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

Abstract

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.

Review of Image Security approaches: Concepts, Issues, Challenges and Applications

“…Firstly, a fractional-order simplest memristive chaotic circuit system is designed and analyzed to determine the parameters and pseudo-random sequences used in the encryption scheme. Secondly, an encryption scheme based on compressive sensing is designed to compress the image twice to fully reduce the storage cost, and scrambles the pixel matrix twice through block scrambling and zigzag transformation, and then uses chaotic pseudo-random sequence and GF (17) domain diffusion image matrix to obtain the final cipher image.…”

“…A method based on a new designed S-Box based DNA-like techniques and CFI; and combined with hyper-chaotic maps, is suggested in [17] article. In this method, some considerations were taken to ensure resistance against attacks.…”

“…• NPCR [1,[4][5][6][7][8][9][10][11][12][13][14][15][17][18][19]: For better decryption algorithm NPCR value should be low. • UACI [1,[4][5][6][7][8][9][10][11][12][13][14][15][17][18][19]: For good decrypted image quality UACI value should be low. • PSNR [5,6,10,13,14,17,18]: The larger the PSNR value, the more similar the decrypted image is to the original image.…”

“…4. Correlation Coefficients [1,[4][5][6][7][8][9][10][11][12][13][14][15][17][18][19]: For a plain image, each pixel is highly correlated with its neighbor and adjacent pixels either in horizontal, vertical or diagonal direction. However, an efficient image cryptosystem should produce the cipher image with sufficiently low correlation (close to zero) in the adjacent pixels.…”

“…8. Encryption Efficiency: Peak signal to noise ratio (PSNR) [5,6,10,13,14,17,18] is used to measure the difference between the original image and the encrypted image. Also, the PSNR is usually used to assess the performance of image reconstruction.…”