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 $10^{135}$, 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.

提出了一种基于DNA（脱氧核糖核酸）计算和混沌的双色图像加密方法。与传统算法不同的是，双色图像同时加密，可以保存彼此的信息，使加密更加安全可靠。此外，提出了一种新的混沌分数阶 (FO) 离散改进 Henon 映射 (FODIHM) 作为伪随机数生成器。为保证加密算法对明文的敏感性，FODIHM 的初始值是根据彩色图像的哈希值（SHA-256）和用户输入的三个附加密钥计算得出的。此外，魔方变换会打乱两个图像的每个颜色分量中的像素。然后，两幅图像的每个颜色分量中的每个像素通过不同的 DNA 编码规则进行扩散。最后，基于 FO 离散 Logistic 图和经典 XOR 的 CAT 变换被用于进一步提高安全性能。所提出算法的密钥空间大小是有序的$10^{135}$，这比文献中可用的高约 30 个数量级。信息熵分别为 7.9974 和 7.9973，非常接近理想的熵值 8。统一平均变化强度 (NPCI) 的值为 99.630 和 99.623，而像素数变化率 (UACR) 的值分别为 33.473 和 33.553 ，这也分别接近理想的 NPCR 和 UACR 值 99.6094 和 33.4635。数值结果和安全性分析证明该算法对几种经典攻击具有良好的抵抗能力。