Reality-Preserving Multiple Parameter Discrete Fractional Angular Transform and Its Application to Color Image Encryption

In this paper, we first define a reality-preserving multiple parameter fractional angular transform (RPMPDFrAT), which is a useful tool for image encryption. Then, we propose a new color image encryption algorithm based on the defined RPMPDFrAT. The encryption process consists of two phases: encryption in the spatial domain and RPMPDFrAT domain. In the spatial domain, three color components of the plain image are mapped by dual cylindrical transform, which can nonlinearly hide the original color information. Then, the intermediate output is scrambled by a coupled logistic map to reduce the correlation of adjacent pixels and uniformly distribute the image energy of different color components. Thereafter, the scrambled image is transformed by the proposed RPMPDFrAT, which can ensure that we obtain the real-value output. Finally, a process similar to the spatial domain is performed in the RPMPDFrAT domain to further improve the security of the cryptosystem. Numerical simulations are performed and demonstrate that the proposed image encryption algorithm is effective and sensitive to keys. Moreover, some potential attacks are tested to verify the robustness of the proposed method, and the performance of our method outperforms previously published ones.