基于三维仿射变换的数字图像置乱算法

Image scrambling algorithm based on three-dimensional affine transformations

针对数字图像的特点,基于有限整数域上的二维置乱变换、仿射变换和整数提升变换,提出了适用于任意大小、任意长宽比图像的三维置乱加密算法.考虑了变换矩阵中部分参数取负整数或小数的可行性,明确给出了参数的具体设置方法.该算法引入实数作为参数,扩展了参数选择范围;置乱像素位置的同时改变像素值,改善了置乱效果,加大了置乱周期,提高了数字图像的安全性.

According to the features of digital images, a kind of three-dimensional scrambling and encryption algorithm was proposed based on two-dimensional scrambling transformations in a finite integer domain, affine transformations, and integer lifting transformations. This algorithm applies to images with any length and width or at any length-to-width ratio. The feasibility that some parameters of the transformation matrix are negative integers or decimals is taken into account, and the method of parameter setting is explicitly shown. Real number is used in the algorithm, which expands the space of parameters, scrambles the pixel positions and changes their values, makes the scrambling result better, increases the periodicity of scrambling, and improves the security of digital image transformations.