Shi Guanwen, Yu Simin, Wang Qianxue
College of Automation, Guangdong University of Technology, Guangzhou 510006, China.
Entropy (Basel). 2022 Jul 25;24(8):1023. doi: 10.3390/e24081023.
This paper analyzes the security of the image encryption algorithm based on a two-dimensional (2D) infinite collapse map. The encryption algorithm adopts a permutation-diffusion structure and can perform two or more rounds to achieve a higher level of security. By cryptanalysis, it is found that the original diffusion process can be split into a permutation-diffusion structure, which comes after the original permutation, so these two permutations can be merged into one. Then, some theorems about round-down operation are summarized, and the encryption and decryption equations in the diffusion process are deduced and simplified accordingly. Since the chaotic sequences used in encryption algorithm are independent of the plaintext and ciphertext, there are equivalent keys. The original encryption algorithm with single-round, two-round, and multi-round of permutation-diffusion processes is cracked, and the data complexity of the cryptanalysis attacks is analyzed. Numerical simulation is carried out by MATLAB, and the experimental results and theoretical analysis show the effectiveness of the cryptanalysis attacks. Finally, some suggestions for improvement are given to overcome the shortcomings of the original encryption algorithm.
本文分析了基于二维（2D）无限坍缩映射的图像加密算法的安全性。该加密算法采用置换-扩散结构，可进行两轮或更多轮以实现更高的安全级别。通过密码分析发现，原扩散过程可分解为置换-扩散结构，该结构在原置换之后，因此这两个置换可合并为一个。然后，总结了一些关于向下取整运算的定理，并据此推导和简化了扩散过程中的加密和解密方程。由于加密算法中使用的混沌序列与明文和密文无关，存在等效密钥。破解了具有单轮、两轮和多轮置换-扩散过程的原加密算法，并分析了密码分析攻击的数据复杂度。利用MATLAB进行了数值模拟，实验结果和理论分析表明了密码分析攻击的有效性。最后，针对原加密算法的不足提出了一些改进建议。
