In this paper, the security strength of an enhanced cryptosystem based on interference and the phase-retrieval technique is evaluated. The security strength of the optical cryptosystem was improved through the phase-retrieval technique used to generate a phase-only mask (POM) as the ciphertext. Due to the complex mathematical model of the phase-retrieval technique, it seems that a silhouette problem existing in the conventional interference-based scheme was removed. However, we noted that the random phase mask (RPM) regarded as the only private key was fixed in the encryption path, which is not related to the plaintext and makes it possible to be recovered using a known-plaintext attack (KPA). Moreover, we also found that the RPM has high key sensitivity, and it should be recovered precisely to retrieve information of plaintexts during the attack. Thus, a hybrid KPA where three pairs of known plaintexts and their ciphertexts are regarded as the amplitude and phase constraints to obtain the precise estimation of the RPM is proposed. Then, with the help of the estimated private key, information of the original plaintexts encoded using the cryptosystem under study could be retrieved from an arbitrarily given ciphertext without any knowledge of the private key. Our cryptoanalysis shows that the cryptosystem based on interference and the phase-retrieval technique is vulnerable to the proposed attack, and there is a security leak in it. Numerical simulations have been carried out to demonstrate the performance of our proposed attack.
In this paper, the security strength of an enhanced cryptosystem based on interference and the phase-retrieval technique is evaluated. The security strength of the optical cryptosystem was improved through the phase-retrieval technique used to generate a phase-only mask (POM) as the ciphertext. Due to the complex mathematical model of the phase-retrieval technique, it seems that a silhouette problem existing in the conventional interference-based scheme was removed. However, we noted that the random phase mask (RPM) regarded as the only private key was fixed in the encryption path, which is not related to the plaintext and makes it possible to be recovered using a known-plaintext attack (KPA). Moreover, we also found that the RPM has high key sensitivity, and it should be recovered precisely to retrieve information of plaintexts during the attack. Thus, a hybrid KPA where three pairs of known plaintexts and their ciphertexts are regarded as the amplitude and phase constraints to obtain the precise estimation of the RPM is proposed. Then, with the help of the estimated private key, information of the original plaintexts encoded using the cryptosystem under study could be retrieved from an arbitrarily given ciphertext without any knowledge of the private key. Our cryptoanalysis shows that the cryptosystem based on interference and the phase-retrieval technique is vulnerable to the proposed attack, and there is a security leak in it. Numerical simulations have been carried out to demonstrate the performance of our proposed attack.
This paper presents a security analysis of the optical image encryption scheme based on interference and fixed phase masks. Unlike the traditional interference-based scheme, which uses only one phase-only mask (POMs) generated during the encryption process as the private key, the improved system incorporates fixed phase masks as the additional private keys. While it appears that the security strength of the interference-based scheme is enhanced by expanding the key space, our analysis reveals that these fixed phase masks are independent of the plaintext and can be recovered through a known-plaintext attack (KPA). Once these additional private keys are obtained, the number of unknown private keys is reduced to one, allowing the plaintext information encrypted by the improved interference-based scheme to be recovered from any arbitrarily given ciphertexts without any knowledge of the private key. To show the vulnerability of this cryptosystem, we propose a hybrid attack combining the KPA and ciphertext-only attack (COA) which can break the improved interference-based cryptosystem. Numerical simulations have been performed to confirm the feasibility and effectiveness of the proposed hybrid attack.
This paper offers a security analysis of an optical image cryptosystem that integrates interference and unequal modulus decomposition (EMD). In contrast to the conventional interference-based cryptosystem, which utilizes a single phase-only mask (POM) derived from the encryption process as the private key, the enhanced cryptosystem employs two random phase masks (RPMs) and two POMs derived from the phase-reserved (PR) structure as private keys. This modification addresses the silhouette problem inherent in the conventional interference-based cryptosystem by expanding the key space, thereby enhancing security strength. However, it is determined that the RPM R 2 ( u , v ) and the POM P 2 ( x , y ) exhibited low key sensitivity, thereby limiting their impact on the security enhancement. Additionally, due to the independence from the plaintext, the RPMs employed as private keys can be recovered using a designed known-plaintext attack (KPA). Once the RPMs are recovered, the number of unknown keys is reduced to two. This enables the recovery of plaintext information from its ciphertexts via a subsequent ciphertext-only attack (COA) without any prior knowledge of the POMs. In light of these findings, a novel hybrid attack strategy, to our knowledge, is proposed, integrating four cascaded KPAs and a COA, to effectively compromise the advanced interference and EMD-based cryptosystem. To validate the feasibility and effectiveness of the proposed hybrid attack, numerical simulations have been conducted.
