This paper introduces a novel image cryptographic method that is based on chaotic systems, new recursive cellular automata, and deoxyribonucleic acid sequences. The proposed algorithm in this paper comprises two principal stages: permutation and diffusion. In the permutation stage, the original image p undergoes conversion into a binary matrix \(p(M \times 8N)\) . This binary matrix is then divided into four parts, and a permutation scheme based on the cos wave is applied to each section. The permutation involves rotational shifts of bits in both rows and columns, utilizing chaotic sequences generated by a 2D logistic chaos system. The diffusion process consists of three primary steps. In the first step, the gray levels of the image pixels obtained from the permutation stage are substituted with the proposed new recursive cellular automata. In the second step, a model based on the bit plane modifies the gray levels of the image pixels obtained from the previous step. In the final stage, the gray levels of image pixels obtained from the second stage are altered using a key matrix and deoxyribonucleic acid sequences. Furthermore, the parameters and initial values of the 2D logistic chaos system are derived from the provided values and the SHA 256 hash of the original image. This ensures that distinct chaotic sequences are generated when encrypting different images. Experimental results and security analysis confirm that the suggested method not only achieves superior cryptographic outcomes but also exhibits resistance against various tested attacks.
