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In this paper, we investigate the geodesic motion and scalar perturbations of the Ay\'on-Beato-Garc\'ia (ABG) black hole (BH) coupled with a cloud of strings (CS). By employing the effective potential approach, we analyze the trajectories of massless and massive test particles around this regular BH solution. The interplay between nonlinear electrodynamics (NLED) and CS significantly modifies the spacetime geometry, resulting in distinct dynamical properties for test particles. The behavior of null and timelike geodesics, including their stability and escape conditions, is thoroughly examined. In addition to the geodesic analysis, we study scalar perturbations by deriving the Klein-Gordon equation for massless scalar fields in this spacetime. The resulting Schr\"odinger-like wave equation reveals an effective potential that depends intricately on the NLED and CS parameters. Furthermore, we compute the greybody factors (GFs) to explore the energy transmission and absorption properties of theBH. Our results demonstrate that the NLED parameter $g$ and the CS parameter $\alpha$ play pivotal roles in modulating the GFs, influencing the energy spectrum of scalar radiation. These results provide significant understanding of the observational characteristics of the ABG NLED-CS BH in astrophysical contexts., Comment: 23 pages, 20 figures, 1 table

From an astrophysical perspective, the composition of black holes (BHs), dark matter (DM), and dark energy can be an intriguing physical system. In this study, we consider Schwarzschild BHs embedded in a Dehnen-type DM halo exhibiting a quintessential field. This study examines the horizons, shadows, deflection angle, and quasinormal modes (QNMs) of the effective BH spacetime and how they are affected by the dark sector. The Schwarzschild BH embodied in a Dehnen-type DM halo exhibiting a quintessential field possesses two horizons: the event horizon and the cosmological horizon. We demonstrate that all dark sector parameters increase the event horizon while decreasing the cosmological horizon. We analyze the BH shadow and emphasize the impact of DM and quintessence parameters on them. We show that the dark sector casts larger shadows than a Schwarzschild BH in a vacuum. Further, we delve into the weak gravitational lensing deflection angle using the Gauss-Bonnet theorem (GBT). We then investigate QNMs using the 6th order WKB approach. To visually underscore the dark sector parameters, we present figures that illustrate the impact of varying the parameters of the Dehnen-type DM halo as well as quintessence. Our findings show that the gravitational waves emitted from BHs with a dark sector have a lower frequency and decay rate compared to those emitted from BHs in a vacuum., Comment: It is to be published in Chinese Physics C

This paper investigates scalar perturbations and quasinormal modes (QNMs) associated with cylindrical black holes constructed within the frameworks of $f(\mathcal{R})$-gravity and Ricci-Inverse ($\mathcal{RI}$) gravity. Moreover, we study the modified Hawking radiation in these black hole solutions and analyze the effects of coupling constants. These modified theories, which extend general relativity by introducing higher-order curvature corrections and additional geometric terms, provide a rich platform for exploring deviations from standard gravitational physics. The study begins by revisiting the cylindrical black holes in these modified gravity theories, where the effective cosmological constants respectively, are represented by $\Lambda_m^{f(\mathcal{R})}$ and $\Lambda_m^{\mathcal{RI}}$ related to the coupling constants unique to each framework. Afterwards, the QNMs, intrinsic damped oscillations of the black hole space-time, are analyzed to probe the stability of the system, with the effective potential $V$ revealing the impact of the modified gravity parameters. Additionally, the thermodynamic properties of the black holes are examined through the lens of the Generalized Uncertainty Principle (GUP), which introduces quantum corrections to Hawking radiation. The GUP-modified Hawking temperature and entropy are derived, demonstrating significant deviations from classical results and highlighting the quantum gravitational effects in these modified frameworks. By linking QNMs, thermodynamics, and quantum corrections, this work not only deepens the understanding of modified gravity theories but also offers potential observational pathways to test their validity., Comment: 26 pages, 8 figures

In this paper, we consider a static spherically symmetric black hole (BH) embedded in a Dehnen-(1,4,0) type dark matter (DM) halo in the presence of a cloud string. We examine and present data on how the core density of the DM halo parameter and the cloud string parameter affect BH attributes such as quasinormal modes (QNMs) and shadow cast. To do this, we first look into the effective potential of perturbation equations for three types of perturbation fields with different spins: massless scalar field, electromagnetic field, and gravitational field. Then, using the 6th order WKB approximation, we examine quasinormal modes of the BH disturbed by the three fields and derive quasinormal frequencies. The changes of QNM versus the core density parameter and the cloud string parameter for three disturbances are explored. We also investigate how the core density and the cloud string parameters affect the photon sphere and shadow radius. Interestingly, the study shows that the influence of Dehnen type DM and cloud string increases both photon spheres and shadow radius. Finally, we employ observational data from Sgr $A{^\star}$ and $M87{^\star}$ to set limitations on the BH parameters.

