Image Steganography Technique Using Algebraic Fractals

We consider a solution to the problem of copyright protection by embedding a secret message into a still color or grayscale image using algebraic fractals. The peculiarity of the proposed steganographic method is the use of a two-dimensional fractal image of algebraic type as an intermediate cover image. For this purpose, it is proposed to use a fractal image of algebraic type in the form of a Julia set as an intermediate cover image. An attacker will not be able to generate an identical fractal image without the exact value of some complex number , which is agreed in advance between the sender and the recipient, as well as a number of other parameters, which makes the proposed method resistant to attacks. The advantage of the proposed algorithm is the ability to extract the watermark without knowledge of the original cover image, since the intermediate container for the watermark is a fractal. In this paper we consider fractal image generation techniques. Then generated fractals are used as cover image in steganography system. Watermark embeds in blue component of JPEG image. To assess the quality of obtained results, a quality assessment was made based on the following metrics: normalized mean square error (NMSE) and peak signal-to-noise ratio (PSNR), expressed in decibels. The results of the original cover image and stego image, as well as the original and extracted watermark, are presented. Analysis of the results of the evaluation of the quality of the original cover image and watermarked image, as well as the original and extracted watermark showed that the proposed algorithm provides high quality of hiding confidential information. The use of fractals as an intermediate cover image for the extraction of watermark allows ensuring the extraction practically without losses, while the stego image visually does not differ from the container containing classified information.