RSA algorithm in fractional-rational n-ary forms while encryption-decryption of monochrome images

Abstract

The basis for image protection is the assumption that the image is a stochastic signal. But the image is a specific signal that possesses, in addition to typical informativeness (informativeness of data), also visual informativeness, which brings new challenges to the issue of protection. Therefore, the urgent task is to implement such application of the RSA algorithm that when encrypting an image: the cryptographic stability of the RSA algorithm did not deteriorate; achieves full image noise to prevent the use of visual image processing methods. An algorithm for encryption-decryption of monochrome images in fractional-rational forms of order n using the elements of the RSA algorithm is proposed, as the most resistant to unauthorized decryption of signals. The proposed algorithm is applied to images with strictly separated contours. Elements of the RSA algorithm are applied to construct the coefficients of fractional-rational affine transformations. The developed algorithm is inherent in the higher cryptographic stability compared to the ordinary RSA algorithm. The possibilities of using the elements of the RSA algorithm in affine transformations while encrypting and decrypting images are described. The results of encryption modeling for cryptographic transformations of monochrome images of a given dimension are given. Modified models and algorithmic procedures of key formation processes, direct and inverse cryptographic transformations, reduced to mathematical element-by-element operations, have been developed.