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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]