Innovative chaotic dragon fractal (ChDrFr) shapes for efficient encryption applications: a new highly secure image encryption algorithm

Abstract

In this paper, the generation of new dragon fractal shapes with chaotic iteration parameters is introduced as the main component of a new efficient approach for different cryptographic applications. This process involves applying a chaotic map, which is considered the initiator pattern, to generate different chaotic dragon fractal (ChDrFr) shapes in lieu of lines (which are classically used to generate dragon fractals). This is the new concept of this paper. The used chaotic maps are sensitive to their initial conditions and are characterized by randomness; hence, the resulting scheme is highly secure. As the resulting ChDrFr shapes have sparse structures, the spaces are packed with random values generated from another 5D hyper chaotic map. For encryption applications based on the substitution approach, one of the five generated ChFrDr shapes can be used to construct a chaotic fractal (ChFr) S-Box, while the other four ChDrFr shapes can be used for diffusion purposes. As an application to these new ChDrFr shapes and the ChFr S-Box, we introduce in this paper a new highly secure image encryption algorithm. A Henon chaotic map is used as the initiator of the ChDrFr shapes. The integer wavelet transform (IWT) is used to generate an approximation and three detail sub-bands for the original image. As the approximation sub-band contains a considerable amount of information about the original image, the above-described ChFr S-Box is used as a replacement for each pixel’s value in this sub-band. Then, the resultant substituted image is diffused with one of the generated ChFrDr shapes. The other three ChDrFr shapes are XORed with the details sub-images. Numerical simulation is applied to ensure the efficacy of encrypted images against different attacks. In particular, the correlation coefficient between the initial and the generated images is shown to be nearly zero. Moreover, tests reveal that the information entropy of the encrypted images and UACI were close to their optimum values. The properties of the newly proposed ChDrFr-based encryption algorithm are compared to the ones obtained by other encryption algorithms, and the results prove the superiority of this newly proposed algorithm to other types of encryption methods.