基于小波变换的混沌图像加密算法

Chaotic Image Encryption Algorithm Based on Wavelet Transform

为了解决传统混沌系统加密图像效果不佳,安全性不高以及运行速度较慢的问题,提出了一种将小波变换与改进的二维Logistic混沌映射相结合的图像加密算法。首先利用小波变换算法简单、运算速率高等特点,将图像通过小波变换进行分解,接着对小波变换产生的低频子带系数矩阵和高频系数矩阵进行置乱处理。然后对置乱后的矩阵进行小波逆变换,使用改进的二维Logistic映射产生混沌系列对逆变换后的加密图像进行扩散处理,实现二次加密产生最终的密文图像。最后对密文进行安全性分析,仿真结果表明,上述算法使用两种置乱方式可以更好地加密置乱明文,同时使用改进的二维Logistic映射和小波变换结合的加密方式使密文敏感度高,能够有效抵御统计分析攻击、穷举攻击和差分攻击。

In order to solve the problems of poor image encryption effect,low security and slow running speed of traditional chaotic systems,an image encryption algorithm combining wavelet transform and improved two-dimensional Logistic chaotic map is proposed in this paper.Firstly,using the simplicity and high operation speed of the wavelet transform algorithm,d,the image was decomposed by wavelet transform,and then the low-frequency subband coefficient matrix and high-frequency coefficient matrix generated by wavelet transform were scrambled.Secondly,the scrambled matrix was transformed by inverse wavelet transform,and the improved two-dimensional logistic map was used to generate chaotic series.The encrypted image after inverse transform was diffused to realize secondary encryption to generate the final ciphertext image.Finally,the security of the ciphertext was analyzed.The simulation results show that the algorithm can better encrypt the scrambled plaintext by using two scrambling methods.At the same time,the encryption method combining improved logistic mapping and wavelet transform makes the ciphertext highly sensitive and can effectively resist statistical analysis attacks,exhaustive attacks and differential attacks.