A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.
By making use of the discrete fractional cosine transform, spectrum cutting and combining, rate-distortion control and color space transform, a joint compression and encryption scheme for multiple images and color images is proposed based on the multiple-order discrete fractional cosine transform （MODFrCT）. The spectra coefficients of images gotten by the discrete cosine transform are scanned in a way of zigzag, cut at an appropriate position, and combined into a single spectrum image sequentially encrypted by the MODFrCT. Rate-distortion control is utilized during the spectrum cutting to balance the qualities of the multiple reconstructed images. A color image can be decomposed into Y, Cb, and Cr components prior to the encryption, and these three components are then encrypted in the same way as that for multiple images. The numerical simulations demonstrate the validity and efficiency of these schemes, and the robustness of the schemes against occlusion attack is examined.
