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Optics Letters

Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask

Xiaogang Wang, Daomu Zhao

Published Sep 12, 2013• 82 citations
Publisher

Abstract

We propose a simple amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask (RAM). The RAM that is not saved during the encryption provides extremely high security for the two private keys, and no iterative calculations are involved in the nonlinear encryption process. Lack of enough constraints makes the specific attack based on iterative amplitude-phase retrieval algorithms unusable. Numerical simulation results are given for testing the validity and security of the proposed approach.

DOI
10.1364/ol.38.003684

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We propose a simple amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask (RAM). The RAM that is not saved during the encryption provides extremely high security for the two private keys, and no iterative calculations are involved in the nonlinear encryption process. Lack of enough constraints makes the specific attack based on iterative amplitude-phase retrieval algorithms unusable. Numerical simulation results are given for testing the validity and security of the proposed approach.
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.
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.
Amplitude-phase retrieval attack (APRA) imposes serious threat upon the asymmetric security system cryptosystems based on equal modulus decomposition (EMD). To resolve that security threat, an APRA free asymmetric cryptosystem based on EMD is proposed by using one random amplitude mask AM and one random phase mask PM, where AM is treated as the private key and PM is treated as the public key. First, AM and PM are input into an optical interference architecture to generate two phase masks. Then, encrypting the plaintext results in one complex-valued cyphertext via EMD with the two-phase masks generated in the first step. This proposed cryptosystem is asymmetric, in which the encryption process is conducted digitally without iteration computation and the decryption procedure are simply accomplished using digital or optical methods. Moreover, constraints are decreased so that APRA does not work for this cryptosystem. Results of the simulation are displayed to verify the suggested cryptosystem's security and feasibility.
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.
A new nonlinear optical image encryption scheme based on a modified amplitude phase retrieval algorithm is proposed. With two random phase masks that serve as the public encryption keys, one iterative amplitude and phase retrieval process is employed to encode the primary image into a stationary white noise. The two private keys generated in the encryption process are randomly distributed binary matrices to be used to perform one-way binary phase modulations. The proposed encryption process is nonlinear and offers enhanced security. Numerical simulations are presented to demonstrate the feasibility and security of the proposed system. The results also illustrate that the computing efficiency of the algorithm is improved and the number of iterations is much less than that of cryptosystem based on Yang-Gu algorithm, which has two iteration processes.
We propose a double image encryption approach based on a hybrid phase-truncation scheme. This approach is realized by spatial and Fresnel encoding, where two plaintexts are encrypted by a random amplitude mask into two private key masks and one ciphertext mask. The random amplitude mask is introduced to break the functional relation of the plaintexts to the ciphertext. Compared with other reported phase-truncation-based techniques, the proposed hybrid scheme is not only free from information leakage but also resistant to several different types of attacks. In addition, the parameters of the Fresnel transform and discrete multiple parameter fractional Fourier transform serve as additional keys to strengthen security significantly. Numerical simulations and a performance analysis are conducted to demonstrate the reliability and validity of the proposed approach.