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Optics Letters

Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain

Xiang Peng, Hengzheng Wei, Peng Zhang

Published Oct 26, 2006• 472 citations
Publisher

Abstract

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.

DOI
10.1364/ol.31.003261

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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.
This paper analyzes the security of double random phase encoding in fresnel domain from the viewpoint of cryptoanalysis. We demonstrate the encryption system is vulnerable to chosen-plaintext attack with a prior knowledge of diffraction distance and wavelength. With this attack an opponent can access double random phase keys with the help of the impulse functions as chosen plaintext. The significant feature of 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.
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.