Fault tolerance properties of a double phase encoding encryption technique

Javidi, Bahram; Sergent, Arnaud; Zhang, Guanshen; Guibert, Laurent

doi:10.1117/1.601144

Cited by 131 publications

(51 citation statements)

References 6 publications

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“…The result is then convolved with the function . The encrypted function is complex, with amplitude and phase, and is given by the following expression: (2) where the symbol ( ) denotes convolution. The encrypted function in (2) has a noise-like appearance that does not reveal the content of the primary image.…”

Section: The Drpementioning

confidence: 99%

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Optical Image Encryption Based on Chaotic Baker Map and Double Random Phase Encoding

Elshamy

Rashed

Mohamed

et al. 2013

J. Lightwave Technol.

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This paper presents a new technique for optical image encryption based on chaotic Baker map and Double Random Phase Encoding (DRPE). This technique is implemented in two layers to enhance the security level of the classical DRPE. The first layer is a pre-processing layer, which is performed with the chaotic Baker map on the original image. In the second layer, the classical DRPE is utilized. Matlab simulation experiments show that the proposed technique enhances the security level of the DRPE, and at the same time has a better immunity to noise. The first layer is a pre-processing layer, which is performed with the chaotic Baker map on the original image. In the second layer, the classical DRPE is utilized. Matlab simulation experiments show that the proposed technique enhances the security level of the DRPE, and at the same time has a better immunity to noise.

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Section: The Drpementioning

confidence: 99%

“…Among them, the most widely used and highly successful optical encryption scheme is the DPRE proposed by Refregier and Javidi [1]. This method uses two random phase masks, one in the input plane and the other in the Fourier plane, to encrypt the primary image into stationary white noise [1], [2].…”

Section: Introductionmentioning

confidence: 99%

Optical Image Encryption Based on Chaotic Baker Map and Double Random Phase Encoding

Elshamy

Rashed

Mohamed

et al. 2013

J. Lightwave Technol.

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“…Complex-valued data, when represented on a SLM with a discrete number of levels, leads to quantisation errors. For a double random phase encoding system, 10 Javidi et al 24 and Goudail et al 25 have studied how encrypted image perturbations affect the decrypted image. Treatments of quantisation in holograms can be found in the literature, 26,27 and quantisation of real-valued 28 and complex-valued 29-32 digital holograms, including encrypted digital holograms, has been studied in the context of data compression.…”

Section: 17mentioning

confidence: 99%

<title>Capture, encryption, compression, and display of digital holograms of three-dimensional objects</title>

et al. 2006

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Digital holography can be used to capture the whole Fresnel field from a reflective or transmissive object. Applications include imaging and display of three-dimensional (3D) objects, and encryption and pattern recognition of two-dimensional (2D) and 3D objects. Often, these optical systems employ discrete spatial light modulators (SLMs) such as liquid-crystal displays. In the 2D case, SLMs can encode the inputs and keys during encryption and decryption. For 3D processing, the SLM can be used as part of an optical reconstruction technique for 3D objects, and can also represent the key during encryption and decryption. However, discrete SLMs can represent only discrete levels of data necessitating a quantisation of continuous valued analog information. To date, many such optical systems have been proposed in the literature, yet there has been relatively little experimental evaluation of the practical performance of discrete SLMs in these systems. In this paper, we characterise conventional phase-modulating liquid-crystal devices and examine their limitations (in terms of phase quantisation, alignment tolerances, and nonlinear response) for the encryption of 2D and 3D data. Finally, we highlight the practical importance of a highly controlled discretisation (optimal quantisation) for compression of digital holograms.

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“…If the two phase keys are generated by using statistically independent white noises, then the encrypted image is also stationary white noise. Since its introduction in 1995, the DRPE has generated much interest and has been the focus of many studies [14][15][16][17][18][19][20][21]. The physical implementation of such an optical system gives rise to many practical issues; however, a thorough analysis of the DRPE technique itself is extremely important if it is to be utilized.…”

Section: Introductionmentioning

confidence: 99%

Statistical investigation of the double random phase encoding technique

et al. 2009

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The amplitude-encoding case of the double random phase encoding technique is examined by defining a cost function as a metric to compare an attempted decryption against the corresponding original input image. For the case when a cipher-text pair has been obtained and the correct decryption key is unknown, an iterative attack technique can be employed to ascertain the key. During such an attack the noise in the output field for an attempted decryption can be used as a measure of a possible decryption key's correctness. For relatively small systems, i.e., systems involving fewer than 5 ϫ 5 pixels, the output decryption of every possible key can be examined to evaluate the distribution of the keys in key space in relation to their relative performance when carrying out decryption. However, in order to do this for large systems, checking every single key is currently impractical. One metric used to quantify the correctness of a decryption key is the normalized root mean squared (NRMS) error. The NRMS is a measure of the cumulative intensity difference between the input and decrypted images. We identify a core term in the NRMS, which we refer to as the difference parameter, d. Expressions for the expected value (or mean) and variance of d are derived in terms of the mean and variance of the output field noise, which is shown to be circular Gaussian. These expressions assume a large sample set (number of pixels and keys). We show that as we increase the number of samples used, the decryption error obeys the statistically predicted characteristic values. Finally, we corroborate previously reported simulations in the literature by using the statistically derived expressions.

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Fault tolerance properties of a double phase encoding encryption technique

Cited by 131 publications

References 6 publications

Optical Image Encryption Based on Chaotic Baker Map and Double Random Phase Encoding

Optical Image Encryption Based on Chaotic Baker Map and Double Random Phase Encoding

<title>Capture, encryption, compression, and display of digital holograms of three-dimensional objects</title>

Statistical investigation of the double random phase encoding technique

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