A new measure of image scrambling degree based on statistical hypothesis testing

Digital image scrambling is an effective tool in preprocessing and post-pressing of data hiding, digital watermarking and image encryption. In order to evaluate the image scrambling performance, different scrambling methods have been proposed by different authors based on different assumptions. In this paper, a new measure of image scrambling degree based on the method of Chi square good of fitness hypothesis testing is proposed. Using the Chi square estimator and its P-value, we can evaluate the image scrambling degree by testing the randomness of any specific region. Scrambling degrees constructed using the method of hypothesis testing have solid theoretical foundation and are more rational than some constructive way. Experiments on the images scrambled by the Arnold transformation and the sub-affine transformation show that the new scrambling degree (Chi square or its P-value) has good consistency with the inspection result of human visual system.