Abstract: In view of the low chaos performance of the traditional Logistic chaotic system and the poor randomness of generated pseudo-random sequences, in this paper, a new improved Logistic chaotic equation is proposed, and a multi-chaotic image compression and encryption system is constructed by combining Lorenz hyperchaotic system and compressed sensing theory. In the process of encryption, the encryption algorithm is combined with the traditional encryption algorithm to obtain the ciphertext image by scrambling and spreading. The controlled measurement matrix is constructed by using the improved Logistic chaotic equation to obtain a pseudo-random sequence with better random performance. Simulation experiments show that the PSNR of the controlled measurement matrix constructed by the improved Logistic chaotic equation reaches 34.26 dB under the condition of 75% compression ratio, which is about 10 dB higher than that of the traditional Logistic chaotic equation under the same conditions. And the algorithm has a good anti-differential attack performance, pixel change rate (NPCR) and uniform mean change degree (UACI) are close to the theoretical value. Therefore, the encryption algorithm proposed in this paper has good compressibility, security and signal reconstruction characteristics.

Key words: improved Logistic chaos equation, compression perception, multiple chaos, image compression and encryption