Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys

From the perspective of optical information security, we demonstrate that conventional phase retrieval algorithms, such as the Gerchberg-Saxton algorithm, can be still valid when extended from the Fourier transform domain into the fractional Fourier transform (FRFT) domain. Based on this extension, we propose a method of known-plaintext attack (KPA) on double random phase encoding in the fractional Fourier transform domain (DRPE-FRFT). With this attack, an opponent can access two encryption phase keys with the help of the phase retrieval algorithm in the FRFT domain, and meanwhile obtain the two FRFT order keys by using an exhaustive search. This indicates that the optical encryption scheme based on the DRPE-FRFT scheme is vulnerable to KPA due to the nature of the linearity of FRFT. The validity of this attack is verified by numerical simulations.