Hou Wenjin, Li Shouliang, He Jiapeng, Ma Yide
School of Information Science and Engineering, Lanzhou University, Lanzhou 730000, China.
Entropy (Basel). 2020 Jul 17;22(7):779. doi: 10.3390/e22070779.
Based on a logistic map and Feigenbaum map, we proposed a logistic Feigenbaum non-linear cross-coupled hyperchaotic map (LF-NCHM) model. Experimental verification showed that the system is a hyperchaotic system. Compared with the existing cross-coupled mapping, LF-NCHM demonstrated a wider hyperchaotic range, better ergodicity and richer dynamic behavior. A hyperchaotic sequence with the same number of image pixels was generated by LF-NCHM, and a novel image-encryption algorithm with permutation that is dynamically related to plaintext pixels was proposed. In the scrambling stage, the position of the first scrambled pixel was related to the sum of the plaintext pixel values, and the positions of the remaining scrambled pixels were related to the pixel values after the previous scrambling. The scrambling operation also had a certain diffusion effect. In the diffusion phase, using the same chaotic sequence as in the scrambling stage increased the usage rate of the hyperchaotic sequence and improved the calculation efficiency of the algorithm. A large number of experimental simulations and cryptanalyses were performed, and the results proved that the algorithm had outstanding security and extremely high encryption efficiency. In addition, LF-NCHM could effectively resist statistical analysis attacks, differential attacks and chosen-plaintext attacks.
基于逻辑斯谛映射和费根鲍姆映射，我们提出了一种逻辑斯谛-费根鲍姆非线性交叉耦合超混沌映射（LF-NCHM）模型。实验验证表明该系统是一个超混沌系统。与现有的交叉耦合映射相比，LF-NCHM展现出更宽的超混沌范围、更好的遍历性和更丰富的动态行为。通过LF-NCHM生成了与图像像素数量相同的超混沌序列，并提出了一种新颖的具有与明文像素动态相关的置换的图像加密算法。在置乱阶段，第一个置乱像素的位置与明文像素值之和相关，其余置乱像素的位置与前一次置乱后的像素值相关。置乱操作也具有一定的扩散效果。在扩散阶段，使用与置乱阶段相同的混沌序列提高了超混沌序列的利用率并提升了算法的计算效率。进行了大量的实验模拟和密码分析，结果证明该算法具有出色的安全性和极高的加密效率。此外，LF-NCHM能够有效抵御统计分析攻击、差分攻击和选择明文攻击。
