• Title/Summary/Keyword: Euler Method

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The Improved Estimation of the Least Upper Bound to Search for RSA's Private key

  • Somsuk, Kritsanapong
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.16 no.6
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    • pp.2074-2093
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    • 2022
  • RSA is known as one of the best techniques for securing secret information across an unsecured network. The private key which is one of private parameters is the aim for attackers. However, it is exceedingly impossible to derive this value without disclosing all unknown parameters. In fact, many methods to recover the private key were proposed, the performance of each algorithm is acceptable for the different cases. For example, Wiener's attack is extremely efficient when the private key is very small. On the other hand, Fermat's factoring can quickly break RSA when the difference between two large prime factors of the modulus is relatively small. In general, if all private parameters are not disclosed, attackers will be able to confirm that the private key is unquestionably inside the scope [3, n - 2], where n is the modulus. However, this scope has already been reduced by increasing the greatest lower bound to [dil, n - 2], where dil ≥ 3. The aim of this paper is to decrease the least upper bound to narrow the scope that the private key will remain within this boundary. After finishing the proposed method, the new scope of the private key can be allocated as [dil, dir], where dir ≤ n - 2. In fact, if the private key is extremely close to the new greatest lower bound, it can be retrieved quickly by performing a brute force attack, in which dir is decreased until it is equal to the private key. The experimental results indicate that the proposed method is extremely effective when the difference between prime factors is close to each other and one of two following requirement holds: the first condition is that the multiplier of Euler totient function is very close to the public key's small value whereas the second condition is that the public key should be large whenever the multiplier is far enough.

Numerical Analysis on Turning and Yaw Checking Abilities of KCS in Calm Water a Based on Free-Running Simulations (가상 자유 항주를 이용한 KCS 선형의 정수 중 선회 및 변침 성능 해석)

  • Yang, Kyung-Kyu;Kim, Yoo-Chul;Kim, Kwang-Soo;Yeon, Seong Mo
    • Journal of the Society of Naval Architects of Korea
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    • v.59 no.1
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    • pp.1-8
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    • 2022
  • To understand physical phenomena of ship maneuvering deeply, a numerical study based on computational fluid dynamics is required. A computational method that can simulate the interaction between the ship hull, propeller, and rudder will provide informative local flows during ship maneuvering tests. The analysis of local flows can be applied to improve a physical model of ship maneuvering that has been widely used in maneuvering simulations. In this study, the numerical program named as WAVIS that has been developed for ship resistance and propulsion problems is extended to simulate ship maneuvering by free-running tests. The six degree-of-freedom of ship motion is implemented based on Euler angles and the overset technique is applied to treat the moving grid of ship hull and rudder. The propulsion force due to a propeller is calculated by a panel method that is based on the lifting-surface theory. The newly extended code is applied to simulate turning and zig-zag tests of KCS and the comparison with the available experimental data has been made.

Parametric study of the wave dispersion in the hydro-elastic system consisting of an inhomogeneously prestressed hollow cylinder containing compressible inviscid fluid

  • Surkay D. Akbarov;Gurbaneli J. Veliyev
    • Coupled systems mechanics
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    • v.12 no.1
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    • pp.41-68
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    • 2023
  • The present work is concerned with the study of the influence of inhomogeneous initial stresses in a hollow cylinder containing a compressible inviscid fluid on the propagation of axisymmetric longitudinal waves propagating in this cylinder. The study is carried out using the so-called three-dimensional linearized theory of elastic waves in bodies with initial stresses to describe the motion of the cylinder and using the linearized Euler equations to describe the flow of the compressible inviscid fluid. It is assumed that the inhomogeneous initial stresses in the cylinder are caused by the internal pressure of the fluid. To solve the corresponding eigenvalue problem, the discrete-analytic solution method is applied and the corresponding dispersion equation is obtained, which is solved numerically, after which the corresponding dispersion curves are constructed and analyzed. To obtain these dispersion curves, parameters characterizing the magnitude of the internal pressure, the ratio of the sound velocities in the cylinder material and in the fluid, and the ratio of the material densities of the fluid and the cylinder are introduced. Based on these parameters, the influence of the inhomogeneous initial stresses in the cylinder on the dispersion of the above-mentioned waves in the considered hydro-elastic system is investigated. Moreover, based on these results, appropriate conclusions about this influence are drawn. In particular, it is found that the character of the influence depends on the wavelength. Accordingly, the inhomogeneous initial stresses before (after) a certain value of the wavelength lead to a decrease (increase) of the wave propagation velocity in the zeroth and first modes.

