二维Arnold变换及非等长图像置乱变换

2-D Arnold transformation and non-equilateral image scrambling transformation

二维Arnold变换因对于等长数字图像都存在变换周期,而常常应用于等长数字图像加密过程中的置乱变换过程。但对于非等长数字图像其变换周期一般不存在而不应用于图像加密过程。给出并证明了采用二维Arnold变换对数字图像进行置乱变换时,使变换周期存在图像高和宽需满足的充分必要条件,找到并证明了一个对任意高宽的数字图像都存在置乱变换周期的变换矩阵。该变换矩阵可广泛应用于对任意尺寸数字图像的置乱变换过程。

2-dimention Arnold transformation is always used in the scrambling transformation process of the encryption process for equilateral digital images because the transformation periods exist at all time. But for non-equilateral digital images it is not used in the encryption process because the transformation periods don＇t commonly exist. The sufficient and necessary condition of image height and width that makes the period exist when scrambling digital images with 2-dimention Arnold transformation is proposed and proved. And a transformation matrix which makes scrambling transformation period exist for digital images with any height and width is found and proved. This transformation matrix is widely applied to scrambling transformation for digital images with any size.