This paper proposes two measures for the evaluation of permutation techniques used in image encryption. First, a general mathematical framework for describing the permutation phase used in image encryption is presented. Using this framework, six different permutation techniques, based on chaotic and non-chaotic generators, are described. The two new measures are, then, introduced to evaluate the effectiveness of permutation techniques. These measures are (1) Percentage of Adjacent Pixels Count (PAPC) and (2) Distance Between Adjacent Pixels (DBAP). The proposed measures are used to evaluate and compare the six permutation techniques in different scenarios. The permutation techniques are applied on several standard images and the resulting scrambled images are analyzed. Moreover, the new measures are used to compare the permutation algorithms on different matrix sizes irrespective of the actual parameters used in each algorithm. The analysis results show that the proposed measures are good indicators of the effectiveness of the permutation technique. © 2016 Elsevier Ltd. All rights reserved.
Abd-El-Hafiz S.K., Abdelhaleem S.H., Radwan A.G.
Chaos; Chess horse movement; Image encryption; Pixel permutations
Optics and Lasers in Engineering, Vol. 85, PP. 72 to 83, Doi: 10.1016/j.optlaseng.2016.04.023