Development of methods for generation of digital watermarks resistant to distortion




digital watermarks, chaotic maps, Henon maps, Arnold’s cat map


Active attacks and natural impacts can lead to two types of image-container distortions: noise-like and geometric. There are also image processing operations, e.g. scaling, rotation, truncation, pixel permutation which are much more detrimental to digital watermarks (DWM). While ensuring resistance to removal and geometric attacks is a more or less resolved problem, the provision of resistance to local image changes and partial image deletion is still poorly understood. The methods discussed in this paper are aimed at ensuring resistance to attacks resulting in partial image loss or local changes in the image. This study's objective is to develop methods for generating a distortion-resistant digital watermark using the chaos theory. This will improve the resistance of methods of embedding the digital watermark to a particular class of attacks which in turn will allow developers of DWM embedding methods to focus on ensuring the method resistance to other types of attacks. An experimental study of proposed methods was conducted. Histograms of DWMs have shown that the proposed methods provide for the generation of DWM of a random obscure form. However, the method based on a combination of Arnold’s cat maps and Henon maps has noticeable peaks unlike the method based on shuffling the pixels and their bits only with Arnold’s cat maps. This suggests that the method based only on Arnold’s cat maps is more chaotic. This is also evidenced by the value of the coefficient of correlation between adjacent pixels close to zero (0.0109) for color DWMs and 0.030 for black and white images.

Author Biographies

Vitalii Martovytskyi, Kharkiv National University of Radio Electronics

PhD, Associate Professor

Department of Electronic Computers

Igor Ruban, Kharkiv National University of Radio Electronics

Doctor of Technical Sciences, First Vice-Rector

Nataliia Bolohova, Kharkiv National University of Radio Electronics


Department of Electronic Computers

Оleksandr Sievierinov, Kharkiv National University of Radio Electronics

PhD, Associate Professor

Department of Information Technology Security

Oleg Zhurylo, Corel Corporation

Software Developer

Oleksandr Permiakov, National Defence University of Ukraine named after Ivan Cherniakhovskyi

Doctor of Technical Sciences, Professor

Department of Communication and Automated Control Systems

Andrii Nosyk, National Теchnical University "Kharkiv Polytechnic Institute"

PhD, Senior Research

Department of Information Technology and Multimedia Systems

Dmytro Nepokrуtov, Ivan Kozhedub Kharkiv National Air Force University

Аssociate Professor

Department of Radioelectronic Systems of Control Points of Air Forces

Ivan Krylenko, Military Institute of Armored Forces of National Technical University "Kharkiv Polytechnic Institute"

PhD, Head of Department

Department of Social and Humanitarian Desciplines


Mitekin, V. A. (2015). An algorithm for generating digital watermarks robust against brute-force attacks. Computer Optics, 39 (5), 808–817. doi:

Artru, R., Roux, L., Ebrahimi, T. (2019). Digital watermarking of video streams: review of the state-of-the-art. Available at:

Delannay, D., Macq, B. (2000). Generalized 2-D cyclic patterns for secret watermark generation. Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101). doi:

Dutta, M. K., Singh, A., Soni, K. M., Burget, R., Riha, K. (2013). Watermark generation from fingerprint features for digital right management control. 2013 36th International Conference on Telecommunications and Signal Processing (TSP). doi:

Dutta, M. K., Singh, A., Burget, R., Atassi, H., Choudhary, A., Soni, K. M. (2013). Generation of biometric based unique digital watermark from iris image. 2013 36th International Conference on Telecommunications and Signal Processing (TSP). doi:

Zotin, A., Favorskaya, M. (2020). Application of bar coding for digital watermarking of video sequences based on frequency transforms. Information and Control Systems, 5, 12–23. doi:

Cho, D.-J. (2013). Study on Method of New Digital Watermark Generation Using QR-Code. 2013 Eighth International Conference on Broadband and Wireless Computing, Communication and Applications. doi:

Li, D., Deng, L., Bhooshan Gupta, B., Wang, H., Choi, C. (2019). A novel CNN based security guaranteed image watermarking generation scenario for smart city applications. Information Sciences, 479, 432–447. doi:

Mooney, A., Keating, J. G., Heffernan, D. M. (2006). A detailed study of the generation of optically detectable watermarks using the logistic map. Chaos, Solitons & Fractals, 30 (5), 1088–1097. doi:

Schöpf, H.-G. (1970). V. I. Arnold and A. Avez, Ergodic Problems of Classical Mechanics. (The Mathematical Physics Monograph Series) IX + 286 S. m. Fig. New York/Amsterdam 1968. W. A. Benjamin, Inc. Preis geb. $ 14.75, brosch. $ 6.95 . ZAMM - Zeitschrift Für Angewandte Mathematik Und Mechanik, 50 (7-9), 506–506. doi:

Peterson, G. (1997). Arnold’s cat map. Available at:

Hsu, C. S. (1987). Cell-to-cell mapping: a method of global analysis for nonlinear systems. Springer, 354. doi:

Wu, J., Liao, X., Yang, B. (2018). Image encryption using 2D Hénon-Sine map and DNA approach. Signal Processing, 153, 11–23. doi:

Ye, G., Huang, X. (2017). An efficient symmetric image encryption algorithm based on an intertwining logistic map. Neurocomputing, 251, 45–53. doi:

Akhavan, A., Samsudin, A., Akhshani, A. (2011). A symmetric image encryption scheme based on combination of nonlinear chaotic maps. Journal of the Franklin Institute, 348 (8), 1797–1813. doi:

What is Tokenization? Available at:

Makoveichuk, O., Ruban, I., Bolohova, N., Kovalenko, A., Martovytskyi, V., Filimonchuk, T. (2021). Development of a method for improving stability method of applying digital watermarks to digital images. Eastern-European Journal of Enterprise Technologies, 3 (2 (111)), 45–56. doi:

Bradley, D., Roth, G. (2007). Adaptive Thresholding using the Integral Image. Journal of Graphics Tools, 12 (2), 13–21. doi:

Makoveychuk, O. (2019). A new type of augmented reality markers. Advanced Information Systems, 3 (3), 43–48. doi:



How to Cite

Martovytskyi, V., Ruban, I., Bolohova, N., Sievierinov О., Zhurylo, O., Permiakov, O., Nosyk, A., Nepokrуtov D., & Krylenko, I. (2021). Development of methods for generation of digital watermarks resistant to distortion. Eastern-European Journal of Enterprise Technologies, 6(2 (114), 103–116.