Double-image encryption using discrete fractional random transform and logistic maps

• The discrete fractional random transform is generated based on logistic map.
• An expansion-and-shrink strategy is designed to combine plaintexts and vice versa.
• The histograms of scrambled plaintexts are nearly uniform based on a confusion–diffusion process.
• The encryption scheme is based on asymmetric technique and the security is enhanced.

A double-image encryption is proposed based on the discrete fractional random transform and logistic maps. Firstly, an enlarged image is composited from two original plaintexts, in which the pixel positions are relocated and the intensity values are changed by a chaotic confusion–diffusion process, and then two scrambled plaintexts are recovered from the enlarged image. Secondly, the two scrambled plaintexts are encoded into the phase and amplitude part of a complex function which is encrypted into a ciphertext with stationary white noise distribution by using the discrete fractional random transform generated based on logistic map. Not only the initial values of the logistic maps used in the cryptosystem but also the phase distribution produced in the encryption process can be used as private keys, which makes the proposed scheme has the characteristic of asymmetric encryption technique and high resistance against to the conventional attacks such as chosen plaintext attack, ciphertext-only attack. Simulation results and security analysis verify the feasibility and effectiveness of the proposed method.