In this paper, we investigate the geodesic motion of test particles in the spacetime surrounding a static, spherically symmetric black hole, which is described by an AdS-Schwarzschild-like metric and incorporates a quantum correction. This black hole also features phantom global monopoles, which modify the structure of the black hole space-time. We begin by deriving the effective potential governing the motion of test particles in this system and carefully analyze the impact of quantum correction in the presence of both phantom and ordinary global monopoles. Furthermore, we extend our study to include the spin-dependent Regge-Wheeler (RW) potential, which characterizes the dynamics of perturbations in this quantum-corrected black hole background. By examining this RW potential for various spin fields, we show how quantum corrections affect its form in the presence of both phantom and ordinary global monopoles. Our analysis demonstrate that quantum correction significantly alter the nature of the RW-potential, influencing the stability, and behavior of test particles and perturbations around the black hole., Comment: 24 pages, 17 Figures

This paper aims to explore the quasinormal modes (QNMs) and effective potential profiles of massless and rotating BTZ black holes within the frameworks of $f(\mathcal{R})$ and Ricci-Inverse ($\mathcal{RI}$) modified gravity theories, which, while producing similar space-time structures, exhibit variations due to distinct cosmological constants, $\Lambda_m$. We derive wave equations for these black hole perturbations and analyze the behavior of the effective potential $V_{\text{eff}}(r)$ under different values of mass $m$, cosmological constant $\Lambda_m$, and modified gravity parameters $\alpha_1$, $\alpha_2$, $\beta_1$, $\beta_2$, and $\gamma$. The findings indicate that increasing mass and parameter values results in a raised potential barrier, implying stronger confinement of perturbations and impacting black hole stability. Incorporating the generalized uncertainty principle, we also study its effect on the thermodynamics of rotating BTZ black holes, demonstrating how GUP modifies black hole radiation, potentially observable in QNM decay rates. Additionally, we investigate the motion of particles through null and timelike geodesics in static BTZ space-time, observing asymptotic behaviors for null geodesics and parameter-dependent shifts in potential for timelike paths. The study concludes that modified gravity parameters significantly influence QNM frequencies and effective potential profiles, offering insights into black hole stability and suggesting that these theoretical predictions may be tested through gravitational wave observations., Comment: 28 pages and 10 Figures

In this paper, we derive a novel Schwarzschild-like black hole (BH) solution describing a static and asymptotically flat BH surrounded by a dark matter (DM) halo with a Dehnen-type density distribution in the surrounding environment. We investigate the properties of the obtained BH by studying the curvature properties and energy conditions in Einstein gravity. Furthermore, we explore the features of a novel Schwarzschild-like BH embedded in a DM halo with Dehnen-type density profile by analyzing the timelike geodesics of particles along with BH observable properties., Comment: 20 pages, 7 captioned figures

The notion that collaborative machine learning can ensure privacy by just withholding the raw data is widely acknowledged to be flawed. Over the past seven years, the literature has revealed several privacy attacks that enable adversaries to extract information about a model's training dataset by exploiting access to model parameters during or after training. In this work, we study privacy attacks in the gray-box setting, where the attacker has only limited access - in terms of view and actions - to the model. The findings of our investigation provide new insights for the development of privacy-preserving collaborative learning solutions. We deploy SmartCryptNN, a framework that tailors homomorphic encryption to protect the portions of the model posing higher privacy risks. Our solution offers a trade-off between privacy and efficiency, which varies based on the extent and selection of the model components we choose to protect. We explore it on dense neural networks, where through extensive evaluation of diverse datasets and architectures, we uncover instances where a favorable sweet spot in the trade-off can be achieved by safeguarding only a single layer of the network. In one of such instances, our approach trains ~4 times faster compared to fully encrypted solutions, while reducing membership leakage by 17.8 times compared to plaintext solutions., Comment: 19 pages, 7 figures, in submission

