A compact image encryption system based on Arnold transformation
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A compact image encryption system based on Arnold transformation Jingjing Wu1 · Zhengjun Liu2 · Jicheng Wang1 · Lifa Hu1 · Shutian Liu2 Received: 10 October 2019 / Revised: 23 August 2020 / Accepted: 28 August 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A novel compact image encryption system is proposed based on Arnold transformation (AT). In general, AT is a pixel-scramble tool in image encryption, but its security is not high enough as an independent cryptosystem because of its periodicity. Hence, extra diffusion operations are needed to diffuse the pixel values to acquire the higher security. Here an encryption algorithm is proposed by AT. Firstly, the corresponding coordinates of each pixel in original image are calculated by AT. Secondly, the pixel values of the two corresponding coordinates are disturbed by another AT. These two processes can diffuse the pixel values of the original image. At last, the diffused image is pixel scrambled by AT with different parameters. This is the confusion process. In proposed scheme, the diffusing and confusing operations are both realized by AT. At the same time, the image is encrypted as a pixel distribution instead of a data stream. The key space, key sensitivity, the correlation, the cost time and the security of proposed cryptosystem are analyzed and the results confirm that the proposed image encryption algorithm demonstrates extraordinary performance. Keywords Image encryption · Arnold transformation · Data security · Image processing
1 Introduction With the development of computer and internet, the information exchanging processes are becoming faster and more convenient. In the process of sharing and transmitting information, data security is an important issue that must be considered. Digital image encryption technique has been developed rapidly as an effective scheme to provide the security of information. Recently, different kinds of digital image encryption algorithms based on chaotic map [11, 16, 17] wave perturbations [20], magic cube [9] et al. have been studied. Chaotic maps are very suitable tools and has wide applications in digital image encryption area because of their special properties, such as the sensitivity of the initial condition, non-periodicity and ergodicity. Jingjing Wu
[email protected] 1
School of Science, Jiangnan University, Wuxi, China
2
Department of Physics, Harbin Institute of Technology, Harbin, China
Multimedia Tools and Applications
Arnold transformation (AT) is a chaos system which used widely in the area of image encryption [3, 4, 6, 19]. As a popular pixel-scramble tool, two-dimension AT [6] of a N × N pixels image is defined as s x 1 a x + 1 = mod(N ), y s2 y b ab + 1 (x, y, x , y = 0, 1, · · · , N − 1),
(1)
in which N is the size of the 2D original image, a and b are positive integers, s1 and s2 are the displacement values used to change the corresponding coordinate of (0,0). (x, y) and (x , y ) are the coordinates of the image pixel before and af
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