Double color image encryption based on fractional order discrete improved Henon map and Rubik’s cube transform

Abstract

A double color image encryption method based on DNA (deoxyribonucleic acid) computation and chaos is proposed. Differently from the conventional algorithms, double color images are encrypted at the same time so that we can save information of each other, which makes the encryption more safe and reliable. In addition, a new chaotic fractional order (FO) discrete improved Henon map (FODIHM) is proposed as a pseudo-random number generator. To ensure the plain-image sensitivity of the encryption algorithm, the initial value of FODIHM is calculated from the hash value of the color image (SHA-256) and from the three additional keys entered by the user. Furthermore, a Rubik’s cube transform scrambles the pixels in each color component of the two images. Then, each pixel in each color component of the two images is diffused by means of different DNA coding rules. Finally, the CAT transform, based on FO discrete Logistic map and the classic XOR, is used to further improve the security performance. The key space size of the proposed algorithm is of order 10135, which is about 30 orders of magnitude higher than those available in the literature. The information entropies are 7.9974 and 7.9973, which are very close to the ideal entropy value of 8. The values of the unified average changing intensity (NPCI) are 99.630 and 99.623, while the number of pixels change rate (UACR) are 33.473 and 33.553, which are also close to the ideal NPCR and UACR value of 99.6094 and 33.4635, respectively. The numerical results and security analysis prove that the algorithm has good resistance to several classic attacks.