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb-Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge ($Q$) and the Lorentz-violating parameter ($b$) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., $a/M \sim 1$ thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both $b$ and $Q$ increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters $b$ and $Q$. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss-Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

We investigate shadows, deflection angle, quasinormal modes (QNMs), and sparsity of Hawking radiation of the Schwarzschild string cloud black hole's solution after applying quantum corrections required by the Generalised Uncertainty Principle (GUP). First, we explore the shadow's behaviour in the presence of a string cloud using three alternative GUP frameworks: linear quadratic GUP (LQGUP), quadratic GUP (QGUP), and linear GUP. We then used the weak field limit approach to determine the effect of the string cloud and GUP parameters on the light deflection angle, with computation based on the Gauss-Bonnet theorem. Next, to compute the quasinormal modes of Schwarzschild string clouds incorporating quantum correction with GUP, we determine the effective potentials generated by perturbing scalar, electromagnetic and fermionic fields, using the sixth-order WKB approach in conjunction with the appropriate numerical analysis. Our investigation indicates that string and linear GUP parameters have distinct and different effects on QNMs. We find that the greybody factor increases due to the presence of string cloud while the linear GUP parameter shows the opposite. We then examine the radiation spectrum and sparsity in the GUP corrected black hole with the cloud of string framework, which provides additional information about the thermal radiation released by black holes. Finally, our inquiries reveal that the influence of the string parameter and the quadratic GUP parameter on various astrophysical observables is comparable, however the impact of the linear GUP parameter is opposite., Comment: 32 pages, 7 tables, 14 captioned figures. Accepted for publication in Eur. Phys. J. C

This article considers a static and spherical black hole (BH) in f(Q) gravity. f(Q) gravity is the extension of symmetric teleparallel general relativity, where both curvature and torsion are vanishing, and gravity is described by nonmetricity. In this study, we investigate the possible implications of quasinormal modes (QNM) modified Hawking spectra, and deflection angles generated by the model. The WKB method is used to solve the equations of motion for massless Dirac perturbation fields and explore the impact of the nonmetricity parameter ($Q_{0}$). Based on the QNMs computation, we can ensure that the BH is stable against massless Dirac perturbations and as $Q_{0}$ increases the the oscillatory frequency of the mode decrease. We then discuss the weak deflection angle in the weak field limit approximation. We compute the deflection angle up to the fourth order of approximation and show how the nonmetricity parameter affects it. We find that the $Q_{0}$ parameter reduces the deflection angle.

The purpose of this study is to investigate the quasinormal modes (QNMs), greybody factors (GFs) and shadows in a plasma of a black hole (BH) surrounded by an exotic fluid of quintessence type in a scalar-vector-tensor modified gravity. The effects of a quintessence scalar field and the modified gravity (MOG) field on the QNM, GF, and shadow are examined. Using the sixth-order WKB approach, we investigate the QNMs of massless scalar and electromagnetic perturbations. Our findings show that as the quintessence and the MOG parameter ($\epsilon$ and $\alpha$) increase, the oscillation frequencies decrease significantly. Gravitational wave damping, on the other hand, decreases with increasing $\epsilon$ and $\alpha$. In addition, we obtain an analytical solution for the transmission coefficients (GF) and demonstrate that more thermal radiation reaches the observer at spatial infinity as both the $\epsilon$ and $\alpha$ parameters increase. We also investigate the effect of the plasma background on the BH shadow and show that as the plasma background parameter increases, the shadow radius slightly shrinks. Nevertheless, the shadow radius increases as $\alpha$ and $\epsilon$ increase. Particularly intriguing is the fact that increasing $\epsilon$ has a greater impact on the shadow radius than increasing $\alpha$, indicating that the quintessence parameter has a greater impact than the MOG parameter.

A hairy black hole (HBH) emerges due to matter surrounding the Schwarzschild metric when using the Extended Gravitational Decoupling (GD) approach. The fermionic greybody factors (GFs) and quasinormal modes (QNMs) as well as Hawking spectra and sparsity of HBH solutions are investigated. We consider massive and massless spin- 1/2 fermions, along with massless spin- 3/2 fermions. The equations of the effective potential for fermions with different spins are derived in HBH spacetime. Then, the rigorous bound method is used to calculate the fermionic spin- 1/2 and spin- 3/2 GFs. With the time domain integration method at our disposal, we illustrate the impact of additional parameters on the ringdown waveform of the massless fermionic spin -1/2 and spin -3/2 fields and, in turn, on their quasinormal modes. We then delve into investigating the Hawking spectra and sparsity of the radiation emitted by an HBH. Hairy parameters significantly affect the sparsity of Hawking radiation as well. We observe that the total power emitted by the BH increases both with $\alpha$ and $Q$ but decreases with $l_{0}$. Our study conclusively shows the significant impact of the additional parameters on important astrophysical phenomena such as quasinormal modes, Hawking spectra, and sparsity.

