۱- Introduction

۲- Preliminaries

۳- The proposed encryption and decryption scheme

۴- Simulation results

۵- Performance analyses

۶- Conclusions

References

Abstract

In this paper, we propose an image encryption algorithm based on the memristive chaotic system, elementary cellular automata (ECA) and compressive sensing (CS). Firstly, the original image is transformed by discrete wavelet transform, and the sparse coefficient matrix is obtained. Next, a zigzag scrambling method and the ECA are adopted to scramble the sparse coefficient matrix successively, and this process may effectively improve the scrambling degree. And then, the measurement matrix produced by the memristive chaotic system is used to compress and perceive the scrambled image, and the final cipher image is obtained. In addition, SHA-512 hash function value of the original image is generated to calculate the parameters for zigzag confusion, the initial values of the chaotic system and the initial configurations of the ECA, which enhances the correlation between the algorithm and the plain image and makes the proposed encryption scheme resist the known-plaintext and chosen-plaintext attacks. Moreover, our algorithm can compress and encrypt the image simultaneously by use of CS, which may reduce the amount of data and storage space. Simulation results and performance analyses demonstrate the security and robustness of the proposed scheme.

Introduction

With the advent of the Internet era, the vast majority of information in our lives cannot be separated from the support of the Internet. We use it for video conferencing, sending some information and so on. Some image information may be involved in personal privacy, trade secrets, military secrets and even national security, thus it will be very serious that attackers copy, malicious spread and tamper with the images in the transmission process through the network [1–۳]. Therefore, in order to protect the image information over the network, many image encryption algorithms have been presented by use of optical transformations [4,5], DNA computing [6–۹], Arnold transform [10,11], Latin squares [12], bit-level permutation [13–۱۵] and other methods. These algorithms can encrypt image information effectively and ensure data security. Recently, with the arrival of big data era, the volume of information is constantly increasing, the amount of data that needs to be transmitted is generally larger and the information redundancy is high. In order to reduce the amount of data transmitted through the network, the image needs to be compressed and then entered into transmission channel. At present, it has become a hotspot of information security research to encrypt images with compressive sensing (CS) and other encryption methods, which has great application potential and high practical value. The theory of CS points out that: by developing the sparse characteristic of the signal, the discrete sample of the signal is obtained by random sampling under the condition of far less than the Nyquist sampling rate, and then the reconstruction signal is perfect by the nonlinear reconstruction algorithm. In 2006, Candes and Donoho formally proposed the concept of CS [16,17], and after that many compression and encryption algorithms have also been presented based on CS [18–۲۱].