A Difference-Equation-Based Robust Image Encryption Scheme with Chaotic Permutations and Logic Gates

Abstract

Image encryption has become an indispensable tool for achieving highly secure image-based communications. Numerous encryption approaches have appeared and demonstrated varying degrees of robustness to adversarial attacks. In this paper, an efficient and robust image encryption algorithm is established based on randomized difference equations, random permutations and randomized logic circuits. Specifically, hyperchaotic and chaotic systems are used to generate pseudo-random sequences. These sequences are thus used to define random first-order difference equations, chaotic permutations and logic circuits. Image encryption based on these three randomized modules shows high computational efficiency as well as strong robustness against statistical, differential, and chosen-plaintext attacks. The proposed scheme leads to almost zero correlation in the encrypted images, entropy values of more than 7.99 for the test images, and a key space size of 2^{572}. Furthermore, differential analysis shows that the number of pixel change rate (NPCR) and the unified average change intensity (UACI) for the proposed technique are on average 99.61 and 33.35%, respectively.