In this paper, we study the dynamics of a test particle around a regular black hole (BH) in a non-minimal Einstein Yang Mills (EYM) theory and examine the BH shadow. The EYM theory is a non-minimally coupled theory in which curvature couples to non-Abelian gauge fields. We investigate particle motion with parameters in EYM BH for massless and massive particles. This work provides the horizon structure, photon radius and inner stable circular orbit (ISCO) of a mass particle with EYM BH parameters. An analysis is provided of the effective potential as well as the possible orbits for test particles under various EYM BH parameters values. In timelike radial geodesics, we find that for smaller values of magnetic charge, particles following a timelike radial geodesic are hastier in EYM BH, and hence arrive at the center faster than those traveling a Schwarzschild BH geodesic. However, at larger values of the magnetic charge, the inverse effect is observed. The effect of model parameters is investigated in order to study the ISCO, photon radius, orbit stability (Lyapunov exponent), and effective force on particles for the BH in the EYM theory. Finally, we investigate the BH shadow. We find that higher magnetic charge values and non-minimal coupling parameters result in smaller shadow radius values.

In this manuscript, we delve into an analytic and numerical probe of shadow with different accretion models, quasinormal modes, Hawking radiation, and gravitational lensing to study observational impacts of quantum effect introduced throughh linear-quadratic GUP(LQG). Our investigation reveals that the shadows of LQG modified black holes are smaller and brighter than Schwarzschild black holes. To examine the impact of the quantum correction on the quasinormal mode, linear-quadratic GUP modified black holes are explored under scalar and electromagnetic field perturbation. Here, linear-quadratic GUP is used to capture quantum corrections. It is observed that the incorporation of quantum correction by linear-quadratic GUP alters the singularity structure of the black hole. To compute the quasinormal modes of this linear-quadratic GUP-inspired quantum-corrected black holes, we compute the effective potential generated under the perturbation of scalar and electromagnetic field, and then we use the sixth-order WKB approach in conjunction with the appropriate numerical analysis. We find that the greybody factor decreases with the GUP parameter $\alpha$ implying that the probability of transmission decreases with the GUP parameter. The total power emitted by LQG modified black hole is found to be greater than that emitted by Schwarzschild black hole. Finally, we study weak gravitational lensing and make a comparison with quadratic GUP and linear GUP modified black holes.

We investigate the impact of the modified gravity (MOG) field and the quintessence scalar field on horizon evolution, black hole (BH) shadow and the weak gravitational lensing around a static spherically symmetric BH. We first begin to write the BH metric associated with the MOG parameter and quintessence scalar field. We then determine the BH shadow and obtain numerical solutions for the photon sphere and shadow radius. We show that the MOG ($\alpha$) and the quintessence ($c$) parameters have a significant impact on BH shadow and photon sphere. Based on the analysis, we further show that the combined effects of the MOG parameter and quintessential field can increase the values of BH shadow and photon sphere radii. We also obtain constraints on the BH parameters by applying the observational data of Sgr A$^{\star}$ and M87$^{\star}$. Finally, we consider the weak deflection angle of BH within the context of the Gauss-Bonnet theorem (GBT) and show that the combined effects of the MOG and quintessence parameters do make the value of the deflection angle grow, referring to remarkable property being in well agreement with the physical meaning of both parameters that can maintain the strong gravitational field in the surrounding environment of BH., Comment: 14 pages, 2 tables, 9 captioned figures

In this paper, we investigate the optical properties of a charged black hole in Einstein-Maxwell-scalar (EMS) theory. We evaluate the shadow cast by the black hole and obtain analytical solutions for both the radius of the photon sphere and the shadow radius. We observe that the black hole parameters $\gamma$ and $\beta$ both influence the shadow of black hole. It is shown that the photon sphere and the shadow radius increase as a consequence of the presence of parameter $\gamma$. Interestingly, we show that shadow radius decreases first and then remains unchanged due to the impact of parameter $\beta$. Finally, we consider the weak gravitational lensing and the total magnification of lensed images around black hole. We find that the black hole charge and parameter $\beta$ both give rise to a significant effect, reducing the deflection angle. Similarly, the same behavior for the total magnification is observed due to the effect of black hole charge and parameter $\beta$., Comment: 9 pages, one table, 9 captioned figures, Accepted for publication in Chinese Physics C

