Image encryption via discrete fractional Fourier-type transforms generated by random matrices

One of the major application areas of the fractional Fourier transform (FrFT) and the discrete fractional Fourier transforms (DFrFT) is in signal and information security, particularly in signal and image encryption. Recently, many researchers proposed techniques that implemented not only the fractional transforms, but also various randomized versions of the DFrFT, which add more security features to signal's encryption. In this paper, we propose new DFrF-type transforms whose eigensystems are generated using a novel random-matrix scheme. We give theoretical justifications for the importance of our transforms and show their statistical significance in comparison to recently proposed transforms in the context of image encryption. Experimental results show also that the encryption keys based on the proposed transforms have high sensitivities against decryption attacks.