Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps

A new discrete fractional transform defined by the fractional order, periodicity and vector parameters is presented, which is named as the discrete multiple-parameter fractional angular transform. Based on this transform and two-coupled logistic map, a double-image encryption scheme is proposed. First, an enlarged image is obtained by connecting two plaintext images sequentially and scrambled by using a chaotic permutation process, in which the sequences of chaotic pairs generated by using the two-coupled logistic map. Then, the scrambled enlarged image is decomposed into two new components. Second, a chaotic random phase mask is generated based on the logistic map, with which one of two components is converted to the modulation phase mask. Another component is encoded into an interim matrix with the help of the modulation phase mask. Finally, the two-dimensional discrete multiple-parameter fractional angular transform is performed on the interim matrix to obtain the ciphertext with stationary white noise distribution. The proposed encryption scheme has an obvious advantage that no phase keys are used in the encryption and decryption process, which is convenient to key management. Moreover, the security of the cryptosystem can be enhanced by using extra parameters such as initial values of chaos functions, fractional orders and vector parameters of transform. Simulation results and security analysis verify the feasibility and effectiveness of the proposed scheme.