Image encryption using the two-dimensional logistic chaotic map

Chaos maps and chaotic systems have been proved to be useful and effective for cryptography. In this paper, the two-dimensional logistic map with complicated basin structures and attractors are first used for image encryption. The proposed method adopts the classic framework of the permutation-substitution network in cryptography and thus ensures both confusion and diffusion properties for a secure cipher. The proposed method is able to encrypt an intelligible image into random-like from the statistical point of view and the human visual system point of view. Extensive simulation results using test images from the USC-SIPI image database demonstrate the effectiveness and robustness of the proposed method. Security analysis results of using both the conventional and the most recent tests show that the encryption quality of the proposed method reaches or excels the current state-of-the-arts. Similar encryption ideas can be applied to digital data in other formats, e.g. digital audio and video. We also publish the cipher MATLAB open-source code under the web page https://sites.google.com/site/tuftsyuewu/source-code.