A. Abdullahi, U. Sani, and Z. L. Hassan, “Secure document and image transmission through an encrypted network system,” Dutse Journal of Pure and Applied Sciences, vol. 8, no. 3b, pp. 1–14, Oct. 2022, doi: 10.4314/dujopas.v8i3b.1.

R. Risna, Y. Amaliah, and S. Yunita, “Implementasi Kriptografi Pada Pengamanan Data Pembayaran Piutang Pelanggan Menggunakan Vigenere Cipher,” Sebatik, vol. 26, no. 2, pp. 525–534, Dec. 2022, doi: 10.46984/sebatik.v26i2.2061.

H. Fan, C. Zhang, H. Lu, M. Li, and Y. Liu, “Cryptanalysis of a new chaotic image encryption technique based on multiple discrete dynamical maps,” Entropy, vol. 23, no. 12, pp. 1–17, Dec. 2021, doi: 10.3390/e23121581.

X. Wang, S. Chen, and Y. Zhang, “A chaotic image encryption algorithm based on random dynamic mixing,” Opt Laser Technol, vol. 138, pp. 2–17, Jun. 2021, doi: 10.1016/j.optlastec.2020.106837.

T. Adi Putra, I. Ruslianto, and S. Bahri, “Penerapan Metode Arnold Cat Map dan Logistic Map untuk Pengamanan Citra Data Penduduk,” Journal of Computing Engineering, System and Science, vol. 2, pp. 470–481, Jul. 2022, doi: 10.24114/cess.v7i2.36302.

M. Gupta, S. Bhattacharjee, and B. Chatterjee, “An Enhanced Security in Medical Image Encryption Based on Multi-level Chaotic DNA Diffusion,” Journal of Image and Graphics(United Kingdom), vol. 11, no. 2, pp. 153–160, Jun. 2023, doi: 10.18178/joig.11.2.153-160.

A. Sabah, S. Hameed, and M. A. A. K., “Key Generation based on Henon map and Lorenz system,” Al-Mustansiriyah Journal of Science, vol. 31, no. 1, pp. 41–46, Mar. 2020, doi: 10.23851/mjs.v31i1.734.

S. Kanwal et al., “An Effective Color Image Encryption Based on Henon Map, Tent Chaotic Map, and Orthogonal Matrices,” Sensors, vol. 22, no. 12, Jun. 2022, doi: 10.3390/s22124359.

M. A. Islam, I. R. Hassan, and P. Ahmed, “Dynamic complexity of fifth-dimensional Henon map with Lyapunov exponent, permutation entropy, bifurcation patterns and chaos,” J Comput Appl Math, vol. 466, Oct. 2025, doi: 10.1016/j.cam.2025.116547.

Muslih and L. B. Handoko, “Pengujian Avalanche Effect Pada Kriptografi Teks Menggunakan Autokey Cipher,” 2 st Proceeding STEKOM, vol. 2, no. 1, pp. 127–134, Dec. 2022, doi: 10.51903/semnastekmu.v2i1.162.

R. Saidi, N. Cherrid, T. Bentahar, H. Mayache, and A. Bentahar, “Number of pixel change rate and unified average changing intensity for sensitivity analysis of encrypted inSAR interferogram,” Ingenierie des Systemes d’Information, vol. 25, no. 5, pp. 601–607, Nov. 2020, doi: 10.18280/ISI.250507.

S. A. Mehdi and Z. latif Ali, “Image Encryption Algorithm Based on a Novel Six-Dimensional Hyper- Chaotic System,” Al-Mustansiriyah Journal of Science, vol. 31, no. 1, pp. 54–63, Mar. 2020, doi: 10.23851/mjs.v31i1.739.

S. M. Kareem and A. M. S. Rahma, “A novel approach for the development of the Twofish algorithm based on multi-level key space,” Journal of Information Security and Applications, vol. 50, Feb. 2020, doi: 10.1016/j.jisa.2019.102410.

H. Djamel, H. Abdarrahmane, I. Haddad, B. Aïssa, N. Derouiche, and H. Kahia, “An Algorithm for Image encryption based on chaotic maps,” ICMAR, vol. 1, pp. 110–118, Aug. 2023.

S. S. Nurhaliza and L. ETP, “Sistem Pengenalan Karakter Dokumen Secara Otomatis Menggunakan Metode Optical Character Recognition,” PETIR, vol. 15, no. 1, pp. 166–175, Mar. 2022, doi: 10.33322/petir.v15i1.1610.

W. Alexan et al., “A new multiple image encryption algorithm using hyperchaotic systems, SVD, and modified RC5,” Sci Rep, vol. 15, no. 1, Dec. 2025, doi: 10.1038/s41598-025-92065-x.

A. N. Latifa, C. A. Sari, E. H. Rachmawanto, and M. K. Sarker, “Multi-Level Secure Image Cryptosystem Using Logistic Map Chaos: Entropy, Correlation, and 3D Histogram Validation,” Jurnal Masyarakat Informatika, vol. 16, no. 2, pp. 247–267, Nov. 2025, doi: 10.14710/jmasif.16.2.74537.

Z. A. N. Fauzyah, A. Nugraha, A. Luthfiarta, and M. N. E. Farandi, “An Enhanced Multi-Layered Image Encryption Scheme Using 2d Hyperchaotic Cross-System And Logistic Map With Route Transposition,” Jurnal Teknik Informatika (Jutif), vol. 6, no. 1, pp. 11–22, Feb. 2025, doi: 10.52436/1.jutif.2025.6.1.4007.