A novel image encryption algorithm based on hyperchaotic system with cross-feedback structure and diffusive DNA coding operations

Chaotic systems, characterized by complex nonlinear dynamical behaviors, are suitable for generating abundant key streams for digital image encryption. Nevertheless, some encryption systems suffer from weak key space and inadequate key randomness due to a narrow chaotic parameter range and small Lyapunov exponents. Additionally, we must address the crucial issue of keys lacking or weakly relating to plaintext, as this can hinder the algorithm’s ability to effectively defend against differential attacks. This paper proposes a hybrid one-dimensional and two-dimensional cross-feedback hyperchaotic system framework to enhance key security. We combine the system with a diffusive DNA coding operation to enhance the statistical relationship between plaintext and ciphertext. Firstly, our method associates the current pixel of plaintext images with hyperchaotic sequences to determine the DNA encoding rule for the next pixel. Secondly, we transform ordinary images into DNA matrices through DNA-coding operations with diffusivity. Thirdly, we rearrange the hyperchaotic sequence to change the position of the corresponding DNA matrix elements during scrambled diffusion. Finally, we XOR it with the DNA-encoded hyperchaotic sequence to generate the ciphertext image. The experimental results demonstrate that the performance of our proposed algorithm has significantly improved in terms of information entropy, correlation, histogram, and other analytical parameters. Additionally, the algorithm exhibits a notably robust resistance to differential attacks.