This paper introduces a new image encryption scheme using a mixing technique as a way to encrypt one or multiple images of different types and sizes. The mixing model follows a nonlinear mathematical expression based on Cramer’s rule. Two 1D systems already developed in the literature, namely, the May-Gompertz map and the piecewise linear chaotic map, were used in the mixing process as pseudo-random number generators for their good chaotic properties. The image to be encrypted was first of all partitioned into N subimages of the same size. The subimages underwent a block permutation using the May-Gompertz map. This was followed by a pixel-based permutation using the piecewise linear chaotic map. The result of the two previous permutations was divided into 4 subimages, which were then mixed using pseudo-random matrices generated from the two maps mentioned above. Tests carried out on the cryptosystem designed proved that it was fast due to the 1D maps used, robust in terms of noise and data loss, exhibited a large key space, and resisted all common attacks. A very interesting feature of the proposed cryptosystem is that it works well for simultaneous multiple-image encryption.

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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.