• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.105-121
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• 2009

In this paper we will be interested in characterizing and computing matrices $X\;{\in}\;C^{n{\times}n}$ that satisfy $e^X$ = A, that is logarithms of A. The study in this work goes through two lines. The first is concerned with a theoretical study of the solution set, S(A), of $e^X$ = A. Along the second line computational approaches are considered to compute the principal logarithm of A, LogA.

• 대한수학회지
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• 제52권4호
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• pp.797-819
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• 2015

A trapdoor discrete logarithm group is a cryptographic primitive with many applications, and an algorithm that allows discrete logarithm problems to be solved faster using a pre-computed table increases the practicality of using this primitive. Currently, the distinguished point method and one extension to this algorithm are the only pre-computation aided discrete logarithm problem solving algorithms appearing in the related literature. This work investigates the possibility of adopting other pre-computation matrix structures that were originally designed for used with cryptanalytic time memory tradeoff algorithms to work as pre-computation aided discrete logarithm problem solving algorithms. We find that the classical Hellman matrix structure leads to an algorithm that has performance advantages over the two existing algorithms.

• Journal of Multimedia Information System
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• 제8권1호
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• pp.45-56
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• 2021

This document traces the new technologies development based on a deep classical Hill method improvement. Based on the chaos, this improvement begins with the 256 element body construction, which is to replace the classic ring used by all encryption systems. In order to facilitate the application of algebraic operators on the pixels, two substitution tables will be created, the first represents the discrete logarithm, while the second represents the discrete exponential. At the same time, a large invertible matrix whose structure will be explained in detail will be the subject of the advanced classical Hill technique improvement. To eliminate any linearity, this matrix will be accompanied by dynamic vectors to install an affine transformation. The simulation of a large number of images of different sizes and formats checked by our algorithm ensures the robustness of our method.

• Korea-Australia Rheology Journal
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• 제16권4호
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• 한국인터넷방송통신학회논문지
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• 제16권6호
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• pp.319-327
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• 2016

본 논문에서는 나무나 염소 뿔처럼 대부분의 동식물이 대칭임을 살펴본다. 또한 DNA를 가지고 있는 인간의 신체 역시 대칭이다. 피보나치수열, 식물의 나선, 동물의 대수 나선에서 볼 수 있는 것은 대칭이다. 해바라기 꽃은 원형이다. 원(元)은 원점을 중심으로 회전을 해도 모양이 꼭 같으므로 회전대칭이다. 공간상의 회전변환을 넘어서, 시간 공간의 대칭적 변환으로 일반화하면 아인슈타인의 특수상대성 이론이 시공간 변환관계이다. 동식물의 나선은 좌우 나선들이 대칭을 이루며 그 속에는 element-wise inverse가 존재한다. Hadamard 행렬 중 가운데 하중 값을 2로 준 것은 자연대수의 밑 2와 같고, 나선 행렬은 Symmetric하며 역행렬은 element-wise inverse이다.

• 한국재료학회지
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• 제21권9호
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• pp.477-481
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• 2011

Composites of insulating polyethylene and carbon black are widely used in switching elements, conductive paint, and other applications due to the large gap of resistance value. This research addresses the critical exponent of dielectric breakdown strength of polymer matrix composites (PMC) made with carbon black and polyethylene below the percolation threshold (Pt) for the first time. Here, Pt means the volume fraction of carbon black of which the resistance of the PMC is transferred from its sharp decrease to gradual decrease in accordance with the increase of carbon-black-filled content. First, the Pt is determined based on the critical exponents of resistivity and relative permittivity. Although huge cohesive bodies of carbon black are formed in case of being less than the Pt, a percolation path connecting the conducting phases is not formed. The dielectric breakdown strength (Dbs) of the PMC below Pt is measured by using an impulse voltage in the range from 10 kV to 40 kV to avoid the effect of joule heating. Although the observed Dbs data seems to be well fitted to a straight line with a slope of 0.9 on a double logarithm of (Pt-$V_{CB}$) and Dbs, the least squares method gives a slope of 0.97 for the PMC. It has been found that finite carbon-black clusters play an important role in dielectric breakdown.

