A Generalized Matrix-based Scrambling Transformation and its Properties

This paper presents a generalized scrambling scheme based on matrix transformation. We deduce some important properties of the scrambling transformation including its periodicity and synchronousness based on this generalized model and the matrix algebra theory. For the widely used equi-module transformation scrambling, a few theorems about how to calculate the scrambling transformation period and the recovery transformation for the scrambled image are given. A new measure of scrambling degree based on the modified ratio of unchanged pixels is proposed. Experimental results show that these newly proposed theorems are useful in calculating the period and the recovery transformation. The calculated scrambling degree using the new measure for scrambling performance analysis is well accordant with that of inspection by human visual system.