Development and validation of multiphysics PWR core simulator KANT

  • Taesuk Oh;Yunseok Jeong;Husam Khalefih;Yonghee Kim
    • Nuclear Engineering and Technology
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    • v.55 no.6
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    • pp.2230-2245
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    • 2023
  • KANT (KAIST Advanced Nuclear Tachygraphy) is a PWR core simulator recently developed at Korea Advance Institute of Science and Technology, which solves three-dimensional steady-state and transient multigroup neutron diffusion equations under Cartesian geometries alongside the incorporation of thermal-hydraulics feedback effect for multi-physics calculation. It utilizes the standard Nodal Expansion Method (NEM) accelerated with various Coarse Mesh Finite Difference (CMFD) methods for neutronics calculation. For thermal-hydraulics (TH) calculation, a single-phase flow model and a one-dimensional cylindrical fuel rod heat conduction model are employed. The time-dependent neutronics and TH calculations are numerically solved through an implicit Euler scheme, where a detailed coupling strategy is presented in this paper alongside a description of nodal equivalence, macroscopic depletion, and pin power reconstruction. For validation of the steady, transient, and depletion calculation with pin power reconstruction capacity of KANT, solutions for various benchmark problems are presented. The IAEA 3-D PWR and 4-group KOEBERG problems were considered for the steady-state reactor benchmark problem. For transient calculations, LMW (Lagenbuch, Maurer and Werner) LWR and NEACRP 3-D PWR benchmarks were solved, where the latter problem includes thermal-hydraulics feedback. For macroscopic depletion with pin power reconstruction, a small PWR problem modified with KAIST benchmark model was solved. For validation of the multi-physics analysis capability of KANT concerning large-sized PWRs, the BEAVRS Cycle1 benchmark has been considered. It was found that KANT solutions are accurate and consistent compared to other published works.

SARS-CoV-2 detection and infection scale prediction model in sewer system (하수도 체계에서의 SARS-CoV-2 검출 및 감염 확산 예측)

  • Kim, Min Kyoung;Cho, Yoon Geun;Shin, Jung gon;Jang, Ho Jin;Ryu, Jae Won
    • Proceedings of the Korea Water Resources Association Conference
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    • 2022.05a
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    • pp.392-392
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    • 2022
  • 세계적 규모의 팬데믹 감염병의 출현은 전 세계적으로 경제적, 문화적, 사회적 파급효과가 매우 강력하며 전 인류를 위협하고 있다. 최근에 발병한 중증급성 호흡기질환 코로나바이러스 2(Severe Acute Respiratory Syndrome Coronavirus 2, SARS-CoV-2)는 2019년 12월 중국 우한에서 첫 보고 되었고 2022년 현재까지 종식되지 않고 있으며 바이러스의 전파력과 치명률이 높고 무증상 감염상태일 때에도 전염이 가능하여 현재 역학조사의 사후적 대응에 대한 한계가 있어 선제적 대응을 위한 수단이 필수 불가결해지고 있는 실정이다. 하수기반역학(Waste Based Epidemiology, WBE)이란 하수처리장으로 유입되기 전의 하수를 분석하여 하수 집수구역 내 도시민의 생활상을 예측하는 것으로 하수로 배출된 감염자의 분비물 및 배설물 속 바이러스를 하수관로에서 신속하게 검출함으로써 특정지역의 감염성 질환 전파 정도와 유행하는 타입(변이)등을 분석하고 기존 역학조사의 문제점을 극복할 수 있으며 선제적인 대응이 가능하다. 현재 COVID-19의 대유행과 관련하여 WBE를 기반으로 한 다양한 연구가 진행되고 있으며 실제 환자의 발생과 상관관계가 있음이 확인되고 있고 백신 접종과 새롭게 발생한 변이바이러스의 관계 속에서 발생하는 변수를 고려한 모델이 없다는 점을 들어 새로운 감염병 확산 예측 모델에 대한 필요성 또한 커지고 있다. 본 연구에서는 병원에서부터 하수처리장까지의 하수관거와 하수처리장에서의 SARS-CoV-2 검출농도 및 거동을 파악하는 것을 목적으로 하고 있으며 COVID-19의 감염규모 확산에 관한 방법론에서 수학적모델 (Euler Method, RK4 Method, Gillespie Algorithm)과 딥러닝 기반의 Nowcasting model과 Fore casting model을 살펴보고자 한다.

