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IEEE photonics journal

Security Analysis on an Optical Encryption and Authentication Scheme Based on Phase-Truncation and Phase-Retrieval Algorithm

Yi Xiong, Ravi Kumar, Chenggen Quan

Published Aug 22, 2019• 20 citations
Publisher

Abstract

In this paper, the security of the cryptosystem based on phase-truncation Fourier transform (PTFT) and Gerchberg-Saxton (G-S) algorithm is analyzed. In this cryptosystem, the phase key generated using phase-truncated (PT) operation is bonded with the phase key generated in G-S algorithm to form the first private key, which improves the complexity of the first private key. In addition, since the second private key is generated using the G-S algorithm, the number of known constraints decreases compared to the traditional PTFT-based cryptosystem, which will lead the non-convergence of special attacks. However, it has been found that two private keys generated in the cryptosystem based on PTFT and G-S algorithm are related to one phase key generated in the G-S algorithm, which provides an additional constraint to retrieve the other private key when one private key is disclosed. Based on this analysis, two iterative processes with different constraints are proposed to crack the cryptosystem based on PTFT and G-S algorithm. This is the first time to report the silhouette problem existing in the cryptosystem based on PTFT and G-S algorithm. Numerical simulations are carried out to validate the feasibility and effectiveness of our analysis and proposed iterative processes.

DOI
10.1109/jphot.2019.2936236

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In this paper, the security of the cryptosystem based on phase-truncation Fourier transform (PTFT) and Gerchberg-Saxton (G-S) algorithm is analyzed. In this cryptosystem, the phase key generated using phase-truncated (PT) operation is bonded with the phase key generated in G-S algorithm to form the first private key, which improves the complexity of the first private key. In addition, since the second private key is generated using the G-S algorithm, the number of known constraints decreases compared to the traditional PTFT-based cryptosystem, which will lead the non-convergence of special attacks. However, it has been found that two private keys generated in the cryptosystem based on PTFT and G-S algorithm are related to one phase key generated in the G-S algorithm, which provides an additional constraint to retrieve the other private key when one private key is disclosed. Based on this analysis, two iterative processes with different constraints are proposed to crack the cryptosystem based on PTFT and G-S algorithm. This is the first time to report the silhouette problem existing in the cryptosystem based on PTFT and G-S algorithm. Numerical simulations are carried out to validate the feasibility and effectiveness of our analysis and proposed iterative processes.
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.
This paper presents two different aspects of cryptanalysis of the optical phase-truncated Fourier transform (PTFT)-based cryptosystem. In the first part, a comparative study is carried out for a specific attack on the PTFT-based scheme in different optical transformation domains. In the second part, a new attack algorithm is proposed. The existing attack algorithms devised for the PTFT-based cryptosystem require knowledge of both the encryption keys for successful retrieval of phase through phase-retrieval algorithms to extract information about the plaintext. The proposed new attack method eliminates the requirement of one of the encryption keys to carry out the attack on the PTFT-based scheme. The numerical results support the proposed method.
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.
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.
We propose an asymmetric cryptosystem based on a phase-truncated Fourier transform. With phase truncation in Fourier transform, one is able to produce an asymmetric ciphertext as real-valued and stationary white noise by using two random phase keys as public keys, while a legal user can retrieve the plaintext using another two different private phase keys in the decryption process. Owing to the nonlinear operation of phase truncation, high robustness against existing attacks could be achieved. A set of simulation results shows the validity of proposed asymmetric cryptosystem.