Scrambling matrix generation algorithm for high dimensional image scrambling transformation

Conventional scrambling method based on high dimensional matrix transformation has the following deficiencies: (1) there is no generalized high dimensional scrambling matrix generation algorithm, so the prevalent scrambling methods are to use special matrices such as high dimensional Arnold transformation matrix, Fibonacci-Q transformation matrix, A-type Arnold transformation matrix, B-type Arnold transformation matrix and T-matrix, which decreases the security in fact; (2) because of the long iterative period, the cost to recover the scrambled image by obverse iteration is usually expensive especially when the corresponding inverse transformation matrix is unknown. To address these two problems, in this study, we present a new scrambling matrix generation algorithm for high dimensional scrambling transformation. The proposed algorithm has following advantages: (1) low cost to generate a random high dimensional scrambling matrix, (2) low cost to generate its corresponding integer coefficients inverse transformation matrix and (3) an enormous transformation matrix generation space to increase the security. Experiments show the proposed algorithm is validity in generating the transformation matrix and its corresponding integer coefficients matrix, low cost to recover the scrambled image and still has a wonderful one time scrambling performance.