基于随机分数梅林变换的光学图像加密

Optical image encryption based on random fractional Mellin transform

为了实现光学图像的非线性加密,设计了一种基于随机分数梅林变换的光学图像加密方法,构造了相应的光学加密装置。该装置采用混沌映射生成一对共轭随机相位掩模放置于分数傅里叶变换光学装置的两端,对分数傅里叶变换的核函数进行随机化处理,得到随机分数傅里叶变换。随机分数梅林变换由对数-极坐标变换和随机分数傅里叶变换组成,光学图像经随机分数梅林变换得到复值密文,从而完成图像的像素值和像素点位置的双重加密。对应所有密钥计算了输入图像和解密图像的均方误差,混沌映射的初值增大10-16时,解密图像的均方误差放大200倍以上,其作为密钥扩大了加密算法的密钥空间;随机分数梅林变换的分数阶次作为密钥也具有很高的敏感度。数值分析验证了该光学加密系统的可行性和有效性,噪声叠加和抗裁剪性能分析表明该算法具有良好的鲁棒性。

To realize nonlinear encryption of optical images, an optical encryption method based on ran- dom Fractional Mellin Transform （FrMT） was established and a corresponding encryption configura- tion was constructed. In this configuration, two mutually conjugated random phase masks generated by the chaotic map were placed on the input and output planes of an optical Fractional Fourier Trans- form （FrFT） lens, respectively. The essential role of random phase masks was used to process ran- domly the kernel function of the FrFT to obtain the random FrFT. The random FrMT was composed of a log-polar transformation and a random FrFT. An optical image was encrypted into one complex- valued ciphertext with the random FrMT, by which the dual encryption of was implemented by the se- crecy of pixel value and pixel position simultaneously. The mean square error （MSE） between the de- crypted image and the input image for all keys were calculated. It shows that the MSE of the decryp- tion image can be magnified over 200 times when the seed of the chaotic map as the key is increased 10 16, which expands the key space of the encryption algorithm. Moreover, the fractional order of the random FrMT which is taken as a key also has a high sensitivity. Numerical simulation results demon- strate the feasibility and the effectiveness of the proposed method, and the performance analysis for noise addition and occlusion of the encrypted image shows that the algorithm is robust.