Abstract: A novel image encryption algorithm is proposed by combining 1D Logistic chaotic system, 4D new hyperchaotic system (NHS), compressed sensing (CS), double random phase coding (DRPE), and 2D discrete cosine transform (DCT). Firstly, 2D DCT is used to represent the gray image sparsely, and the sparse matrix obtained by index sort scrambling is scrambled. Secondly, the measurement is made using CS, and the measurement matrix is generated by the 4D NHS. Finally, the second encryption of DRPE is carried out, the Logistic chaotic mapping and 4D NHS are used as the double key to realize DRPE, and the final encrypted image is obtained. The algorithm makes full use of the advantages of CS to realize compression and encryption at the same time, and combines CS with DRPE, which not only reduces the storage space and transmission bandwidth, but also improves the security performance of encryption. Simulation experiments and comparative analysis show that the proposed image encryption algorithm has good security, robustness and decryption quality.

Key words: double chaotic system, compressed sensing, double random phase encoding, 2D discrete cosine transform