A novel technique of multiplexing complex images is proposed in which each image may be demultiplexed only if a set of random encryption keys is known. The technique utilizes the ability of the double random phase encoding method to spread a signals' energy in both the space and spatial frequency domains in a controlled manner. To multiplex, images are independently encrypted with different phase keys, and then superimposed by recording sequentially on the same material. Each image is extracted using the particular key associated with it. During decryption the energy from the other images is further spread making it possible to minimize their effects using suitable filters. Wigner analysis is applied to the technique, and numerical results, supporting the results, are presented. Â© 2007 American Institute of Physics.