THE USE OF FRACTAL CONVERTINGS AND THEIR SYSTEMS IN THE ENCRYPTION – DECRYPHATION OF MONOCHROME IMAGES
A. M. Kovalchuk · Ukrainian Journal of Information Technology · 2024
Fractals occupy a rather important and defining place in computer graphics. This is the construction of landscapes, trees, plants, even animals and the generation of fractal textures, as well as fractal image compression. Modern physics and mechanics are just beginning to study the behavior of fractal objects. And of course, fractals are used directly in mathematics itself, as well as in cryptography when protecting images. The article describes the use of elements of the RSA algorithm in fractal quadratic transformations and systems of fractal transformations for encryption / decryption of monochrome images. Images are one of the most used types of information. Because of this, protecting images from unauthorized use and access is an urgent task. The main condition for creating image protection is the assumption that the image is a stochastic signal. This allows us to transfer classical signal encryption methods to the case of images. But the image is such a signal that, in addition to the typical informativeness of data, also has visual informativeness, which brings new challenges to the protection problems. In fact, creating an attack on an encrypted image is possible in two cases: through traditional hacking of encryption methods, or through methods of visual image processing (methods of extracting contours, filtering, etc.). The latter do not provide a complete reproduction of the input image, but provide an opportunity to obtain some information from the image. In this regard, another requirement is put forward to encryption methods in the case of their use in relation to images – complete noise of the encrypted image. This is necessary in order to prevent the use of visual image processing methods. Therefore, the urgent task is to develop such a use of the RSA algorithm in order to: preserve the resistance to decryption and ensure full noise of the image in order to make it impossible to use the methods of further visual image processing. One of the ways to solve this problem is to use elements of the RSA algorithm in fractal algorithmic transformations and their systems. One of the ways to solve this problem is to use elements of the RSA algorithm in mathematical transformations, in particular, in fractal algorithmic transformations. Fractal transformations can be both linear and quadratic. And also systems of such fractal transformations. Encryption – decryption can be performed both with additional noise and without additional noise.