Selection of Intelligent Rules for the Evolution of Elementary Cellular Automata for Image Encryption

Abstract

The paper is devoted to the search for new approaches to the formation of key arrays for encryption of color images. Emphasis is placed on using the initial key sequence of the smallest length. In this case, the key is the initial state of an elementary cellular automaton for implementing evolution based on a given rule. The use of an evolutionary approach on cellular automata to the formation of large key arrays made it possible to achieve unpredictable image encryption based on a single rule of an elementary cellular automata. The task of the research is to search for the rules of elementary cellular automata, which, based on a small initial key bit sequence, allow one to form a reliable key array of large dimensions for encrypting the bit layers that make up the image. To solve this problem, an experiment was carried out, on the basis of which the search for the necessary rules and options for choosing the elements of each bit array was carried out to encrypt the bit layers of the image. To form each bit key array, different initial conditions were used for elementary cellular automata. It is shown that for different initial conditions and for the chosen rules, the encryption quality is preserved. The most reliable encryption is the use of two key arrays formed on the basis of the evolution of one rule for different initial conditions. As a result of the experiments, the rules were determined (rules 90, 105, 150 and XOR function based on the two previous steps of evolution), which can be used without additional rules. Each bit layer of the image is encrypted using different subarrays of each generated one key array of the same dimension. It has been established that the most effective for encryption is the rule 105 and the XOR function based on the two previous steps of evolution. The resulting histograms of the distribution of brightness for each color of the encrypted image confirm the high quality of encryption based on the proposed method.