Meaningful image encryption algorithm based on compressive sensing and integer wavelet transform

Abstract

A new meaningful image encryption algorithm based on compressive sensing (CS) and integer wavelet transformation (IWT) is proposed in this study. First of all, the initial values of chaotic system are encrypted by RSA algorithm, and then they are open as public keys. To make the chaotic sequence more random, a mathematical model is constructed to improve the random performance. Then, the plain image is compressed and encrypted to obtain the secret image. Secondly, the secret image is inserted with numbers zero to extend its size same to the plain image. After applying IWT to the carrier image and discrete wavelet transformation (DWT) to the inserted image, the secret image is embedded into the carrier image. Finally, a meaningful carrier image embedded with secret plain image can be obtained by inverse IWT. Here, the measurement matrix is built by both chaotic system and Hadamard matrix, which not only retains the characteristics of Hadamard matrix, but also has the property of control and synchronization of chaotic system. Especially, information entropy of the plain image is employed to produce the initial conditions of chaotic system. As a result, the proposed algorithm can resist known-plaintext attack (KPA) and chosen-plaintext attack (CPA). By the help of asymmetric cipher algorithm RSA, no extra transmission is needed in the communication. Experimental simulations show that the normalized correlation (NC) values between the host image and the cipher image are high. That is to say, the proposed encryption algorithm is imperceptible and has good hiding effect.

Graphical abstract

Keywords

image encryption algorithm / compressive sensing / integer wavelet transform / Hadamard matrix

Xiaoling Huang received the Master degree in Mathematics in June 2008 at Shantou University, China, and then joined in Guangdong Ocean University, China. She is currently an Associate Professor in Faculty of Mathematics and Computer Science at Guangdong Ocean University, China. The interesting areas are mathematical model, nonlinear analysis, cryptography, Image processing, and information security

Youxia Dong received the Bachelor degree from Anhui University of Science and Technology, China, and then joined in Guangdong Ocean University, China. She is currently pursuing the Master degree of Computer Science and Technology at Guangdong Ocean University, China. The interesting areas are cryptography, image encryption, and information security

Guodong Ye received the PhD degree in department of Electronic Engineering at City University of Hong Kong, China. From 2016 to 2018, He did the Post-doctoral research at Zhejiang University, China. At present, Dr. Ye is a Professor in Faculty of Mathematics and Computer Science at Guangdong Ocean University, China. His areas of interests are cryptography, application of chaotic system, compressive sensing, reversible information hiding, image encryption, etc

Yang Shi is a Professor at the School of Software Engineering in Tongji University, China. He received the PhD degree from Tongji University, China in 2005. His research interests include cryptography, privacy computing, blockchain technology, information security, and software protection. Dr. Shi has published a number of refereed papers in top journals and conferences, including IEEE TC, IEEE TII, IEEE TETC, IEEE T-CE, etc

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Acknowledgements

The authors would like to thank sincerely the Editor and the anonymous Reviewers for their helpful comments and suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61972103, 61772371, 62172301), the Natural Science Foundation of Guangdong Province of China (2019A1515011361), the Fundamental Research Funds for the Central Universities of China (22120210545), the Key Scientific Research Project of Education Department of Guangdong Province of China (2020ZDZX3064), and the Postgraduate Education Innovation Project of Guangdong Ocean University of China (202143).

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