New DNA Coded Fuzzy Based (DNAFZ) S-Boxes: Application to Robust Image Encryption Using Hyper Chaotic Maps

This article proposes a novel approach of improvising the cryptographic features of substitution-boxes (S-Box) based on the Choquet Fuzzy Integral (CFI) and DNA techniques. First, we propose a strong structure for the construction of four S-Boxes using CFI. The key for generating the CFI based (FZ) S-Boxes consists of two parts, namely, an external secret key and a secret image. Each of these FZ S-boxes is then encoded using DNA techniques, with dynamic rules selection which is dictated by a secret control code. The resultant four S-boxes are designated as DNAFZ S-Boxes. To apply for image encryption, the plain image is, at first 8-bit binary-coded, shuffled by an M-sequence, and down-sampled into four sub-images. Subsequently, the pixel values of each sub-image are replaced with the corresponding values of one of the four DNAFZ S-Boxes. Next, each DNAFZ encoded sub-image is diffused with a different DNA encoded chaotic sequence from Chen's hyper-chaotic map. Finally, the four DNAFZ/Chaotic encoded sub-images are combined to build the final encrypted image. The proposed DNAFZ S-boxes shows excellent statistical properties under majority logic criterions such as correlation, homogeneity, energy, entropy, and contrast. Moreover, numerical simulation is used to examine the efficacy of encrypted images against different attacks. In particular, the values of the pixel correlation coefficient are found to be quite small either horizontally, vertically, or diagonally (between 7.8597e-04 and 0.00527, between 8.7856e-04 and 0.00452, and between 0.00241 and 0.00021, respectively). In addition, the information entropy of the encrypted image is found to be within the range of (7.9965:7.9989) which is very near to the ideal value of 8. As for the UACI and the NPCR, they are in the ranges between 33.46 and 33.32 and between 99.58 and 99.62, respectively. These values are also very close to the optimum ones. The results are compared to those of other encryption algorithms and proved that the proposed encryption method delivers better results than other conventional ones including LSS chaotic map, Arnold transforms, Dynamic Henon map, Hybrid chaotic map optimized substitution, and cubic S-Box.