A discussion and a cryptanalysis of the optical phase-truncated Fourier-transform-based cryptosystem are presented in this paper. The concept of an optical asymmetric cryptosystem, which was introduced into the optical image encryption scheme based on phase-truncated Fourier transforms in 2010, is suggested to be retained in optical encryption. A new method of attack is also proposed to simultaneously obtain the main information of the original image, the two decryption keys from its cyphertext, and the public keys based on the modified amplitude-phase retrieval algorithm. The numerical results illustrate that the computing efficiency of the algorithm is improved and the number of iterations is much less than that by the specific attack, which has two iteration loops.

The earlier proposed interference-based encryption method with two phase-only masks (POMs), which actually is a special case of our method, is quite simple and does not need iterative encoding. However, it has been found recently that the encryption method has security problems and cannot be directly applied to image encryption due to the inherent silhouette problem. Several methods based on chaotic encryption algorithms have been proposed to remove the problem by postprocessing of the POMs, which increased the computation time or led to digital inverse computation in decryption. Here we propose a new method for image encryption based on optical interference and analytical algorithm that can be directly used for image encryption. The information of the target image is hidden into three POMs, and the silhouette problem that exists in the method with two POMs can be resolved during the generation procedure of POMs based on the interference principle. Simulation results are presented to verify the validity of the proposed approach.

The asymmetric cryptosystem, which is based on phase-truncated Fourier transforms (PTFTs), can break the linearity of conventional systems. However, it has been proven to be vulnerable to a specific attack based on iterative Fourier transforms when the two random phase masks are used as public keys to encrypt different plaintexts. An improvement from the asymmetric cryptosystem may be taken by relocating the amplitude values in the output plane. In this paper, two different methods are adopted to realize the amplitude modulation of the output image. The first one is to extend the PTFT-based asymmetrical cryptosystem into the anamorphic fractional Fourier transform domain directly, and the second is to add an amplitude mask in the Fourier plane of the encryption scheme. Some numerical simulations are presented to prove the good performance of the proposed cryptosystems.