Cryptoanalysis of multiple-image encryption scheme based on amplitude- and phase-truncation in the Fourier domain
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This paper presents a comprehensive cryptoanalysis of a multiple-image encryption scheme based on amplitude truncation (AT) and phase truncation (PT) in the Fourier domain. In contrast to the conventional single-image cryptosystem based on phase-truncated Fourier transform (PTFT), the enhanced PTFT-based cryptosystem was proposed to encode multiple images efficiently and to augment the security strength by expanding the key space. Nevertheless, we found that the amplitude key exhibits low sensitivity, which has a restricted impact on the security enhancement and makes the scheme vulnerable. Moreover, the two random phase masks (RPMs) employed as private keys are uncorrelated with the plaintexts, which can be recovered through a devised known-plaintext attack (KPA). Once these additional private keys are recovered, the number of unknown keys is reduced to two, making it possible to recover plaintext information encrypted by this advanced PTFT-based cryptosystem using an iterative attack without any knowledge of the private keys. Based on these findings, a hybrid attack consisting of two cascaded KPAs and chosen-ciphertext attacks (CCAs) is proposed to successfully crack the improved PTFT-based cryptosystem. Numerical simulations have been performed to validate the feasibility and effectiveness of the proposed hybrid attack.Keywords:
Truncation (statistics)
Fourier optics
Abstract This article focuses on hypocoristic truncation in Sardinian. Besides disyllabic truncation, hypocoristic truncation in Sardinian also yields trisyllabic truncated forms by means of a process of reduplicative prefixation (e.g., Totore ← Servatore ) and, more interestingly, a process of copy of what is analyzed as an internally layered ternary foot (e.g., (Va(tore)) ← Servatore ). In this paper we develop an OT analysis of hypocoristic truncation based on output-output correspondence relations between bases and truncated morphemes that gives further support to internally layered ternary feet in the domain of the phonology–morphology interface.
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Truncation of long-range electrostatic interactions gives rise to an excess truncation potential, Φex, that is uniform in bulk solution but varies at an interface. Predictions of a first-order theory for Φex at an interface are compared with explicit simulations of an air—water interface employing different truncation centres. The orientational structure of water and a macroscopic air—water surface potential are shown to change systematically with the truncation centre which can be attributed to Φex.
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Two truncation schemes for cranking the many-particle states of a deformed potential (including monopole pairing) are compared with some exact results. A truncation emphasizing alignment properties proves much better than a truncation which includes only the low-lying many-particle configurations at zero rotational frequency.
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Zero (linguistics)
Particle (ecology)
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The effect of surface truncation on the electromagnetic density of modes (DOM) in photonic crystals (PCs) is investigated theoretically. It shows that for PCs with surface truncation parameter τ≠0 or τ≠0.5, the DOM has asymmetric properties on the two edges of the first bandgap in normal incidence. Moreover, DOM at band edges has much larger values in the PC with appropriate truncation than that in the PC without truncation. Also, the effect of surface truncation on a band-edge laser is discussed, and the case of the oblique incident is also discussed.
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The three-dimensional imaging properties of a light microscope are traditionally described through an intensity point spread function (PSF) or its Fourier transform, the optical transfer function (OTF). However, the imaging properties can be more compactly described by a generalized two-dimensional pupil function. Use of the pupil function allows easy modification of an observed PSF to introduce known aberrations, a much more difficult task when using a PSF or OTF. Unfortunately, it is not straightforward to determine the complex-valued pupil function from the measured intensity PSF, because of the lack of phase information. This is the problem of phase retrieval. Several phase retrieval algorithms have been developed for two-dimensional imaging in astronomy. We have modified one such algorithm to be appropriate for the high-aperture, non-paraxial case of high resolution light microscopy. PSFs reconstructed from phase-retrieved pupil functions, modified by calculated aberrations closely reproduce the features of measured, aberrated PSFs.
Point spread function
Pupil function
Optical transfer function
Ptychography
Fourier optics
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Spatial frequency
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Abstract In the construction of global primitive equation models, based on the spherical harmonic method, two forms of truncation are in general use. Theoretical considerations suggest the triangular truncation method is superior, but the easily coded rhomboidal truncation is more commonly used. A verification experiment employing the Canadian Operational Spectral Model has been performed to determine if the theoretical superiority of the triangular truncation can be realized in practice. It was found that at least in the restricted case of extra‐tropical forecasts of less than 48 h, that the two truncation methods produced forecasts of equivalent accuracy.
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Harmonic
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Summary This paper considers the truncation of normal distributions by means of planes. The moment-generating function for the truncated distribution is obtained, and it is shown that, by suitable transformations, the problem reduces to the case of rectangular truncation.
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Truncated normal distribution
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Truncation of long-range electrostatic interactions gives rise to an excess truncation potential, Φex, that is uniform in bulk solution but varies at an interface. Predictions of a first-order theory for Φex at an interface are compared with explicit simulations of an air—water interface employing different truncation centres. The orientational structure of water and a macroscopic air—water surface potential are shown to change systematically with the truncation centre which can be attributed to Φex.
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Truncation error
Interface (matter)
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Truncation (statistics)
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Truncation error
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As an important inverse imaging problem in diffraction optics, Fourier phase retrieval aims at estimating the latent image of the target object only from the magnitude of its Fourier measurement. Although in real applications alternating methods are widely-used for Fourier phase retrieval considering the constraints in the object and Fourier domains, they need a lot of initial guesses and iterations to achieve reasonable results. In this paper, we show that a proper sensor mask directly attached to the Fourier magnitude can improve the efficiency of the iterative phase retrieval algorithms, such as alternating direction method of multipliers (ADMM). Furthermore, we refer to the learning-based method to determine the sensor mask according to the Fourier measurement, and unrolled ADMM is used for phase retrieval. Numerical results show that our method outperforms other existing methods for the Fourier phase retrieval problem.
Fourier optics
Phase correlation
Phase problem
Ptychography
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