A chaotic image encryption algorithm based on a counting system and the semi-tensor product
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A chaotic image encryption algorithm based on a counting system and the semi-tensor product Xingyuan Wang 1 & Suo Gao 1 Received: 13 November 2019 / Revised: 25 August 2020 / Accepted: 19 October 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Based on the n-ary counting system, combined with the matrix semi-tensor product theory and Hilbert curve, a chaotic image encryption algorithm is designed. Different from the traditional encryption method, the algorithm proposed in this paper is an encryption algorithm with scrambling and diffusion at the same time. First, the pixel value is converted from decimal to n-ary. In the n-ary counting system, the plaintext image is randomly divided into some groups, and the Hilbert curve is used for scrambling to each group. The blocks are converted into scrambled images, so that the scrambling and diffusion can be carried out at the same time. Then, in order to improve the security of the algorithm, another round of diffusion is carried out based on matrix semi-tensor product mechanism. Chaotic sequence is generated by Chen system. This chaotic sequence performs matrix semi-tensor product operation with the first round of encrypted image, and generate second encrypted images. Finally, this encryption method is applied to color image encryption. Compared with some representative algorithms, the experimental results show that the algorithm proposed in this paper is secure and it can resist common attacks. Keywords Matrix semi-tensor product . n-ary counting system . Chaotic image encryption . Hilbert fractal curve
1 Introduction In 1963, Professor Lorentz published a paper which is “Deterministic nonperiodic flow” [21]. Thus, the prelude to chaos is opened. With more and more low-dimensional chaotic systems, high-dimensional chaotic systems, spatiotemporal chaotic systems and other systems, combined with chaos theory, the field of image encryption has been widely investigated [13, 33, 34, 39], and a lot of achievements have been made [2, 28, 30, 40].
* Suo Gao [email protected]
1
School of Information Science and Technology, Dalian Maritime University, Dalian, China
Multimedia Tools and Applications
Chaotic image encryption is divided into two categories according to the minimum unit of encryption. In one category, the pixel level is considered to be the smallest unit of image encryption [37, 38], and the other is that the bit level is the smallest unit of image encryption [18, 44]. In this paper, an encryption algorithm is designed which is different from the above. This paper presents a third type of encryption, the minimum unit of encryption is between pixel level and bit level. The n-ary counting system is used to encrypt the plaintext image. Because traditional encryption methods are considered unsafe (scrambling and diffusion are not happened at the same time) [15, 36], so in this paper scrambling and diffusion happen at the same time. The hilbert curve is used in the first round of encryption. Because the Hilbert can traverse the w
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