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Symposium on Photonics and Optoelectronics

Improved Known-Plaintext Attack on Optical Encryption Based on Double Random Phase Encoding

Wan Qin, Xiang Peng, Xiangfeng Meng, Wenqi He

Published Jun 1, 2010• 13 citations
Publisher

Abstract

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.

DOI
10.1109/sopo.2010.5504346

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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 conventional symmetric encryption, it is common for the encryption/decryption key to be reused for multiple plaintexts. This gives rise to the concept of a known-plaintext attack. In optical image encryption systems, such as double random phase encoding (DRPE), this is also the case. With optical encryption, if one knows a plaintext-ciphertext pair, one can carry out a known-plaintext attack more efficiently than a bruteforce attack, using heuristics based on phase retrieval or simulated annealing. However, it is more likely that an attacker will find an imperfect encryption/decryption key using such heuristics. Such an imperfect key will work for the known plaintext-ciphertext pair, but not an arbitrary unseen plaintext-ciphertext pair using the original key. In this paper, we illustrate the problem and attempt to characterise the increase in security it affords optical encryption.
In conventional symmetric encryption, it is common for the encryption/decryption key to be reused for multiple plaintexts. This gives rise to the concept of a known-plaintext attack. In optical image encryption systems, such as double random phase encoding (DRPE), this is also the case; if one knows a plaintext-ciphertext pair, one can carry out a known-plaintext attack more efficiently than a brute-force attack, using heuristics based on phase retrieval or simulated annealing. However, we demonstrate that it is likely that an attacker will find an imperfect decryption key using such heuristics. Such an imperfect key will work for the known plaintext-ciphertext pair, but not an arbitrary unseen plaintext-ciphertext pair encrypted using the original key. In this paper, we illustrate the problem and attempt to characterise the increase in security it affords optical encryption.
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.
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.