We investigate the behavior of the regular modified gravity (MOG) static spherically symmetric black hole (BH) under massless scalar perturbation, gravitational perturbation, and massless Dirac perturbation. The dimensionless parameter $\left( \alpha \right) $ distinguishes this BH from a Schwarzschild BH. We derive the effective potential equations for three perturbations in the regular MOG BH. Using the derived potentials, we calculate the bounds of greybody factors (GFs). Next, we investigate the quasinormal mode (QNM) of the MOG BH by implementing the WKB method of sixth order. By analyzing the influence of the MOG parameter $\alpha $ for the BH we study on GF and QNM, we found that as $\alpha $ increases, the GFs increase proportionally. However, both gravitational wave oscillation frequency and damping decrease as $\alpha $ increases. Moreover, we examine the behavior of QNMs by considering how their frequency changes with the shape of potentials. As a result, we found that the frequency behavior is like the quantum mechanical one. The faster the wave decays, the larger the potential.

In this paper, we study the greybody factors (GFs) for fermions with different spins and bosons in the regular black hole (BH) predicted by a non-minimal Einstein-Yang-Mills (EYM) theory. We investigate the effect of magnetic charge on effective potentials and GFs. For this purpose, we consider the Dirac and Rarita-Schwinger, as well as Klein-Gordon equations. First, we study the Dirac equation in curved spacetime for massive and massless spin-1/2 fermions. We then separate the Dirac equation into sets of radial and angular equations. Using the analytical solution of the angular equation, the Schr\"{o}dinger-like wave equations with potentials are derived by decoupling the radial wave equations via the tortoise coordinate. We also consider the Rarita-Schwinger equation for massless spin-3/2 fermions and derive the one-dimensional Schr\"odinger wave equation with gauge-invariant effective potential. For bosons, we study the Klein-Gordon equation in the regular non-minimal EYM BH. Afterward, semi-analytic methods were used to calculate the fermionic and bosonic GFs. Finally, we discuss the graphical behavior of the obtained effective potentials and bounds on the GFs. According to graphs, the GF is highly influenced by the potential's shape, which is determined by the parameterization of the model. This is in line with quantum theory.

Secure computation is of critical importance to not only the DoD, but across financial institutions, healthcare, and anywhere personally identifiable information (PII) is accessed. Traditional security techniques require data to be decrypted before performing any computation. When processed on untrusted systems the decrypted data is vulnerable to attacks to extract the sensitive information. To address these vulnerabilities Fully Homomorphic Encryption (FHE) keeps the data encrypted during computation and secures the results, even in these untrusted environments. However, FHE requires a significant amount of computation to perform equivalent unencrypted operations. To be useful, FHE must significantly close the computation gap (within 10x) to make encrypted processing practical. To accomplish this ambitious goal the TREBUCHET project is leading research and development in FHE processing hardware to accelerate deep computations on encrypted data, as part of the DARPA MTO Data Privacy for Virtual Environments (DPRIVE) program. We accelerate the major secure standardized FHE schemes (BGV, BFV, CKKS, FHEW, etc.) at >=128-bit security while integrating with the open-source PALISADE and OpenFHE libraries currently used in the DoD and in industry. We utilize a novel tile-based chip design with highly parallel ALUs optimized for vectorized 128b modulo arithmetic. The TREBUCHET coprocessor design provides a highly modular, flexible, and extensible FHE accelerator for easy reconfiguration, deployment, integration and application on other hardware form factors, such as System-on-Chip or alternate chip areas., Comment: 6 pages, 5 figures and 2 tables

