A Watermarking Technique with Chaotic Fractional S-Box Transformation

In this paper, the system of non-linear ordinary differential equations which defines a continuous-time dynamical system that shows the fractal characteristics of attractor is used to construct chaotic S-box. In this new digital watermarking technique the priority is of importance of robustness along with chaos to create confusion. The inclusion of chaos along with watermarking in frequency domain ensures robustness. As we have proposed a frequency domain watermarking as which we embed watermark into the low or middle frequencies, these changes will be spread all over the image. The strength of fractional S-box is evaluated with the help of bit independence criterion, nonlinearity analysis, strict avalanche criterion, linear approximation probability and differential approximation probability. Additionally, some security analyses in the form of correlation, contrast, energy, entropy, homogeneity, mean square error and peak signal to noise ratio are performed for validity of proposed watermarking scheme. The confidence measure after these analyses indicates the survival aligned with malicious attacks like noise, cropping and compression.