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Recently, few researchers investigated algorithms of image encryption using different chaotic economic maps (CEMs). However, the authors investigated the effect of these maps on the encryption of the plain image. In the current study, an image encryption algorithm via Fisher–Yates shuffling (FYS) combined with a three‐dimensional (3D) CEM is given. FYS is used to generate the random permutation of a finite sequence. First, it is used to shuffle the rows and the columns of the plain image. Second, the 3DCEM is used in the substitution stage to confuse the pixels of the shuffling image. The proposed algorithm is applied to several types of images. Many measurements are performed to check the security and performance of the proposed algorithm. In addition, numerical simulations and experimental results have been implemented to verify that the proposed algorithm can resist different attack types. [ABSTRACT FROM AUTHOR]

In the literature, different types of algorithms that are organised to encrypt and decrypt images have been introduced. Some of these depend on chaotic systems where bifurcation routes to chaos exist. Those algorithms have advantages and disadvantages so far as their security level and computational speed are concerned. This study proposes a robust algorithm based on a pixel shuffling and a one‐dimensional chaotic economic map for encrypting and decrypting images. The proposed algorithm is implemented on many images. The security and performance of the proposed method are analysed thoroughly by using key space, key‐sensitivity, correlation of two adjacent pixels, information entropy, contrast and differential attack. On the basis of the obtained experimental results, the proposed algorithm is characterised by a large size of key space, a high sensitivity to the secret key, very low correlation coefficients, a good information entropy and a high contrast. Finally, the experiments are confirmed that the proposed algorithm can resist statistical and differential attacks with high efficiency. [ABSTRACT FROM AUTHOR]