Period Law of Discrete Two-Dimensional Arnold Transformation

The period of Arnold transformation is a key parameter, which affects its application effectiveness in the fields of image encryption, digital watermark, information hiding, etc. However, the previous research results on the period of discrete two-dimensional Arnold transformation are very rough estimation and lack of practical application value. By analyzing the relationship between the image order and its corresponding period of Arnold transformation, a program of collecting sample data is designed in this paper. With the theory of regression analysis, we fit a regression equation, which can be viewed as an accurate estimation of the Arnold transformation period. The experimental results demonstrate that this estimation is much better than previous research results. This research achievement is important for the applications of Arnold transformation in the fields of image encryption, digital watermarking, information hiding, etc.