中文摘要：

针对二维不等长变换置乱图像效果差且纹理特征明显,难以满足高安全性图像信息保护需要的问题,提出二维不等长Arnold变换的改进方法,并将其用于像素位置置乱和像素值加密中.该方法利用经典可逆二维标准映射的构造思想将二维不等长Arnold变换进行非仿射化修改,获得一种具有非线性变换特性的保面积且具有周期的置乱变换,对任意高宽不等图像置乱加密并用其逆变换来快速恢复原图像.大量实验结果表明,文中方法是有效的,相比现有二维不等长Arnold变换能有效地改善图像置乱效果并降低图像纹理特征,对任意高宽图像的高性能置乱加密具有一定的推广价值.

英文摘要：

For existing two-dimensional non-equilateral transform with scrambling effect poor and obvious texture feature, it is difficult to satisfy high security image information protection, so an improved two-dimensional non-equilateral Arnold transform is proposed and applied in scrambling pixel positions and encrypting pixel values to protect image information security. This method firstly makes good use of the constructing thought of classical invertible discrete standard map in hyperbolic dynamical systems, and embeds the nonlinear expressions of output results of one congruence equation for classical two-dimensional non-equilateral discrete Arnold transform into input item of the other congruence equation for two-dimensional non-equilateral discrete Arnold transform. Then a new good nonlinear transform with preserving area and period characteristics is constructed on the basis of two-dimensional non-equilateral discrete Arnold transform to improve the scrambling effect and reduce the image texture features. In the end, the original image can be restored from the scrambled and encrypted image by its periodic properties or inversed transform. Some experimental results show that the proposed nonlinear transform is effective, and can quickly obtain better scrambling quality and weaker texture features than the existing discrete two-dimensional non-equilateral discrete Arnold transform, meanwhile it has more practical value than the standard non-equilateral Arnold transform in view of security.