不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。

New encrypted transform method for digital image based on dissymmetrical discrete fractional Fourier transform

By using the two parameters of dissymmetrical discrete fractional Fourier transform as secret keys, a new encrypted transform method of digital image was presented. The fractional Fourier transform of the input image was performed by two one_dimensional FRT with different orders in the x and y directions in cascade. The two orders are considered to keys, only when the transform order in each direction is respectively matched with that of the asymmetry fractional Fourier transform, the encoded image can be reconstructed exactly. Because of its particularity of image reconstruction, it is regarded as a new optical security system and can be used in anti_counterfeiting. The digital computation experiment validated the correctness and feasibility of the method.