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The Wavelet Series Analysis for the Fourth-order Elliptic Differential Equation (4계 타원형 미분 방정식을 위한 웨이블릿 급수해석)

  • Jo, Jun-Hyung;Woo, Kwang-Sung;Sin, Young-Sik
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.24 no.4
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    • pp.355-364
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    • 2011
  • In this study, the details of WSA(wavelet series analysis) have been demonstrated to solve the 4th-order elliptic differential equation. It is clear to solve the 2nd-order elliptic differential equation with the basis function of Hat wavelet series that is used in the previous study existed in $H^1$-space. However, it is difficult to solve the 4th order differential equation with same basis function of Hat wavelet series because of insufficient differentiability and integrability. To overcome this problem, the linear equations in terms of moment and deflection have been formulated and solved sequentially that are similar to extension of Elastic Load Method and Moment Area Method in some senses. Also, the differences and common points between the proposed method and the meshless method are discussed in the procedure of WSA formulation. As we expect, it is easy to ascertain that the more terms of Hat wavelet series are used, the better numerical solutions are improved. Also the solutions obtained by WSA have been compared with the conventional FEM solutions in case of Euler beam problems with stress singularity.

Gravity Field Interpretation for the Deep Geological Structure Analysis in Pohang-Ulsan, Southeastern Korean Peninsula (한반도 남동부 포항-울산지역 심부 지질구조 분석을 위한 중력장 해석)

  • Sohn, Yujin;Choi, Sungchan;Ryu, In-Chang
    • Economic and Environmental Geology
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    • v.53 no.5
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    • pp.597-608
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    • 2020
  • Even after the Gyeongju earthquake and the Pohang earthquake, hundreds of aftershocks and micro-earthquakes are still occurring in the southeastern part of the Korean Peninsula. These phenomena mean that the stress is constantly working, implying that another huge earthquake may occur in the future. Therefore, the gravity field interpretation method was used to analyze the deep geological structure of the Pohang-Ulsan region in the southeastern Korean Peninsula. First, a gravity survey was performed to collect the insufficient data and to calculate the detailed Bouguer gravity anomaly in the study area. Based on the gravity anomaly data, the location, direction, and maximum depth of deep fault lines were analyzed using the inversion methods "Curvature analysis" and "Euler deconvolution method". As a result, it is interpreted that at least six fault lines(C1~C6) exist in deep depth. The deep fault line C1 is well correlated to the Yeonil Tectonic Line(YTL), suggesting that YTL is extended up to about 4000m deep. The deep fault line C2 consists of several segment faults and well correlated to the fault lines on the surface. Inferred fault lines C3, C4, and C5 have an NW-SE direction, which is parallel to the Ulsan fault. The deep fault line C6 has the direction of NE-SW, and it is interpreted that the eastern boundary fault of Eoil Basin is extended to the deep. Comparing the inferred fault lines with the distribution of micro-earthquakes, the location of the deep fault line C1 is well correlated to the hypocenter of micro-earthquakes. This implies that faults in deep depth are related to the recent earthquakes in the southeastern Korean Peninsula.

