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Advantages And Disadvantages Of Permutation

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Permutation plays an important role in image encryption, and is an auxiliary step for diffusion operations. Permutation using a 2D chaotic map, such as 2D Arnold Cat map, results the images to seem as a repeat pattern. This makes almost all pixels to move a similar distance in the same direction. The benefit of such permutation algorithms is its time complexity for implementation and its disadvantage is that encryption system is largely dependent on diffusion step. However, in the case of permutation based on sorting, the method is different. Generally, one or more sequence of random numbers is generated according to pseudo-random numbers. A mapping rule between two relative positions in the sequence before sorting and after sorting is achieved. Then permutation is applied to rows, columns or pixels. In this method only a small amount of numbers are required to be sorted [13]. In order to disturb the relations between pixel images using permutations of rows and columns, we need arrays so that the permutations are taken based on them. Using the 3D Arnold cat map three chaos sequences x, y, z of length M are generated according to Eq. (15) and three chaos sequences r, s, t of length N are made according to Eq. (16). (■(x_(n+1)@y_(n+1)@z_(n+1) ))=A (■(x_n@y_n@z_n )) mod M (15) …show more content…

For example, in a fully uniform image with 256 gray levels which the probability of all pixels are the same, the entropy would have its maximum value, i.e. 8, which corresponds to the most irregularities among image pixels. The entropy value close to 8 means the efficiency of the proposed method in image encryption. Table 7 shows the entropy of original Peppers image before and after encryption. Table 8 compares entropy with other encryption algorithms. The results show that the entropy value of our proposed scheme is much closer the ideal entropy

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