Method of encrypting images based on two multidimensional chaotic systems using fuzzy logic

Abstract

The subject of the study: it is proposed to develop a method of image encryption with pixel permutation implemented using fuzzy logic and Hainaut mapping, as well as diffusion, which is implemented using the Lorenz system. Study objectives: To propose an effective way to apply the rules of fuzzy logic in relation to the values generated by the Henon mapping to implement the permutation of pixels in the image, which will provide a random permutation and increase the efficiency of the encryption method. Also, to achieve better security in the process of image encryption, the use of the diffusion process implemented using the Lorenz system. In addition, to increase the sensitivity of the encryption method to change the initial value of the component colors of the pixels will also be used in the encryption process. Investigation methods and research results: developed and presented a method of image encryption with pixel permutation implemented using fuzzy logic and Henon mapping, as well as diffusion, implemented using the Lorenz system. The initial values for the Henon mapping and the Lorenz system will be determined from the entered keyword, and the control parameters are set by the operator, while the values of the component colors of the pixels will also participate in the encryption process. In addition, before the process of rearranging the pixels in the image, the rules of fuzzy logic are implemented by Henon mapping. Also, the values of the component pixels before and after the diffusion procedure will be reduced to a single interval. Thus, as a result of image encryption, the original image changes completely, loses its content and shape, and the color intensity distribution of pixels becomes uniform. The program implementation of the proposed encryption method was also carried out and the qualitative characteristics of the proposed image encryption method were evaluated, namely: analysis of histograms of original and encrypted images, correlation of adjacent image pixels, root mean square error (MSE), peak signal-to-noise ratio (PSNR), entropy before changing the color components of the pixels. Conclusions: the implementation of the method has shown that it has a large number of encryption keys, which makes brute force (the process of their selection) resource-intensive and complex, and the implementation of the encryption process in two stages and using two different chaotic systems significantly improves the security of the encrypted image. The resulting cryptosystem is also resistant to the following attacks: approximation of chaotic orbits, correlation, analytical and statistical attacks.