A novel fast chaos-based algorithm for generating random permutations with high shift factor suitable for image scrambling

The good qualities of permutations with a high shift factor in terms of speech scrambling have been proven in the last 20 years. Nevertheless, the absence of a fast algorithm for generating them has limited their use in cryptographic applications. In this paper, we propose a new fast chaos-based method for generating random permutations with a high shift factor, and we compare it with some similar schemes, classical or chaos-based. The permutations generated by the proposed method have very few fixed points, too, making them theoretically suitable for image scrambling or for use as a diffusion stage in an image cryptosystem. We prove this fact using some standard indicators as MSE, UACI, NPCR, PCC, etc. and by comparisons to the results obtained for other algorithms of this type. All the results obtained are very good, including a speed of pixels permutation of 14 MB/s, allowing us to say that the proposed algorithm is a fast and efficient one, which can be used even in real-time scrambling.