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.

Image encryption and steganography techniques are receiving a lot of interest and investigations due to their high importance in multimedia communication systems. A novel highly efficient image encryption and steganography technique are presented in this paper. For the first time, the proposed technique uses hybrid DNA encoding and Choquet's Fuzzy Integral sequences. At first, a confused version of the image, using a simple chaotic map, is encoded using DNA's bases. Four coded images are generated using the four DNA bases, namely AT, CG, GC, and TA. Parallel to that, a Choquet's fuzzy Integral sequence is generated and DNA encoded similarly to obtain four pseudo-random sequences. Secondly, the resulting four fuzzy/DNA sequences are used to diffuse the four DNA encoded images using the complementary DNA XOR rule, according to certain control code. Finally, the wavelet fusion algorithm is then used to fuse the resulting four fuzzy-DNA encoded images, to get the encrypted image. For added security, a new steganography approach is used. In particular, the encrypted image is divided into four sub-images, each of which is hidden in a different carrier image selected from a known group of carrier images according to a given key. The simulation results and security analysis confirmed the efficiency of the proposed image encryption algorithm as well as the steganography approach used for enhanced security. Ten different images with a size of 256 × 256 are used to test the proposed method. The results show that the proposed algorithm has a higher key sensitivity. The pixel correlation coefficient values are very small (between 5.3220e-04 and 0.0011 horizontally, between 8.7670e-04 and 0.0022 vertically and between 0.0002 and 0.0045 diagonally). Furthermore, the measured information entropy of the encrypted images is between 7.9970 and 7.9979 which are very close to the ideal value of 8. Additionally, the measured unified average changing intensity and number of pixels change rate values take the values between 33.46 and 33.39 and between 99.61 and 99.64, respectively, which are again closed to the ideal values. The steganography test shows that the hidden encrypted images are almost invisible at high values of SNR and are characterized by good NCC values under different types of attacks. The performance of the new proposed algorithm is proved to overcomes many other previously published image encryption techniques.

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