A new image compression-encryption scheme based on compressive sensing and cyclic shift

This paper proposes a digital image compression-encryption scheme based on the theory of compressive sensing and cyclic shift, which use random Gauss matrix and sparse transform to compress the digital image, and then cyclic shift and diffusion operation are developed subsequently to the compressive sensing (CS) phase. The algorithm has three advantages: First, the measurement matrix used in the algorithm is generated by Chebyshev mapping, which increases the key space and reduces the burden of key transmission. Second, The Sigmoid function is used to transform the range of compressed data to 0 similar to 255, which are stored as 8-bit binary data, thus further reducing the amount of data transmission and avoiding the expansion of encrypted data. Third, the generation of key stream in encryption phase is related to ciphertext, there are different key streams for different plain images. Thus, our algorithm can resist against the chosen-plaintext and known-plaintext attacks effectively. In addition, the implementation of cyclic shift and diffusion operation further enhances the security of the system. Each pixel of the encrypted image is output in the form of 8-bit integer to facilitate data storage, display and transmission. The experimental results and security analysis show that the algorithm has the advantages of large key space, no obvious statistical characteristics of ciphertext, sensitive to plaintext and key, and able to resist chosen-plaintext attack.