• Wind and Structures
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• 제10권1호
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• pp.61-82
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• 2007

This paper presents a novel finite element (FE) model for analyzing coupled flutter of long-span bridges using the commercial FE package ANSYS. This model utilizes a specific user-defined element Matrix27 in ANSYS to model the aeroelastic forces acting on the bridge, wherein the stiffness and damping matrices are expressed in terms of the reduced wind velocity and flutter derivatives. Making use of this FE model, damped complex eigenvalue analysis is carried out to determine the complex eigenvalues, of which the real part is the logarithm decay rate and the imaginary part is the damped vibration frequency. The condition for onset of flutter instability becomes that, at a certain wind velocity, the structural system incorporating fictitious Matrix27 elements has a complex eigenvalue with zero or near-zero real part, with the imaginary part of this eigenvalue being the flutter frequency. Case studies are provided to validate the developed procedure as well as to demonstrate the flutter analysis of cable-supported bridges using ANSYS. The proposed method enables the bridge designers and engineering practitioners to analyze flutter instability by using the commercial FE package ANSYS.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제6권6호
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• pp.1627-1648
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• 2012

We propose an adaptive method for detecting plagiarized pairs from a large set of source code. This method is adaptive in that it uses an adaptive algorithm and it provides an adaptive threshold for determining plagiarism. Conventional algorithms are based on greedy string tiling or on local alignments of two code strings. However, most of them are not adaptive; they do not consider the characteristics of the program set, thereby causing a problem for a program set in which all the programs are inherently similar. We propose adaptive local alignment-a variant of local alignment that uses an adaptive similarity matrix. Each entry of this matrix is the logarithm of the probabilities of the keywords based on their frequency in a given program set. We also propose an adaptive threshold based on the local outlier factor (LOF), which represents the likelihood of an entity being an outlier. Experimental results indicate that our method is more sensitive than JPlag, which uses greedy string tiling for detecting plagiarism-suspected code pairs. Further, the adaptive threshold based on the LOF is shown to be effective, and the detection performance shows high sensitivity with negligible loss of specificity, compared with that using a fixed threshold.

• 한국정보과학회논문지:소프트웨어및응용
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• 제33권12호
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• pp.1090-1102
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• 2006

본 논문에서는 대학생들의 프로그래밍 과제물이나 프로그래밍 경진대회에 제출된 프로그램과 같이 동일한 기능을 요구받는 프로그램 소스 집합들에서 표절행위가 있었는지를 탐색하는 새로운 알고리즘을 제시하고 있다. 지금까지 보편적으로 사용되어 온 대표적인 알고리즘은 부분 스트링간의 완전 일치를 통한 Greedy-String-Tiling이나 두 스트링간의 지역정렬(local alignment)을 이용한 유사도 분석이 주된 방법론이었다. 본 논문에서는 해당 프로그램 소스의 집합에서 추출된 키워드들의 빈도수에 기반한 로그 확률값을 가중치로 하는 적응적(adaptive) 유사도 행렬을 만들어 이를 기반으로 주어진 프로그램의 유사구간을 탐색하는 새로운 방법을 소개한다. 우리는 10여개 이상의 프로그래밍 대회에서 제출된 실제 프로그램으로 본 방법론을 실험해 보았다. 실험결과 이 방법은 이전의 고정적 유사도 행렬(match이면 +1, mismatch이면 -1, gap이면 -2)에 의한 유사구간 탐색에 비하여 여러 장점이 있음을 알 수 있었으며, 제시한 적응적 유사도 행렬을 보다 다양한 표절탐색 목적으로 사용할 수 있음을 알 수 있었다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권12호
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• pp.6116-6132
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• 2017

The proxy re-encryption allows an intermediate proxy to convert a ciphertext for Alice into a ciphertext for Bob without seeing the original message and leaking out relevant information. Unlike many prior identity based proxy re-encryption schemes which are based on the number theoretic assumptions such as large integer factorization and discrete logarithm problem. In this paper, we first propose a novel identity based proxy re-encryption scheme which is based on the hardness of standard Learning With Error(LWE) problem and is CPA secure in the standard model. This scheme can be reduced to the worst-case lattice hard problem that is able to resist attacks from quantum algorithm. The key step in our construction is that the challenger how to answer the private query under a known trapdoor matrix. Our scheme enjoys properties of the non-interactivity, unidirectionality, anonymous and so on. In this paper, we utilize primitives include G-trapdoor for lattice and sample algorithms to realize simple and efficient re-encryption.