基于点阵行列变换的图像置乱算法  

Image scrambing algorithm based on row and column transformation of lattice

作　　者：石玲玉 吴雁南 周铭 邹艳妮[3] SHI Lingyu;WU Yannan;ZHOU Ming;ZOU Yanni(Zhejiang Guangsha Vocational and Technical University of construction,Jinhua Zhejiang 322100,China;Nanchang Medical College,Nanchang,330004,China;School of Mathematics and Computer Sciences,Nanchang University,Nanchang,330031,China)

机构地区：[1]浙江广厦建设职业技术大学信息学院,浙江金华322100 [2]南昌医学院,江西南昌330004 [3]南昌大学数学与计算机学院,江西南昌330031

出　　处：《南昌大学学报（理科版）》2022年第6期674-681,共8页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(62262040)。

摘　　要：基于空间域的图像置乱变换,一般需要若干次迭代且有周期性,安全性不高;基于混沌的图像置乱的安全性比基于空间域的图像置乱变换高,但算法比较复杂;基于素数映射的图像置乱,其置乱效果依赖于密钥的选取。针对这些不足,设计了一种基于点阵行列变换的图像置乱算法,该算法利用素数的取模变换,采取逐行逐列的置乱方式,彻底打乱了像素点的空间位置,使得原图像的像素点在置乱图像中的排列杂乱无章。置乱图像的还原是置乱的逆过程,需要置乱时选取的密钥,若用错误的密钥还原就相当于对置乱图像的再次置乱,密钥的敏感性高。实验结果表明,该算法进行图像置乱无需迭代,置乱图像灰度分布均匀,置乱效果与密钥的选取无关,置乱图像抗干扰强,显示该算法的稳定性和鲁棒性。Image scrambling transformation based on spatial domain generally needs several iterations and is periodic, so its security is not high;The security of image scrambling based on prime number is higher than that of image scrambling based on spatial domain, but the algorithm is more complicated;Image scrambling based on prime mapping depends on key selection.Aim at these shortages, an image scrambling algorithm based on lattice row and column transformation is designed.The algorithm uses the modulo transformation of prime number to scramble the pixels row and column, which completely scrambles the spatial positions of pixels and makes the original pixels in the scrambled image arranged in a disorderly way.Restoring the scrambled image is the inverse process of scrambling and it is necessary to select the key during scrambling.If the key is not restored correctly, it is equivalent to scrambling the scrambled image again and the sensitivity of the key is high.The experiment result shows that the algorithm does not need iteration for image scrambling, the gray distribution of the scrambled image is uniform, the scrambling effect is independent of the key selection and the scrambled image is strong anti-interference, which shows the stability and robustness of the algorithm.

关 键 词：行列变换 图像置乱 密钥 素数 灰度均方差 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]