On the Security of Optical Ciphers Under the Architecture of Compressed Sensing Combining With Double Random Phase Encoding

This work investigates the security of optical ciphers integrating compressed sensing (CS) with double random phase encoding. Theoretical analysis demonstrates that the combined system, regardless of the implementation order of the two procedures, can be normalized as a single CS projection process, whose equivalent measurement matrix can be recovered by plaintext attack. The proved restricted isometry property of the equivalent measurement matrices further renders the adversary great convenience to recover the plaintext with only a single-step <inline-formula> <tex-math notation="LaTeX">${\ell _1}$</tex-math></inline-formula> optimization. Computer simulations are also carried out for verification.