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Journal of Optics

Double random phase encoding using phase reservation and compression

Wen Chen, Xudong Chen

Published Jan 22, 2014• 75 citations
Publisher

Abstract

In recent years, various studies have been conducted to illustrate the vulnerability of double random phase encoding (DRPE). In this paper, we propose a novel method via phase reservation and compression to enhance DRPE security. Only a compressed phase distribution is available in the CCD plane, and the amplitude component is not available or requested for optical decryption. Since only noise-like distributions can be obtained by using the correct security keys during optical decryption, a nonlinear correlation algorithm is further applied for authenticating the decrypted image. It is demonstrated that valid conditions for attack algorithms are broken and high security can be achieved for the DRPE system.

DOI
10.1088/2040-8978/16/2/025402

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In recent years, various studies have been conducted to illustrate the vulnerability of double random phase encoding (DRPE). In this paper, we propose a novel method via phase reservation and compression to enhance DRPE security. Only a compressed phase distribution is available in the CCD plane, and the amplitude component is not available or requested for optical decryption. Since only noise-like distributions can be obtained by using the correct security keys during optical decryption, a nonlinear correlation algorithm is further applied for authenticating the decrypted image. It is demonstrated that valid conditions for attack algorithms are broken and high security can be achieved for the DRPE system.
Although initial research shows that double-random phase encoding (DRPE) is vulnerable to known-plaintext attacks that use phase retrieval algorithms, subsequent research has shown that phase-only DRPE, in which the Fourier amplitude component of an image encrypted with classical DRPE remains constant, is resistant to attacks that apply phase retrieval algorithms. Herein, we numerically analyze the key-space of DRPE and investigate the distribution property of decryption keys for classical and phase-only DRPE. We determine the difference in the distribution property of successful decryption keys for these DRPE techniques from the numerical analysis results and then discuss the security offered by them.
We investigate a full phase based photon-counting double-random-phase encryption (PC-DRPE) method. A photon-counting technique is applied during the encryption process creating sparse images. The statistical distribution of the photon-counting decrypted data for full phase encoding and amplitude phase encoding are derived and their statistical parameters are used for authentication. The performance of the full phase PC-DRPE is compared with the amplitude-based PC-DRPE method. The photon-counting decrypted images make it difficult to visually authenticate the input image; however, advanced correlation filters can be used to authenticate the decrypted images given the correct keys. Initial computational simulations show that the full phase PC-DRPE has the potential to require fewer photons for authentication than the amplitude-based PC-DRPE.\nIn addition, we propose an optical security method for object authentication using photon-counting encryption implemented with phase encoded QR codes. By combining the full phase double-random-phase encryption with photon-counting imaging method and applying an iterative Huffman coding technique, we are able to encrypt and compress an image containing primary information about the object. This data can then be stored inside of an optically phase encoded QR code for robust read out, decryption, and authentication. The optically encoded QR code is verified by examining the speckle signature of the optical masks using statistical analysis. Optical experimental results are presented to demonstrate the performance of the system. In addition, experiments with a commercial Smartphone to read the optically encoded QR code are presented. To the best of our knowledge, this is the first report on integrating photon-counting security with optically phase encoded QR codes.
We investigate a full-phase-based photon-counting double-random-phase encryption (PC-DRPE) method. A PC technique is applied during the encryption process, creating sparse images. The statistical distribution of the PC decrypted data for full-phase encoding and amplitude-phase encoding are derived, and their statistical parameters are used for authentication. The performance of the full-phase PC-DRPE is compared with the amplitude-based PC-DRPE method. The PC decrypted images make it difficult to visually authenticate the input image; however, advanced correlation filters can be used to authenticate the decrypted images given the correct keys. Initial computational simulations show that the full-phase PC-DRPE has the potential to require fewer photons for authentication than the amplitude-based PC-DRPE.
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.
Double random phase encoding (DRPE) is a classical optical symmetric-key encryption method. DRPE prevents the key length from being determined because of its redundancy between encryption and decryption, unlike digital symmetric-key cryptographies. In our study, we numerically analyzed the key length of DRPE based on key-space analysis. We estimated the key length of DRPE by calculating the inverse value of the cumulative probability of the normal distribution that was estimated from samples of DRPE and then discuss security against brute-force attacks.
In this paper, we develop a new optical information authentication system based on compressed double-random-phase-encoded images and quick-response (QR) codes, where the parameters of optical lightwave are used as keys for optical decryption and the QR code is a key for verification. An input image attached with QR code is first optically encoded in a simplified double random phase encoding (DRPE) scheme without using interferometric setup. From the single encoded intensity pattern recorded by a CCD camera, a compressed double-random-phase-encoded image, i.e., the sparse phase distribution used for optical decryption, is generated by using an iterative phase retrieval technique with QR code. We compare this technique to the other two methods proposed in literature, i.e., Fresnel domain information authentication based on the classical DRPE with holographic technique and information authentication based on DRPE and phase retrieval algorithm. Simulation results show that QR codes are effective on improving the security and data sparsity of optical information encryption and authentication system.