Chinese Journal of Computers   Full Text
Title	On the Period of 2D Random Matrix Scrambling Transformation and Its Applications in Image Information Hiding
Authors	WANG Ze-Hui
Address	(Department of Scientific Computation and Computer Applications, Sun Yat-Sen University, Guangzhou 510275)
Year	2006
Issue	No.12(2218—2225)
Abstract &   Background	Abstract 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((log2N)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. keywords digital image; scrambling transformation; periodicity; polynomial time; chosen plaintext attack; security background The scrambling transformation is one of the important technologies in digital image information hiding. It is the basis in this technology to compute out the precise period T of the transformation. Many works in some literature have been done on determining the transformation periods of some special matrix or for some classes of modulus. To our knowledge, there is no the general method to determine the transformation period for any matrix of any elements, or for any modulus N period representation. Some methods have been proposed in some literatures for determining the transformation periods for a class of the scrambling transformations without giving the quick transformation period computation algorithms. A method for determining the transformation period T(A,N) for any matrix A and any modulus N is proposed in this paper. The significant contribution of this paper is the general method and the quick algorithm taking 96(log2N)2+O(log2N) multiplications modulus N for solving the problems with any periods. A new probabilistic cryptosystem which can be effectively against chosen plaintext attack is constructed. The method given is for 2-dimension images but it can be easily extended to m-dimensions with m>2. This work is supported by the a grant from the Science and Technique Program of Guangdong (No.2006B15401009).