Cryptanalysis of an optical cryptosystem based on phase-truncated Fourier transform and nonlinear operations

In this paper, the security of a nonlinear optical cryptosystem is evaluated. Compared with traditional cryptosystems based on phase-truncated Fourier transform (PTFT), nonlinear operations are introduced to amplify the error between the estimated and actual ciphertexts during the iterative attack process to improve the security level of the cryptosystem. To figure out the principle of error generation during the iterative process, the error analysis on the classical PTFT-based cryptosystem and the cryptosystem with nonlinear operations is conducted However, from the error analysis, it is found that the amplification effect of error by those nonlinear operations is affected by the initial value of the plaintexts and can be reduced by a normalization operation. Hence, a specific phase-retrieval attack with normalization and a bilateral filter is proposed to break the cryptosystem. The bilateral filter is introduced to improve the convergence rate and quality of the retrieved images. To the best of our knowledge, it is the first time that the cryptosystem based on PTFT and nonlinear operations is cracked successfully. Numerical simulation is carried out to show the feasibility and effectiveness of the proposed attack.