光学图像加密与多参数加权类分数傅里叶变换

为了提高图像加密的安全性, 提出了一种多参数加权类分数傅里叶变换。此类多参数加权类分数傅里叶变换是C.C.Shih提出的四项加权类分数傅里叶变换的一种扩展, 除了分数阶数, 还有四个在四项加权系数之中的自由参数, 称其为向量参数。同时给出此多参数加权类分数傅里叶变换的离散形式, 并把这种算法应用到光学图像加密中。此算法在应用一次二维分数傅里叶变换可以有十个密键：一类为阶数参数; 另一类为向量参数, 因此这种加密算法在增加了安全性的同时, 加密过程的复杂度降低。数值仿真验证了此算法的有效性和可靠性。

Optical Image Encryption and Multiple Parameter Weighted Fractional Fourier Transform

In order to increase the security of the image encryption, the weighted fractional Fourier transform with dilation parameter (PWFRFT) is proposed. This PWFRFT is an extension of four-item weighted fractional Fourier transform (FRFT) defined by C.C.Shih. It owns four free parameters, which is called the vector parameter here, in the weight coefficients besides the order of the fractional Fourier transform. A novel optical image encryption algorithm is presented by the PWFRFT. The method owns ten secret keys when two-dimensional PWFRFT is operated one time: one kind is the order parameter and other kind is the vector parameter. Therefore, the new encryption method makes the security of image information better and the encryption process simpler. Digital simulations are presented to verify the validity and efficiency of the algorithm.