Development of methods for generation of digital watermarks resistant to distortion

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.