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Image Encryption Algorithm Based on Compressive Sensing and Fractional DCT via Polynomial Interpolation

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Abstract

Based on compressive sensing and fractional discrete cosine transform (DCT) via polynomial interpolation (PI-FrDCT), an image encryption algorithm is proposed, in which the compression and encryption of an image are accomplished simultaneously. It can keep information secret more effectively with low data transmission. Three-dimensional piecewise and nonlinear chaotic maps are employed to obtain a generating sequence and the exclusive OR (XOR) matrix, which greatly enlarge the key space of the encryption system. Unlike many other fractional transforms, the output of PI-FrDCT is real, which facilitates the storage, transmission and display of the encrypted image. Due to the introduction of a plain-image-dependent disturbance factor, the initial values and system parameters of the encryption scheme are determined by cipher keys and plain-image. Thus, the proposed encryption scheme is very sensitive to the plain-image, which makes the encryption system more secure. Experimental results demonstrate the validity and the reliability of the proposed encryption algorithm.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 61662047 and 61462061).

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Authors and Affiliations

  1. School of Engineering, Jiangxi Agricultural University, Nanchang, 330045, China

    Ya-Ru Liang

  2. School of Software, Jiangxi Agricultural University, Nanchang, 330045, China

    Zhi-Yong Xiao

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  1. Ya-Ru Liang
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Correspondence to Zhi-Yong Xiao.

Additional information

Recommended by Associate Editor Zhi-Jie Xu

Ya-Ru Liang received the B. Sc. degree in automation from Heilongjiang Institute of Technology, China in 2002, the M. Sc. degree in power electronics and power drives from Shenyang University of Technology, China in 2008, and the Ph. D. degree in mechanical engineering from Nanchang University, China in 2016. Currently, she is a lecturer in Department of Electronic Information Engineering, Jiangxi Agricultural University, China.

Her research interests include image processing, image encryption and information security.

Zhi-Yong Xiao received the B. Sc. degree in electronic information engineering from Nanchang Hangkong University, China in 2001, and the M. Sc. degree in control theory and engineering from East China University of Technology, China in 2008. He is a Ph. D. degree candidate in mechanical engineering at School of Mechatronic Engineering, Nanchang University, China.

His research interests include image processing, computer vision and pattern recognition.

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Liang, YR., Xiao, ZY. Image Encryption Algorithm Based on Compressive Sensing and Fractional DCT via Polynomial Interpolation. Int. J. Autom. Comput. 17, 292–304 (2020). https://doi.org/10.1007/s11633-018-1159-2

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