Application of a Fictitious Axial Force Factor to Determine Elastic and Inelastic Effective Lengths for Column Members of Steel Frames (강프레임 기둥 부재의 탄성 및 비탄성 유효좌굴길이 산정을 위한 가상축력계수의 적용)

  • Choi, Dong Ho;Yoo, Hoon;Lee, Yoon Seok
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.30 no.2A
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    • pp.81-92
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    • 2010
  • In design of steel frames, it is generally believed that elastic system buckling analysis cannot predict real behaviors of structures, while inelastic system buckling analysis can give informative buckling behaviors of individual members considering inelastic material behavior. However, the use of Euler buckling equation with these system buckling analyses have the inherent problem that the methods evaluate unexpectedly large effective lengths of members having relatively small axial forces. This paper proposes a new method of obtaining elastic and inelastic effective lengths of all members in steel frames. Considering a fictitious axial force factor for each story of frames, the proposed method determines the effective lengths using the inelastic stiffness reduction factor and the iterative eigenvalue analysis. In order to verify the validity of the proposed method, the effective lengths of example frames by the proposed method were compared to those of previously established methods. As a result, the proposed method gives reasonable effective lengths of all members in steel frames. The effect of inelastic material behavior on the effective lengths of members was also discussed.

Implicit Numerical Integration of Two-surface Plasticity Model for Coarse-grained Soils (Implicit 수치적분 방법을 이용한 조립토에 관한 구성방정식의 수행)

  • Choi, Chang-Ho
    • Journal of the Korean Geotechnical Society
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    • v.22 no.9
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    • pp.45-59
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    • 2006
  • The successful performance of any numerical geotechnical simulation depends on the accuracy and efficiency of the numerical implementation of constitutive model used to simulate the stress-strain (constitutive) response of the soil. The corner stone of the numerical implementation of constitutive models is the numerical integration of the incremental form of soil-plasticity constitutive equations over a discrete sequence of time steps. In this paper a well known two-surface soil plasticity model is implemented using a generalized implicit return mapping algorithm to arbitrary convex yield surfaces referred to as the Closest-Point-Projection method (CPPM). The two-surface model describes the nonlinear behavior of coarse-grained materials by incorporating a bounding surface concept together with isotropic and kinematic hardening as well as fabric formulation to account for the effect of fabric formation on the unloading response. In the course of investigating the performance of the CPPM integration method, it is proven that the algorithm is an accurate, robust, and efficient integration technique useful in finite element contexts. It is also shown that the algorithm produces a consistent tangent operator $\frac{d\sigma}{d\varepsilon}$ during the iterative process with quadratic convergence rate of the global iteration process.

Elastic Local Buckling Analysis of Orthotropic Structural Shapes Using Bleich's Approximate Method (Bleich의 근사해법을 이용한 직교이방성 구조용부재의 탄성국부좌굴해석)

  • Lee, Won Bok;Yoon, Soon Jong;Lee, Seok Soon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.14 no.4
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    • pp.795-805
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    • 1994
  • This paper presents the analytical results for the prediction of elastical local buckling stress of fiber reinforced plastic (orthotropic) structural shapes manufactured from pultrusion process. In the derivation, existing Bleich's approach which was originally derived for the isotropic structural shapes was extended and non-dimensionalized parameters which can simplify the numerical calculations were adopted. Analytical results were compared with reported closed-form solutions and experimental results. It is graphically shown that the results can be used effectively to predict the local buckling stress of pultruded fiber reinforced plastic structural shapes. Numerical results were presented graphically to estimate the local buckling stress of various cross-sectional dimensions and lengths of columns. In addition, limits of width to thickness ratio of flange and web of pultruded structural shapes were suggested in which material failure or overall buckling occurs prior to local buckling.

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