A synergetic image encryption method based on discrete fractional random transform and chaotic maps

The discrete fractional random transform (DFrRT) has excellent mathematical properties and inherent randomness feature from the Fourier Transform which makes it to be a suitable candidate for digital image encryption. However, we have found that this method has an encryption flaw of the linear property and the flaw has been analyzed in this paper. After that, we propose a synergetic encryption algorithm which combines DFrRT and chaotic maps to overcome the presented flaw in the original DFrRT. All the image correlation coefficient values between different test images have decreased from 1 to almost 0, which means the linearity between different images preserved by the original DFrRT has been effectively eliminated. Experimental results show that our proposed encryption algorithm not only maintains the merits of both the original DFrRT and the chaotic maps, but also has better cryptographic performances in terms of the key space, the key sensitivity, the plain image sensitivity, the statistical characteristics and the ability to resist common attacks.