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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 762652, 22 pages
Research Article

Chaotic Image Encryption Design Using Tompkins-Paige Algorithm

1Computer Engineering Department, Faculty of Computer and Electrical Engineering, Shahid Beheshti University, Evin, Tehran 1983963113, Iran
2Computer Engineering Department, Faculty of Engineering, University of Isfahan, Isfahan 8174673441, Iran

Received 1 February 2009; Revised 29 April 2009; Accepted 14 July 2009

Academic Editor: Elbert E. Neher Macau

Copyright © 2009 Shahram Etemadi Borujeni and Mohammad Eshghi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper, we have presented a new permutation-substitution image encryption architecture using chaotic maps and Tompkins-Paige algorithm. The proposed encryption system includes two major parts, chaotic pixels permutation and chaotic pixels substitution. A logistic map is used to generate a bit sequence, which is used to generate pseudorandom numbers in Tompkins-Paige algorithm, in 2D permutation phase. Pixel substitution phase includes two process, the tent pseudorandom image (TPRI) generator and modulo addition operation. All parts of the proposed chaotic encryption system are simulated. Uniformity of the histogram of the proposed encrypted image is justified using the chi-square test, which is less than 𝜒 2 (255, 0.05). The vertical, horizontal, and diagonal correlation coefficients, as well as their average and RMS values for the proposed encrypted image are calculated that is about 13% less than previous researches. To quantify the difference between the encrypted image and the corresponding plain-image, three measures are used. These are MAE, NPCR, and UACI, which are improved in our proposed system considerably. NPCR of our proposed system is exactly the ideal value of this criterion. The key space of our proposed method is large enough to protect the system against any Brute-force and statistical attacks.