Image Encryption Based on Development of Hénon Chaotic Maps using Fractional Fourier Transform

Image Encryption Based on Development of Hénon Chaotic Maps using Fractional Fourier Transform

Mona F. M. Mursi (Department of Electrical Engineering, Benha University, Qalyubia, Egypt), Hossam Eldin H. Ahmed (Department of Electronics and Communication, Menufiya University, Menufiya, Egypt), Fathi E. Abd El-Samie (Department of Electronics and Communication Engineering, Menufiya University, Menufia, Egypt) and Ayman H. Abd El-Aziem (Department of Electrical Engineering, Shubra Faculty of Engineering, Benha University, Qalyubia, Egypt)
DOI: 10.4018/ijsita.2014070105

Abstract

In this paper, the authors propose an image encryption scheme based on the development of a Hénon chaotic map using fractional Fourier transform (FRFT) which is introduced to satisfy the necessity of high secure image. This proposed algorithm combines the main advantages of confusion and diffusion with (FRFT), it use Arnold Cat map for confusion and Hénon chaotic map or one of the proposed Hénon chaotic maps for diffusion. The proposed algorithm is compared with some image encryption algorithms based on Arnold Cat map, Baker chaotic map, Hénon chaotic map and RC6. The authors perform a comparison between them in several experimental tests as statistical analyses, processing time and security analysis. The authors find from these comparison tests that the proposed algorithm demonstrates good result even better than RC6 and other chaotic maps in some cases.
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2. Two Dimensional Chaotic Maps

We introduce some different chaotic maps and analyze the resulting simulation by using MATLAB (R 2013b), with processor Core2 Duo (2.16 GHz) and 2 GB RAM on Windows 8.

2.1. Arnold Cat Map

The Arnold cat map is one of the most important 2-D chaotic map (Shang, Ren, & Zhang, 2008; Liehuang, Wenzhuo, Lejian, & Hong, 2006). It is used in image encryption to shuffle the pixel positions of the plain image. Without any losses in generality, we assume the dimension of the original image to be N N. The Arnold Cat map can be described as follows:

(1) where p and q are positive integers, Determinant (A) = 1. When Arnold Cat map is performed once the position of the pixel will be in the new position , after applying Arnold Cat map with number of iteration iterating R, it satisfied that it reaches to its original case this depend on the number of iteration R to and parameters p, q and the size N of the original image. So that we use parameters p, q, and the number of iterations R as the secret keys in the proposed scheme, since the 2-D Arnold Cat map performs a linear transformation, and using mod function, it shuffles the pixel positions with good result in the correlation coefficient among the adjacent pixels.

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