Using Algebraic Fractals in Steganography

Abstract

Steganography is a technology for hiding watermarks inside media files, which is relevant in the field of copyright protection, secret communication, etc. The effectiveness of modern methods of digital image processing allows determining the presence of embedded watermarks in a stegoimage using the original image and its statistical characteristics, as well as a priori information about the method and algorithm of embedding. In contrast to the known approaches, it is proposed to use algebraic fractals for steganographic embedding of watermarks in color images. It is proposed to use algebraic fractals in the form of medium cover image acting as a secret key, which allows the embedding to be more resistant to computer attacks, including JPEG compression. The main advantage of such use of fractals is an increase in the level of secrecy in which the attacker must know the parameters of the fractal image. Without knowledge of these parameters, it will not be enough to have the original stegoimage and a priori information about the embedding method to extract secret data. This chapter analyzes the methods and provides examples of generating algebraic fractals in the form of the Julia set using the escape time algorithm.