二维随机矩阵置乱变换的周期及在图像信息隐藏中的应用

给出了二维随机整数矩阵A决定的置乱变换在任意模N下周期T（A，N）的精确表达式及上界估计．提出了高效算法，只需O（（log2N）^2）次模N乘法便可得到T（A，N），算法可应用于图像信息隐藏．采取位置空间与色彩空间的多轮乘积型置乱变换，可达到高维矩阵置乱的效果．利用A的随机性、长周期和概率密钥，建立一个概率密码体制，可有效防止选择明文攻击，增强信息隐藏的安全性．

On the Period of 2D Random Matrix Scrambling Transformation and Its Applications in Image Information Hiding

This paper provides an precise expression for the period T(A,N) under a 2-D random integer matrix scrambling transformation modulus N for any N, and provides the estimation of the upper bound of the period T(A,N). A high efficient algorithm is also presented, which only takes O((log_ 2 N)~ 2 ) times multiplications modulus N for determining the period T(A,N). This algorithm can be used in image information hiding. By means of the position space and color space, the 2-D integer matrix multiplicative scrambling transformation can attain the effect as the same as the higher dimensions matrix scrambling transformation. By randomness of the integer matrix A, its longer period and the probabilistic key, a new probabilistic cryptosystem is constructed, and it can be effectively against chosen plaintext attack and strengthen the security of information hiding.