基于量子Logistic映射的图像加密算法研究

Image Encryption Algorithm Based on Quantum Logistic Mapping

目的提出将量子Logistic混沌映射与三维Arnold混沌映射相结合的图像加密算法,以提高图像加密的复杂度。方法首先利用量子Logistic混沌映射生成置乱用的伪随机序列与明文进行整体置乱,再利用三维Arnold混沌映射生成一个整数序列,与置乱后的密文进行扩散运算。结果通过仿真实验,加密图像的相关性系数接近于0,密钥敏感性的NPCR和UACI的测试值分别约等于99.60和33.4,信息熵的测试结果约等于7.999,都非常接近于理论值。结论加密算法充分体现了量子混沌映射高复杂度的非线性力学特性。通过仿真实验测试可知,加密算法具有密钥空间大、敏感性强、安全性好的特点。

The work aims to propose an image encryption algorithm combining quantum Logistic chaotic mapping with 3 D Arnold chaotic mapping to improve the complexity of image encryption. Firstly, the quantum Logistic chaotic mapping was used to generate the pseudo random sequence for the scrambling with the plain text as a whole, and then an integer sequence was generated with the 3 D Arnold chaotic mapping. The diffusion operation was carried out with the scrambled ciphertext. Through simulation experiments, the correlation coefficient of encrypted image was close to 0, the test values of NPCR and UACI of key sensitivity were approximately equal to 99.60 and 33.4, respectively, and the test result of information entropy was approximately equal to 7.999, which were very close to the theoretical values. The encryption algorithm fully reflects the nonlinear mechanical property of high complexity of quantum chaotic mapping. Based on the simulation experiment, the encryption algorithm has such advantages as large key space, strong sensitivity and good security.