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Acta Physica Sinica

Known-plaintext attack on double phase encoding encryption technique

Peng Xiang, Peng Zhang, Wei Heng-Zheng, Bin Yu, (1)深圳大学光电子学研究所，教育部光电子器件与系统重点实验室，深圳 518060; (2)深圳大学光电子学研究所，教育部光电子器件与系统重点实验室，深圳 518060;天津大学精密测试技术及仪器国家重点实验室，天津 300072; (3)天津大学精密测试技术及仪器国家重点实验室，天津 300072

Published Jan 1, 2006• 14 citations
Publisher

Abstract

In the field of optical information security, the most attractive work is the so-called double-random-phase encoding encryption scheme proposed by Javidi. However, the security of this cryptosystem has not been analyzed thoroughly from the point of view of cryptoanalysis. In this article, the weakness of Javidi's optical security system is carefully analyzed with a known-plain text attack. It is shown that the double-random-phase encoding encryption scheme is a linear symmetric block cipher cryptosystem and its linearity opens avenues of attacks. Under the known-plaintext attack, attacker can obtain the phase key(s) in the input plane using the typical phase retrieval algorithms and subsequently deduce the phase key(s) in the Fourier domain easily. In addition, an optical implementation of known-plain text attack is also proposed.

DOI
10.7498/aps.55.1130

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In the field of optical information security, the most attractive work is the so-called double-random-phase encoding encryption scheme proposed by Javidi. However, the security of this cryptosystem has not been analyzed thoroughly from the point of view of cryptoanalysis. In this article, the weakness of Javidi's optical security system is carefully analyzed with a known-plain text attack. It is shown that the double-random-phase encoding encryption scheme is a linear symmetric block cipher cryptosystem and its linearity opens avenues of attacks. Under the known-plaintext attack, attacker can obtain the phase key(s) in the input plane using the typical phase retrieval algorithms and subsequently deduce the phase key(s) in the Fourier domain easily. In addition, an optical implementation of known-plain text attack is also proposed.
Security analysis of optical encryption system based on double random phase encoding indicates that the system can be classified as a linear symmetric block-cipher cryptosystem, which may lead to a great vulnerability. Under the ciphertext-only attack (COA), an opponent can attack such a cryptosystem only on the basis of estimated support of wave function in the object plane with iterative phase retrieval methods, and subsequently deduce the phase keys in the Fourier plane easily. The ciphertext-only attack (COA) requires much less resources than other types of attacks. Estimated support of wave function in the object plane could have some translations relative to the true support, so retrieved wave function could also have translations in both the amplitude and the phase, leading to a translation of retrieved plaintext relative to original plaintext. However, attackers can take this translation as a priori knowledge to traverse estimated support in the object plane until finding the best estimated keys, which bring about the best decryption quality.
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.
This paper analysis the security of the optical encryption scheme based on the classical double random phase encoding. We describe a known-plaintext attack which can be used to successfully access the encryption key with the pre-knowledge of only one arbiturary pair of known plaintext-ciphertext. A phase retrieval algorithm is employed in this attack. Computer simulations are made to demonstrate the effectiveness. The results show that even implementing only one round of iteration in the phase retrieval, an attacker can obtain a clear decoded plaintext (a gray-scale image) from an intercept ciphertext.
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 of an optical cryptosystem based on double random phase encoding (DRPE) with perfect forward secrecy (PFS) is analyzed for a particular session. In the cryptosystem, the PFS strategy is utilized to enhance the security and key management of the traditional DRPE scheme. Our analysis reveals that the use of PFS has certain advantages in the key management approach, but the method is still vulnerable against modified plaintext attacks when the attack is performed in the same session. Also, it is noted that the method is safe against conventional plaintext attacks, but it is vulnerable to the modified chosen and known plaintext attacks. The original plaintext can be easily retrieved with the proposed attack algorithms. Numerical simulation results are presented to validate the effectiveness of the proposed attack algorithms.