An image compression-then-encryption algorithm using piecewise asymptotic deterministic random measurement matrix

digital Image Compression Encryption Method (ICEM) is proposed in this work by using the Compressed Sensing (CS), two-dimensional Logistic-adjusted-Sine map, the piecewise asymptotic deterministic system, dynamic diffusion and Hilbert-Logistic permutation. The plain image is pre-processed by a two-dimensional discrete wavelet transform to obtain four kinds of frequency components HH , HL , LH and LL . Dynamic diffusion and the CS are used to process low and high-frequency components, respectively, and then the results are combined to obtain an intermediate cryptographic image. In the process of CS, a measurement matrix is generated by a piecewise asymptotic deterministic random system and a chaotic sequence. To obtain the encrypted image, an improved Hilbert-Logistic permutation method is used to disturb the pixel position of the intermediate cryptographic image. The SHA-256 is utilized to generate the required keys for the encryption process. The proposed ICEM has the ability to resist chosen-plaintext and known-plaintext attacks as the key is selected dynamically. By using the CS the time and space complexity of the algorithm are reduced. It is shown in experimental results that the proposed scheme has good key sensitivity, decryption speed, fast encryption and large key space, and high robustness and security.