Using Boltzmann Entropy to Measure Scrambling Degree of Grayscale Images

Image data security is a key issue in storage, transmission. Some scrambling techniques have been developed to encrypt digital images. However, how to quantitatively measure the scrambling degree of images scrambled by various techniques is an issue. To address such an issue, this study proposes an evaluation scheme of scrambling degree from the perspective of thermodynamics. The whole image is considered an isolated thermodynamics system where pixels are employed to simulate gas molecules. Specifically, Boltzmann entropy (thermodynamics entropy) is employed to measure the scrambling degree of scrambled images. The proposed scheme involves two levels (i.e., the plain image, bit planes). Four images with different complexities are used in simulation experiments. The experimental results show that this proposed scheme is simple and effective in measuring the scrambling degree of grayscale images. This study indicates that Boltzmann entropy can be used to optimize the encryption of images.