Optical image encryption algorithm based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system

Abstract To increase the robustness against common attacks, a novel image encryption algorithm is proposed based on the phase-truncated short-time fractional Fourier transform (PTSTFrFT) and the hyper-chaotic system. In the algorithm, the original image is divided into four sub-images to be encoded independently. Different from the traditional phase truncation coding, the PTSTFrFT is combined with wave-based permutation to construct the encryption unit (EU) for encoding the sub-images, where the confused phase information is recombined with the amplitude information to guarantee the integrity of image information and the nonlinearity of phase truncation. Besides, the encryption unit can be achieved optically. Furthermore, the corresponding results compose an interim image, whose pixel values and pixel positions are modified by the permutation and the diffusion operations. The diffusion operation is designed with the feedback system to increase the anti-interference ability. The proposed image encryption algorithm has large enough key space and high sensitivity to the keys because of the use of hyper-chaotic system. The simulation results demonstrate that the proposed image encryption algorithm based on the PTSTFrFT is secure and robust enough against the common attacks.