Analysis of singular phase based on double random phase encoding using phase retrieval algorithm

We analyze the properties of the singular phase based on phase retrieval. The phase can be estimated from the result of the known-plaintext attack on a typical optical encryption technique, namely double random phase encoding. The key generated by the singular phase for decryption can be used to decrypt only the known ciphertext image used for the attack. However, it is not obvious whether any unknown ciphertext image can be decrypted using the singular key (a phase key image that has the singular property). Therefore, we prepared various ciphertext images by changing two parameters, namely the plaintext image and a random phase mask in the spatial plane, and analyzed the properties of the singular key by decrypting these unknown ciphertext images. The results show that when the unknown ciphertext images generated by changing only the plaintext image are decrypted, the known plaintext pattern is obtained. In contrast, when the unknown ciphertext images generated by changing only the random phase mask are decrypted, no pattern is obtained. These cases both indicate that cryptanalysis failed. Nevertheless, when the known plaintext pattern is obtained, it indicates that the correlation between the known and unknown random phase masks is high, giving the attacker an important clue.