Ring-Learning-with-Errors (RLWE) has emerged as the foundation of many important techniques for improving security and privacy, including homomorphic encryption and post-quantum cryptography. While promising, these techniques have received limited use due to their extreme overheads of running on general-purpose machines. In this paper, we present a novel vector Instruction Set Architecture (ISA) and microarchitecture for accelerating the ring-based computations of RLWE. The ISA, named B512, is developed to meet the needs of ring processing workloads while balancing high-performance and general-purpose programming support. Having an ISA rather than fixed hardware facilitates continued software improvement post-fabrication and the ability to support the evolving workloads. We then propose the ring processing unit (RPU), a high-performance, modular implementation of B512. The RPU has native large word modular arithmetic support, capabilities for very wide parallel processing, and a large capacity high-bandwidth scratchpad to meet the needs of ring processing. We address the challenges of programming the RPU using a newly developed SPIRAL backend. A configurable simulator is built to characterize design tradeoffs and quantify performance. The best performing design was implemented in RTL and used to validate simulator performance. In addition to our characterization, we show that a RPU using 20.5mm2 of GF 12nm can provide a speedup of 1485x over a CPU running a 64k, 128-bit NTT, a core RLWE workload

We investigate the Dirac and Klein-Gordon equations, as well as greybody radiation, for the Hayward black hole (BH) spacetime. We first consider the Dirac equation using a null tetrad in the Newman- Penrose (NP) formalism. The equations are then separated into angular and radial parts. A pair of one-dimensional Schr\"odinger like wave equations with effective potentials is obtained from the radial part. In order to examine the behavior of potentials, they are plotted with respect to radial distances. Additionally, the Klein-Gordon equation is considered in the Hayward BH spacetime. At the end, we compute greybody factors for bosons and fermions and our results are shown graphically and discussed.

The paper studies the spinorial wave equations, namely the Dirac and the Klein Gordon equations, as well as the greybody radiations and quasinormal modes (QNMs) of the charged Taub NUT black hole (CTNBH). To obtain fermionic greybody factors (GFs) and QNMs, we study the charged fermions by employing the Dirac equation. To this end, we use a null tetrad in the Newman-Penrose formalism. Then, we separate the Dirac equation into radial and angular sets. Using the obtained radial equations, we convert them into the typical one dimensional Schr\"{o}dinger like wave equations with the aid of tortoise coordinate and derive the effective potentials. For bosonic GFs and QNMs, we study the Klein Gordon equation in the CTNBH geometry and obtain the radial equation. We then derive the effective potential and investigate the effect of NUT parameter on it. We show that while the fermionic QNMs and GFs individually increase with the increasing NUT parameter, the increase of bosonic GFs with increasing NUT parameter is overwhelmingly greater than that of the bosonic QNMs.

In this paper, we investigated the Dirac and Klein-Gordan equations, as well as the greybody factor for a Schwarzschild black hole (SBH) immersed in quintessence and associated with a cloud of strings. Primarily, we study the Dirac equation using a null tetrad in the Newman- Penrose (NP) formalism. Next, we separate the Dirac equation into radial and angular sets. Using the radial equations, we study the profile of effective potential by transforming the radial equation of motion into standard Schr% \"{o}dinger wave equations form through tortoise coordinate. Similarly, we study the Klein-Gordan equation in this spacetime. The Miller-Good transformation method is employed to compute the greybody factor of bosons. To compute the Gerybody factor for fermions, we use the general method of semi-analytical bounds. We also investigate the effect of string clouds and quintessence parameters on Hawking radiation. According to the results, the greybody factor is strongly influenced by the shape of the potential, which is determined by the model parameters. This is consistent with the ideas of quantum mechanics; as the potential rises, it becomes harder for the wave to penetrate., Comment: 14 pages, 6 figures

We consider the spinorial wave equations, namely the Dirac and the Klein-Gordon equations, and greybody radiation in the NUT black hole spacetime. To this end, we first study the Dirac equation in NUT spacetime by using a null tetrad in the Newman-Penrose (NP) formalism. Next, we separate the Dirac equation into radial and angular sets. The angular set is solved in terms of associated Legendre functions. With the radial set, we obtain the decoupled radial wave equations and derive the one-dimensional Schr\"odinger wave equations together with effective potentials. Then, we discuss the potentials by plotting them as a function of radial distance in a physically acceptable region. We also study the Klein-Gordon equation to compute the greybody factors (GFs) for both bosons and fermions. The influence of the NUT parameter on the GFs of the NUT spacetime is investigated in detail., Comment: 19 Pages and 7 Figures. Accepted for Publication in EPJP: The European Physical Journal Plus

