This paper presents a solution for simultaneous image encryption and compression. The primary introduced techniques are compressed sensing (CS) using structurally random matrix (SRM), and permutation-diffusion type image encryption. The encryption performance originates from both the techniques, whereas the compression effect is achieved by CS. Three-dimensional (3-D) cat map is employed for key stream generation. The simultaneously produced three state variables of 3-D cat map are respectively used for the SRM generation, image permutation and diffusion. Numerical simulations and security analyses have been carried out, and the results demonstrate the effectiveness and security performance of the proposed system.