Security analysis on an interference-based optical image encryption scheme

In this paper, the security strength of the improved optical cryptosystem based on interference has been evaluated. Compared to the previous interference-based cryptosystems in which the plaintext is encoded into two phase-only masks (POMs), here the plaintext is encoded into a POM and an amplitude mask (AM). Since the information of the plaintext cannot be recovered directly when one of the masks is released in the decryption process of the improved cryptosystem, it seems that it is free from the silhouette problem. However, we found that the random phase mask (RPM) serving as the encryption key is not related to the plaintext. Thus, it is possible to recover the RPM first by using the known-plaintext attack (KPA). Moreover, the POM and the AM generated in the encryption path only contains the phase and amplitude information, respectively. Thus, these can be utilized as additional constraints in the proposed iterative process. Based on these findings, two kinds of hybrid attacks, including a KPA and the iterative processes with different constraints, are proposed to crack the improved cryptosystem. In the designed KPA with a pair of the known plaintext and its corresponding masks, the RPM is recovered first. With the aid of the recovered RPM, two iterative processes with different released masks are proposed to recover the information of the plaintext without any knowledge of another mask. To the best of our knowledge, this is the first time that the existence of the silhouette problem in the cryptosystem under study has been reported. Numerical simulation has been carried out to validate the feasibility and effectiveness of the proposed hybrid attacks.