The need for privacy-preserving analytics is higher than ever due to the severity of privacy risks and to comply with new privacy regulations leading to an amplified interest in privacy-preserving techniques that try to balance between privacy and utility. In this work, we present an efficient method for Text Classification while preserving the privacy of the content using Fully Homomorphic Encryption (FHE). Our system (named \textbf{Priv}ate \textbf{F}ast \textbf{T}ext (PrivFT)) performs two tasks: 1) making inference of encrypted user inputs using a plaintext model and 2) training an effective model using an encrypted dataset. For inference, we train a supervised model and outline a system for homomorphic inference on encrypted user inputs with zero loss to prediction accuracy. In the second part, we show how to train a model using fully encrypted data to generate an encrypted model. We provide a GPU implementation of the Cheon-Kim-Kim-Song (CKKS) FHE scheme and compare it with existing CPU implementations to achieve 1 to 2 orders of magnitude speedup at various parameter settings. We implement PrivFT in GPUs to achieve a run time per inference of less than 0.66 seconds. Training on a relatively large encrypted dataset is more computationally intensive requiring 5.04 days., Comment: 13 pages, 3 figures, 4 tables, 5 Algorithms

The exact solutions of the Dirac equation that describe a massive, non-charged particle with spin-(1/2) in the curved spacetime geometry of regular Bardeen black hole surrounded by quintessence (BBHSQ) are investigated. We first derive the Dirac equation in the BBHSQ background using a null tetrad in the Newman-Penrose formalism. Afterward, we separate the Dirac equation into ordinary differential equations for the radial and angular parts. The angular equations are solved exactly in terms of standard spherical harmonics. The radial part equations are transformed into a Schr\"odinger like differential wave equations with effective potentials. The effect of the quintessence on the regular Bardeen black hole is studied by understanding the physical behavior of the effective potentials. In addition, the potentials are plotted with changing the quintessence parameters, magnetic monopole charge parameter and the frequency of the particle in the physically acceptable regions. Finally, we study the greybody radiation of spin-0 particles from the BBHSQ., Comment: 20 Pages, 7 Figures

Convolutional neural networks (CNNs) have enabled significant performance leaps in medical image classification tasks. However, translating neural network models for clinical applications remains challenging due to data privacy issues. Fully Homomorphic Encryption (FHE) has the potential to address this challenge as it enables the use of CNNs on encrypted images. However, current HE technology poses immense computational and memory overheads, particularly for high-resolution images such as those seen in the clinical context. We present CaRENets: Compact and Resource-Efficient CNNs for high performance and resource-efficient inference on high-resolution encrypted images in practical applications. At the core, CaRENets comprises a new FHE compact packing scheme that is tightly integrated with CNN functions. CaRENets offers dual advantages of memory efficiency (due to compact packing of images and CNN activations) and inference speed (due to the reduction in the number of ciphertexts created and the associated mathematical operations) over standard interleaved packing schemes. We apply CaRENets to perform homomorphic abnormality detection with 80-bit security level in two clinical conditions - Retinopathy of Prematurity (ROP) and Diabetic Retinopathy (DR). The ROP dataset comprises 96 x 96 grayscale images, while the DR dataset comprises 256 x 256 RGB images. We demonstrate over 45x improvement in memory efficiency and 4-5x speedup in inference over the interleaved packing schemes. As our approach enables memory-efficient low-latency HE inference without imposing additional communication burden, it has implications for practical and secure deep learning inference in clinical imaging.

Deep Learning as a Service (DLaaS) stands as a promising solution for cloud-based inference applications. In this setting, the cloud has a pre-learned model whereas the user has samples on which she wants to run the model. The biggest concern with DLaaS is user privacy if the input samples are sensitive data. We provide here an efficient privacy-preserving system by employing high-end technologies such as Fully Homomorphic Encryption (FHE), Convolutional Neural Networks (CNNs) and Graphics Processing Units (GPUs). FHE, with its widely-known feature of computing on encrypted data, empowers a wide range of privacy-concerned applications. This comes at high cost as it requires enormous computing power. In this paper, we show how to accelerate the performance of running CNNs on encrypted data with GPUs. We evaluated two CNNs to classify homomorphically the MNIST and CIFAR-10 datasets. Our solution achieved a sufficient security level (> 80 bit) and reasonable classification accuracy (99%) and (77.55%) for MNIST and CIFAR-10, respectively. In terms of latency, we could classify an image in 5.16 seconds and 304.43 seconds for MNIST and CIFAR-10, respectively. Our system can also classify a batch of images (> 8,000) without extra overhead.