Image protection and organizing the associated processes is based on the assumption that an image is a stochastic signal. This results in the transition of the classic encryption methods into the image perspective. However the image is some specific signal that, in addition to the typical informativeness (informative data), also involves visual informativeness. The visual informativeness implies additional and new challenges for the issue of protection. As it involves the highly sophisticated modern image processing techniques, this informativeness enables unauthorized access. In fact, the organization of the attack on an encrypted image is possible in two ways: through the traditional hacking of encryption methods or through the methods of visual image processing (filtering methods, contour separation, etc.). Although the methods mentioned above do not fully reproduce the encrypted image, they can provide an opportunity to obtain some information from the image. In this regard, the encryption methods, when used in images, have another task - the complete noise of the encrypted image. This is required to avoid the use of visual imaging techniques. The paper describes the use of RSA algorithm elements in fractal quadratic transformations and fractal transform systems for encrypting / decrypting grayscale images. The values of pixel intensities in the matrix of such images are known to be in the range from 0 to 255. Noise functions in both methods were linear.