Exploiting 2D compressed sensing and information entropy for secure color image compression and encryption

Compared to 1D compressed sensing (CS), 2D CS is more efficient for compressing the plaintext image from two directions, but security level of current 2D CS-based ciphers is unsatisfactory. To solve this problem, this paper presents a novel color image compression and encryption algorithm by combining 2D CS, information entropy and chaos. Firstly, the color image is decomposed into red, green and blue components, then they are sparsely transformed by the discrete wavelet transform (DWT) to get three sparse matrices. Next, the obtained matrices are observed by two asymptotical deterministic random measurement matrices based on information entropy and counter (ADMMIC), which not only encrypts the plaintext image, but also compresses it in proportion to reduce the transmission bandwidth and storage space. Subsequently, the corresponding measurement value matrices are shuffled by a double random scrambling based on Arnold map and index vector (DRSAIV) to eliminate the correlation between adjacent pixels. Furthermore, the obtained permutated matrices are diffused by a simultaneous multiple random diffusion of inter-intra components (SMRDIC) to obtain the final cipher image, the plaintext pixel to be diffused, the key matrix involved in diffusion and the position of the obtained ciphertext pixel are all unpredictable, which makes statistical attack invalid. In addition, information entropy values of plaintext image are obtained to generate the initial values of the used chaotic systems, which greatly improve the ability to resist the known-plaintext and chosen-plaintext attacks. Simulation results and security analyses verify that this algorithm has good compression and high security.

Automated summary

This paper proposes a novel color image compression and encryption algorithm by combining 2D CS, information entropy and chaos. The algorithm sparsely transforms the color image using DWT and encrypts it with two random measurement matrices, then shuffles and diffuses the measurement value matrices to obtain the final cipher image with improved security.