Assessing the performance of a method of simultaneous compression and encryption of multiple images and its resistance against various attacks

We introduce a double optimization procedure for spectrally multiplexing multiple images. This technique is adapted from a recently proposed optical setup implementing the discrete cosine transformation (DCT). The new analysis technique is a combination of spectral fusion based on the properties of DCT, specific spectral filtering, and quantization of the remaining encoded frequencies using an optimal number of bits. Spectrally multiplexing multiple images defines a first level of encryption. A second level of encryption based on a real key image is used to reinforce encryption. A set of numerical simulations and a comparison with the well known JPEG (Joint Photographic Experts Group) image compression standard have been carried out to demonstrate the improved performances of this method. The focus here will differ from the method of simultaneous fusion, compression, and encryption of multiple images (SFCE) [Opt. Express 19, 24023 (2011)] in the following ways. Firstly, we shall be concerned with optimizing the compression rate by adapting the size of the spectral block to each target image and decreasing the number of bits required to encode each block. This size adaptation is achieved by means of the root-mean-square (RMS) time-frequency criterion. We found that this size adaptation provides a good tradeoff between bandwidth of spectral plane and number of reconstructed output images. Secondly, the encryption rate is improved by using a real biometric key and randomly changing the rotation angle of each block before spectral fusion. By using a real-valued key image we have been able to increase the compression rate of 50% over the original SFCE method. We provide numerical examples of the effects for size, rotation, and shifting of DCT-blocks which play noteworthy roles in the optimization of the bandwidth of the spectral plane. Inspection of the results for different types of attack demonstrates the robustness of our procedure.