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Journal of Optics

Known-plaintext attack-free double random phase-amplitude optical encryption: vulnerability to impulse function attack

Pramod Kumar, Joby Joseph, Kehar Singh

Published Feb 28, 2012• 29 citations
Publisher

Abstract

A security enhanced double random phase-amplitude encryption (DRPAE) scheme is immune against the powerful known-plaintext attack, due to the insertion of an undercover amplitude random mask at the Fourier plane in the conventional double random phase encryption (DRPE) scheme. However, DRPAE, which nullifies the high level known-plaintext attack, is found to be susceptible to a simple impulse function attack. Information about the exact distribution of the amplitude mask as well as that of the Fourier plane random phase mask is divulged from an impulse function attack. A variant form of the impulse function attack is also able to show that the DRPAE scheme is as linear as the conventional DRPE scheme. Numerical simulation results validate the effectiveness of the simple impulse attack on the DRPAE scheme.

DOI
10.1088/2040-8978/14/4/045401

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A security enhanced double random phase-amplitude encryption (DRPAE) scheme is immune against the powerful known-plaintext attack, due to the insertion of an undercover amplitude random mask at the Fourier plane in the conventional double random phase encryption (DRPE) scheme. However, DRPAE, which nullifies the high level known-plaintext attack, is found to be susceptible to a simple impulse function attack. Information about the exact distribution of the amplitude mask as well as that of the Fourier plane random phase mask is divulged from an impulse function attack. A variant form of the impulse function attack is also able to show that the DRPAE scheme is as linear as the conventional DRPE scheme. Numerical simulation results validate the effectiveness of the simple impulse attack on the DRPAE scheme.
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.
We demonstrate a method of chosen-plaintext attack on lensless double-random phase encoding (L-DRPE) in the Fresnel domain. With this attack an opponent can access two encryption keys with help of the impulse functions as chosen plaintexts. This shows that a lensless optical encryption scheme based on DRPE is vulnerable to chosen-plaintext attack. Cryptoanalysis also indicates that the security worry originates from the linearity of the encryption and decryption mechanism of the L-DRPE scheme. One of the interesting features of the proposed attack is that the decryption process is lossless. Numerical simulations show good agreement with theoretical analysis.
In this paper, we analyze the security of the classical double random phase encoding (DRPE) technique in Fourier domain, as well as its extended schemes in Fresnel and fractional Fourier domains. These schemes are resistant to bruteforce attacks, for their large key spaces. However, due to the linearity property of their encryption transformations, they are vulnerable to other attacks, such as chosen-plaintext attack and known-plaintext attack. We successfully break each of the three encryption schemes with the help of a certain quantity of plaintext-ciphertext pairs. Each attack is validated by computer simulations. The cryptanalysis indicates that, to minimize the risks, it is recommendable to introduce nonlinear operations to optical encryption systems.
Conventional double-random phase encoding is vulnerable to a chosen or known plaintext attack owing to the linearity of the system. We introduce a technique to break down this linearity with an undercover amplitude modulation in the encryption scheme. As an additional key, this operation can significantly enhance the security of the system. A series of computer simulations have shown the effectiveness of this method and its resistance against the known plaintext attack. The design and parameter choice of the amplitude modulator is also discussed.
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.
Double random phase encoding (DRPE) is vulnerable to known-plaintext attacks (KPAs) based on phase retrieval algorithms. We previously analyzed DRPE resistance to KPA cryptanalysis with multiple known plaintext-ciphertext image pairs and obtained secret keys at a higher probability rate than when performing KPA cryptanalysis using one known image pair. However, the robustness of KPA in the presence of noise or occlusion in DRPE is unclear. We analyzed KPA properties in relation to DRPE when white Gaussian noise was gradually added to the Fourier amplitude or phase of a known ciphertext complex amplitude image. Additionally, we analyzed KPA properties when the Fourier phase of the known ciphertext image was gradually occluded by zero-valued pixels. The results showed that KPAs performed using multiple known plaintext-ciphertext image pairs were largely affected by noise added to the Fourier phase and thus are not always a strong tool for DRPE cryptanalysis.