Multiple-Image Fusion Encryption (MIFE) Using Discrete Cosine Transformation (DCT) and Pseudo Random Number Generators

This chapter proposes a new multiple-image encryption algorithm based on spectral fusion of watermarked images and new chaotic generators. Logistic-May (LM), May-Gaussian (MG), and Gaussian-Gompertz (GG) were used as chaotic generators for their good properties in order to correct the flaws of 1D chaotic maps (Logistic, May, Gaussian, Gompertz) when used individually. Firstly, the discrete cosine transformation (DCT) and the low-pass filter of appropriate sizes are used to combine the target watermarked images in the spectral domain in two different multiplex images. Secondly, each of the two images is concatenated into blocks of small size, which are mixed by changing their position following the order generated by a chaotic sequence from the Logistic-May system (LM). Finally, the fusion of both scrambled images is achieved by a nonlinear mathematical expression based on Cramer’s rule to obtain two hybrid encrypted images. Then, after the decryption step, the hidden message can be retrieved from the watermarked image without any loss. The security analysis and experimental simulations confirmed that the proposed algorithm has a good encryption performance; it can encrypt a large number of images combined with text, of different types while maintaining a reduced Mean Square Error (MSE) after decryption.