基于Arnold变换的图像逆置乱算法

针对Arnold变换的周期依赖于图像的阶数这一特性,提出了一种反变换算法.该算法通过分析加密图像任一点处两坐标分量间关系,得到原图像相应点的坐标,从而实现图像的解密.该反变换也可作为图像置乱的正变换,相应的反变换就是Arnold变换.在此基础上,把二维反变换算法推广到m维的情形.实验结果表明,对于已应用Arnold变换进行预处理的置乱图像,在无须计算原图像变换周期的前提下可快速实现图像的逆置乱,该过程具有确定性,其迭代次数与预处理置乱次数相等.

An image inverse-scramble algorithm based on Arnold transformation

A new algorithm of Arnold inverse transformation is proposed for the fact that the period of Arnold transformation depends on the image size.The algorithm can get the coordinates of any pixel in the original image through analyzing the relation between two coordinates of the cor- responding pixel in the encrypted image.In this way,the anti-scramble can be realized.Moreover,the inverse transformation can be an image scramble transformation and its anti-scramble transformation is Arnold transformation.On this basis,the 2-dimensional algorithm of Arnold inverse transformation is generalized to m-dimension transformation.The experimental results show that the inverse transforma- tion can quickly decrypt the scrambled image without computing the period of Arnold transformation. The process is fixed and its iterative times equal the pretreatment scrambling times.