一种新的n维广义Arnold矩阵构造方法及其在图像置乱中的应用

A new construction method for n-dimensional generalized Arnold matrixes and its application in image scrambling

提出了基于具有输入密钥的等差数列来构造一类n维广义Arnold变换矩阵的方法,并给出了构造变换矩阵和逆变换矩阵的计算算法,算法仅与密钥有关,其时间复杂度相当于n(n+1)/2次乘法运算.在图像置乱时用该矩阵作为变换矩阵,采取图像位置空间与色彩空间的多轮乘积型双置乱,算法具有周期长和算法完全公开等特点,可有效防止多种攻击,增强了系统的安全性.此外,通过逆变换对置乱图像进行恢复,无须计算变换矩阵的周期.实验结果表明,该置乱变换算法效率高,安全性强.

Based on an arithmetic progression with an input secret key,a method is proposed to construct n-dimensional generalized Arnold transformation matrixes.Direct calculation algorithms are also presented for the transformation matrix and the inverse transformation matrix.The algorithms are only relevant to the secret key and their time complexity is equal to n（n＋1）/2 times multiplication operation.Using the n-dimensional generalized Arnold transformation matrix as a transform matrix,and adopting double product-like scrambling in the image position space and the hue space,the image scrambling method has long period and is public,and can prevent many attacks and thus greatly enhances the system’s security.Moreover,when the inverse transformation matrix is applied to restore the scrambled image,the period of the transformation matrix is not needed to calculate.Simulation experiments show that the proposed method is effective and very secure