Hybrid attack on an optical cryptosystem based on phase-truncated Fourier transforms and a random amplitude mask

In this paper, the security of a cryptosystem based on phase-truncated Fourier transforms (PTFTs) and a random amplitude mask (RAM) is evaluated. In the cryptosystem, fake keys used as encryption keys in the second PTFT-based structure are generated by the first PTFT-based structure in which the RAM is encoded by random phase masks (RPMs) used as public keys. Compared to the classical PTFT-based encryption scheme, the security level of the cryptosystem is improved by using cascaded PTFTs to encode the encryption keys and the plaintext simultaneously. However, it is found that a known plaintext-ciphertext pair can provide enough constraints in the iterative process to retrieve the fake keys, which then can be used to retrieve unknown arbitrary plaintext from the corresponding ciphertext. Based on the analysis, we propose a specific attack based on hybrid iterative processes to break the cryptosystem. Two iterative processes with different constraints are involved in the proposed attack. The first known-plaintext-attack (KPA)-based iterative process is used to retrieve two fake keys with the help of two public keys and a known plaintext-ciphertext pair, while the second amplitude-phase retrieval algorithm-based iterative process with a median filter is employed to retrieve the plaintext from the corresponding ciphertext using two retrieval fake keys. To the best of our knowledge, it is the first time that the cryptosystem is attacked by the KPA-based iterative algorithm successfully. Numerical simulation results validate the feasibility and effectiveness of the proposed attack.