We demonstrate a multispectral double-image-based cryptosystem that exploits only a tiny number of random white noise samples for proper decryption. Primarily, one of the two downsampled images is converted into the phase function after being shuffled by Arnold transform (AT), while the other image is modulated as an amplitude-based image after AT. Consecutively, a full double-image encryption can be achieved by employing classical double random phase encryption (DRPE) technique in the fractional Fourier transform domain with corresponding fractional orders. In this study, the encrypted complex data is randomly sampled via compressive sensing (CS) framework by which only 25% of the sparse white noise samples are being reserved to realize decryption with zero or small errors. As a consequence, together with correct phase keys, fractional orders and proper inverse AT operators, l_pminimization must be utilized to decrypt the original information. Thus, in addition to the perfect image reconstruction, the proposed cryptosystem provides an additional layer of security to the conventional DRPE system. Both the mathematical and numerical simulations were carried out to verify the feasibility as well as the robustness of the proposed system. The simulation results are presented in order to demonstrate the effectiveness of the proposed system. To the best of our knowledge, this is the first report on integrating CS with encrypted complex samples for information security.