An Efficient Chaos-based Image Encryption Scheme Using Affine Modular Maps

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Ruisong Ye 1,* Haiying Zhao 2

1. Department of Mathematics, Shantou University, Shantou, Guangdong, 515063, P. R. China

2. College of Computer Science and Technology, Xinjiang Normal University, Urumqi, 830054, China

* Corresponding author.


Received: 19 Nov. 2011 / Revised: 8 Feb. 2012 / Accepted: 22 Apr. 2012 / Published: 8 Jul. 2012

Index Terms

Affine modular maps, Chaotic system, Image encryption, Permutation, Diffusion


Linear congruential generator has been widely applied to generate pseudo-random numbers successfully. This paper proposes a novel chaos-based image encryption scheme using affine modular maps, which are extensions of linear congruential generators, acting on the unit interval. A permutation process utilizes two affine modular maps to get two index order sequences for the shuffling of image pixel positions, while a diffusion process employs another two affine modular maps to yield two pseudo-random gray value sequences for a two-way diffusion of gray values. Experimental results are carried out with detailed analysis to demonstrate that the proposed image encryption scheme possesses large key space to frustrate brute-force attack efficiently and can resist statistical attack, differential attack, known-plaintext attack as well as chosen-plaintext attack thanks to the yielded gray value sequences in the diffusion process not only being sensitive to the control parameters and initial conditions of the considered chaotic maps, but also strongly depending on the plain-image processed.

Cite This Paper

Ruisong Ye, Haiying Zhao, "An Efficient Chaos-based Image Encryption Scheme Using Affine Modular Maps", International Journal of Computer Network and Information Security(IJCNIS), vol.4, no.7, pp.41-50, 2012. DOI:10.5815/ijcnis.2012.07.05


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