In this paper, the security of a cryptosystem based on phase-truncated Fourier transforms (PTFTs) and a random amplitude mask (RAM) is evaluated. In the cryptosystem, fake keys used as encryption keys in the second PTFT-based structure are generated by the first PTFT-based structure in which the RAM is encoded by random phase masks (RPMs) used as public keys. Compared to the classical PTFT-based encryption scheme, the security level of the cryptosystem is improved by using cascaded PTFTs to encode the encryption keys and the plaintext simultaneously. However, it is found that a known plaintext-ciphertext pair can provide enough constraints in the iterative process to retrieve the fake keys, which then can be used to retrieve unknown arbitrary plaintext from the corresponding ciphertext. Based on the analysis, we propose a specific attack based on hybrid iterative processes to break the cryptosystem. Two iterative processes with different constraints are involved in the proposed attack. The first known-plaintext-attack (KPA)-based iterative process is used to retrieve two fake keys with the help of two public keys and a known plaintext-ciphertext pair, while the second amplitude-phase retrieval algorithm-based iterative process with a median filter is employed to retrieve the plaintext from the corresponding ciphertext using two retrieval fake keys. To the best of our knowledge, it is the first time that the cryptosystem is attacked by the KPA-based iterative algorithm successfully. Numerical simulation results validate the feasibility and effectiveness of the proposed attack.
The security strength of an interference-based optical image cryptosystem with a designed amplitude modulator (AM) is evaluated. Compared to previous improved interference-based cryptosystems in which iterative or post-processing algorithms are involved, to remove the silhouette problem, a pre-designed AM is placed at the image plane to modulate the plaintext directly, which eliminates this drawback. Moreover, the AM is used as an additional private key, which enlarges the key space and further enhances the security system. However, we have noticed that one of the designed parameters in the AM has a low key sensitivity, which is fault-tolerant and is not required for precise reconstruction. Additionally, the AM is plaintext-independent, which means that the AM can be recovered first by using a pair of chosen plaintexts and the corresponding ciphertext. Based on these findings, we propose a hybrid algorithm that includes two chosen-plaintext attacks (CPAs) and a ciphertext-only attack (COA) to break the enhanced cryptosystem. Specially, CPAs with an impulse function and an arbitrarily given plaintext are proposed to retrieve two parameters in the AM. With the retrieved AM, information on the plaintext can be recovered from the corresponding ciphertext by two kinds of COAs without any knowledge of the private keys. To the best of our knowledge, this is the first time that the interference-based cryptosystem with a designed AM has been cracked successfully, which may provide potential evidence for further security improvements. Numerical simulations are carried out to validate the feasibility of the proposed attacks.
In this paper, the security of a cryptosystem based on phase truncation and a designed amplitude modulator (AM) is evaluated. In the cryptosystem, an undercover AM used as an additional key is added to modulate the amplitude information of the spectrum in the Fourier plane. Compared to the conventional phase-truncated Fourier transform (PTFT)-based cryptosystem, the security of the cryptosystem is improved by increasing the number of unknown keys. However, it is found that the designed AM is irrelative to the plaintext, and one of the parameters in the designed AM contributes less to the security enhancement of the cryptosystem due to low key sensitivity. Based on the analysis, a special attack containing two iterative processes is proposed to crack the cryptosystem, in which the known-plaintext-attack-based iterative process I with a specific normalization operator is used to retrieve the designed AM and the amplitude-phase-retrieval-technique-based iterative process II is used to retrieve the corresponding plaintext from the arbitrarily given ciphertext with the help of the retrieved AM. In addition, an inherent drawback widely existing in PTFT-based cryptosystems is reported for the first time: most information of the original image could be retrieved using two correct phase keys (or only the first phase key) generated in the encryption process, even without the corresponding ciphertext in PTFT-based cryptosystems. To address this issue, a security-enhanced cryptosystem is proposed in this paper. Numerical simulation is carried out to demonstrate the effectiveness and feasibility of the proposed attack and cryptosystem.
The optical cryptosystem based on phase-shifting interferometry (PSI) is one of the most interesting optical cryptographic schemes in recent years. However, we find that the PSI technique provides an attractive method to record the ciphertext, but contributes little to the security level of the cryptosystem. From the cryptanalysis point of view, in a certain simplified case, an attacker is only required to crack two equivalent decryption keys instead of the original random phase keys and geometric key. Moreover, a chosen-plaintext attack method is proposed, in which an impulse function is chosen as a known plaintext. By using this attack, the attacker can effectively recover any plaintext from the corresponding ciphertext. The validity of the attack is verified by computer simulations.