Cryptanalysis of phase information based on a double random-phase encryption method

Phase-only information derived using a double random-phase encryption (DRPE) algorithm is not visually recognizable but can be authenticated using a nonlinear cross-correlation method. This can be considered to enhance DRPE security (which is vulnerable to a chosen-plaintext attack). Here, we show that phase-only images derived using the DRPE method remains vulnerable to such an attack; the at-risk images include full- and sparse-phase images and phase information with noise. We develop an encoder–decoder deep-learning method to decrypt phase-only images encrypted using the DRPE method. The deep-learning structure can be trained using only spare phase information from the encrypted image; experimentally, the trained model readily decrypted phase-only or partial-phase-encrypted images based on the DRPE algorithm.