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IEEE photonics journal

A Recovery Method of Double Random Phase Encoding System With a Parallel Phase Retrieval

Zhengjun Liu, Cheng Shen, Jiubin Tan, Shutian Liu

Published Feb 1, 2016• 51 citations
Publisher

Abstract

A novel method composed of phase retrieval is proposed to precisely recover the phase distribution in the double random phase encoding system. The model of a point light source is employed to illuminate the system, in the output side of which several diffracted intensity patterns are recorded in an orderly way. The phase at the output plane of the system is calculated by a parallel iterative phase retrieval algorithm with the recorded images. With the help of the reconstructed phase, the two phase masks can be determined by inverse Fourier transform. As a kind of chosen-plaintext attack, the secret image with high quality can be recovered with the proposed method.

DOI
10.1109/jphot.2016.2527699

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A novel method composed of phase retrieval is proposed to precisely recover the phase distribution in the double random phase encoding system. The model of a point light source is employed to illuminate the system, in the output side of which several diffracted intensity patterns are recorded in an orderly way. The phase at the output plane of the system is calculated by a parallel iterative phase retrieval algorithm with the recorded images. With the help of the reconstructed phase, the two phase masks can be determined by inverse Fourier transform. As a kind of chosen-plaintext attack, the secret image with high quality can be recovered with the proposed method.
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An advanced iterative phase retrieval algorithm is applied to perform a ciphertext-only attack on the fractional Fourier transform-based double random phase encryption system. With the given complex amplitude of ciphertext and definite support of the object image, the original object image can be recovered by estimating the energy of support area in the recovered image. The encryption system can be attacked by analyzing the sensibility of fractional Fourier transform order keys and evaluating the energy of the object image support area. The proposed algorithm can obtain encrypted fractional order and retrieve two random phase keys. Numerical results demonstrate the efficacy of the proposed attacking method.
This paper proposes a multiphase retrieval algorithm and then presents a secret image sharing scheme. The proposed algorithm can divide a secret image into multiple phase-only encodings (shadows) and then overcome the shadow expansion problem. When the shadows are arranged in a certain order, the light intensity detector can directly acquire the secret image using parallel light, and the recovery process is simple and easy to operate. Furthermore, Fresnel transform parameters are used for authentication, which can avoid deceit. The differences in the initial random phase encodings make the same secret image produce different shadows, which can effectively resist statistical analysis attacks. Finally, theoretical analysis and a simulation are used to verify the validity and feasibility of the proposed scheme.
The modified iterative phase retrieval algorithms developed in Part I [Guo et al., Appl. Opt.54, 4698 (2015)] are applied to perform known plaintext and ciphertext attacks on amplitude encoding and phase encoding Fourier-transform-based double random phase encryption (DRPE) systems. It is shown that the new algorithms can retrieve the two random phase keys (RPKs) perfectly. The performances of the algorithms are tested by using the retrieved RPKs to decrypt a set of different ciphertexts encrypted using the same RPKs. Significantly, it is also shown that the DRPE system is, under certain conditions, vulnerable to ciphertext-only attack, i.e., in some cases an attacker can decrypt DRPE data successfully when only the ciphertext is intercepted.
The security of the encryption and verification techniques with significant output images is examined by a known-plaintext attack. We introduce an iterative phase-retrieval algorithm based on multiple intensity measurements to heuristically estimate the phase key in the Fourier domain by several plaintext-cyphertext pairs. We obtain correlation output images with very low error by correlating the estimated key with corresponding random phase masks. Our studies show that the convergence behavior of this algorithm sensitively depends on the starting point. We also demonstrate that this algorithm can be used to attack the double random phase encoding technique.
A novel hierarchical image encryption system based on cascaded multiple-phase retrieval by an iterative Fresnel-transform algorithm is proposed. In this method a series of phase masks cascaded in free space is employed to retrieve different target hidden images in their corresponding hierarchical levels. It can realize different levels of accessibility to the secret data for different authority levels with the same system, and the higher level authority can get access to more hidden images. This approach can achieve fast convergence and high quality of the recovered images without any recognizable cross-talk noise or distortion, and the security level of this system is further enhanced by the use of a series of supplemental keys such as the orders of cascaded phase masks and the geometrical parameters in addition to all the iterated phase masks as principal keys. The feasibility of this method and its unique features are verified and analysed by computer simulations.