物理学报Issue(9)：1-20,20.DOI:10.7498/aps.63.090504
离散Arnold变换改进及其在图像置乱加密中的应用
An improved discrete arnold transform and its application in image scrambling and encryption
摘要
Abstract
To improve the image scrambling and encryption effect in traditional two-dimensional discrete Arnold transform, a new nonlinear transform for image scrambling is proposed which improves the classical discrete Arnold transform with quasi-affine properties, and can be applied in image scrambling and encryption researching. This method first makes good use of the construction thought in classical discrete standard map, and embeds the nonlinear expressions of output results of one congruence equation for classical two-dimensional discrete Arnold transform into the input item of the other congruence equation for two-dimensional discrete Arnold transform. Then a new transform with good nonlinear characteristics is constructed on the basis of classical two-dimensional discrete Arnold transform in order to quickly improve the scrambling effect of the gray image. In the end, through mathematical proof it is shown that the proposed transform no longer has the quasi-affine invariance properties in the existing two-dimensional discrete Arnold transform, but it is still a reversible mapping with periodic properties; and when it is applied in image scrambling encryption, the original image can be restored from the scrambling and encryption in gray image for its periodic properties or inverse transform. Some experimental results show that the proposed nonlinear transform is effective, and can obtain better scrambling and encryption quality than the existing discrete two-dimensional Arnold transform, meanwhile it is more practical than the standard Arnold transform in view of security.关键词
图像置乱/Arnold变换/可逆映射/置乱效果Key words
image scrambling/Arnold transform/invertible map/scrambling effect引用本文复制引用
吴成茂..离散Arnold变换改进及其在图像置乱加密中的应用[J].物理学报,2014,(9):1-20,20.基金项目
国家自然科学基金(批准号:90607008,61073106)和陕西省教育厅科研计划专项(批准号:2013JK1129)资助的课题 （批准号:90607008,61073106）
