Double random phase encoding (DRPE) is vulnerable to known-plaintext attacks (KPAs) based on phase retrieval algorithms. We previously analyzed DRPE resistance to KPA cryptanalysis with multiple known plaintext-ciphertext image pairs and obtained secret keys at a higher probability rate than when performing KPA cryptanalysis using one known image pair. However, the robustness of KPA in the presence of noise or occlusion in DRPE is unclear. We analyzed KPA properties in relation to DRPE when white Gaussian noise was gradually added to the Fourier amplitude or phase of a known ciphertext complex amplitude image. Additionally, we analyzed KPA properties when the Fourier phase of the known ciphertext image was gradually occluded by zero-valued pixels. The results showed that KPAs performed using multiple known plaintext-ciphertext image pairs were largely affected by noise added to the Fourier phase and thus are not always a strong tool for DRPE cryptanalysis.
Double random phase encoding (DRPE) is vulnerable to known-plaintext attacks (KPAs) based on phase retrieval algorithms. We previously analyzed DRPE resistance to KPA cryptanalysis with multiple known plaintext-ciphertext image pairs and obtained secret keys at a higher probability rate than when performing KPA cryptanalysis using one known image pair. However, the robustness of KPA in the presence of noise or occlusion in DRPE is unclear. We analyzed KPA properties in relation to DRPE when white Gaussian noise was gradually added to the Fourier amplitude or phase of a known ciphertext complex amplitude image. Additionally, we analyzed KPA properties when the Fourier phase of the known ciphertext image was gradually occluded by zero-valued pixels. The results showed that KPAs performed using multiple known plaintext-ciphertext image pairs were largely affected by noise added to the Fourier phase and thus are not always a strong tool for DRPE cryptanalysis.
Double Random Phase Encoding (DRPE), which is a typical optical encryption technique, has been reported to be vulnerable to Known Plaintext-Attacks (KPAs) using a Phase Retrieval Algorithm (PRA). But the reported case in which the encryption key is successfully estimated was that the plain image was rather simple such as the image of a character. In addition, although Phase Only DRPE (PO-DRPE) was proposed to achieve more resistance to the KPA than Complex DRPE (C-DRPE) in which both amplitude and phase components are used as an encrypted image, no quantitative results about the relationship between the vulnerability and the plaintext image. In this paper, we show the result of quantitative analysis on KPA by PRA to C-DRPE and PO-DRPE, for the plaintext images of different characteristics. As a result of experiment, KPA to C-DRPE succeeded to estimate the correct key while the probability of success became lower when the number of non-zero pixel increases in the plaintext image. However, KPA to PO-DRPE enabled to estimate only "singular" keys, which are effective for no more than given plaintext/ciphertext image pair and far different from the correct encryption key. We also conducted KPA using two plaintext-ciphertext image pairs for KPA. In the case when two plaintext-ciphertext image pairs were given to KPA, the cryptanalysis succeeded with higher probability than the case of one. Moreover, the probability of success in the KPA was high even in PO-DRPE.
Classical double-random phase encoding (C-DRPE) is an optical symmetric-key encryption technique. C-DRPE is reported to be vulnerable to a known-plaintext attack (KPA) that uses a phase retrieval algorithm. However, although phase-only DRPE (PO-DRPE) is reported to be more resistant to KPAs than C-DRPE, it is not obvious yet that PO-DRPE is sufficiently resistant to a KPA under any condition, because the vulnerability to KPA varies depending on various factors, such as the number of the known plaintext-ciphertext pairs that are given for the KPA, or the gray level of the known-plaintext image (i.e., binary or multivalued image). In this paper, we investigate the resistance of C-DRPE and PO-DRPE to KPA under various conditions related to the number of known plaintext-ciphertext pairs and to the gray level of the known-plaintext image.
Although initial research shows that double-random phase encoding (DRPE) is vulnerable to known-plaintext attacks that use phase retrieval algorithms, subsequent research has shown that phase-only DRPE, in which the Fourier amplitude component of an image encrypted with classical DRPE remains constant, is resistant to attacks that apply phase retrieval algorithms. Herein, we numerically analyze the key-space of DRPE and investigate the distribution property of decryption keys for classical and phase-only DRPE. We determine the difference in the distribution property of successful decryption keys for these DRPE techniques from the numerical analysis results and then discuss the security offered by them.
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.
In this paper, we analyze the security of the classical double random phase encoding (DRPE) technique in Fourier domain, as well as its extended schemes in Fresnel and fractional Fourier domains. These schemes are resistant to bruteforce attacks, for their large key spaces. However, due to the linearity property of their encryption transformations, they are vulnerable to other attacks, such as chosen-plaintext attack and known-plaintext attack. We successfully break each of the three encryption schemes with the help of a certain quantity of plaintext-ciphertext pairs. Each attack is validated by computer simulations. The cryptanalysis indicates that, to minimize the risks, it is recommendable to introduce nonlinear operations to optical encryption systems.
The modified iterative phase retrieval algorithms developed in Part I [Guo et al., Appl. Opt.54, 4698 (2015)] are applied to perform known plaintext and ciphertext attacks on amplitude encoding and phase encoding Fourier-transform-based double random phase encryption (DRPE) systems. It is shown that the new algorithms can retrieve the two random phase keys (RPKs) perfectly. The performances of the algorithms are tested by using the retrieved RPKs to decrypt a set of different ciphertexts encrypted using the same RPKs. Significantly, it is also shown that the DRPE system is, under certain conditions, vulnerable to ciphertext-only attack, i.e., in some cases an attacker can decrypt DRPE data successfully when only the ciphertext is intercepted.