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A chaotic image encryption algorithm based on a counting system and the semi-tensor product

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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.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (No. 61672124), the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund (No. MMJJ20170203), a Project of the Liaoning Province Science and Technology Innovation Leading Talents Program (No. XLYC1802013), the Key R&D Projects of Liaoning Province (No. 2019JH2/10300057), and the Jinan City ‘20 Universities’ Funding Projects Introducing Innovation Team Program (No. 2019GXRC031), “Double First-rate” Construction Project (“Innovation Project”) (No. SSCXXM012).

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  1. School of Information Science and Technology, Dalian Maritime University, Dalian, China

    Wang Xingyuan & Gao Suo

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  1. Wang Xingyuan
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  2. Gao Suo
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Correspondence to Gao Suo.

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Wang, X., Gao, S. A chaotic image encryption algorithm based on a counting system and the semi-tensor product. Multimed Tools Appl 80, 10301–10322 (2021). https://doi.org/10.1007/s11042-020-10101-6

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  • DOI: https://doi.org/10.1007/s11042-020-10101-6

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