• Communications of Mathematical Education
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• v.15
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• pp.215-222
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• 2003

직교좌표의 중요성과 극좌표의 이용을 알리고, 포물선좌표의 정의와 타원좌표의 정의를 소개하고 또 타원좌표를 이용하여 그래프를 그려본다. 타원좌표를 이용한 그래프 그리기를 통해 수학에 대한 흥미와 즐거움을 학생들에게 느끼도록 한다. 다양한 좌표계를 이용한 그래프 그리기를 비교해보고 매개변수로 표현된 방정식의 그래프 그리기에 대해 여러 가지 좌표계에 대한 유용성을 알아본다. Mathematica를 이용하여 여러 가지 좌표계에서 관심있는 곡선의 방정식을 만들어보고 그래프를 그려보며 유용한 좌표계에 대해 알아본다.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.17 no.3
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• pp.265-272
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• 1999

The map coordinate systems of Korea, based on the Bessel 1841 ellipsoid with Tokyo Datum, applied in digital mapping. So, the new geocentric system have some coordinate differences compared to GRS80 ellipsoid with the International Terrestrial Reference Frame(ITRF). Therefore, map transition procedures are needed to establish for the new coordinate system. In this paper, characteristics and tendencies about coordinate differences and map tiles systems are investigated and modules for the map coordinate transformations between two systems are developed and simulated.

• Journal of the Korean Vacuum Society
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• v.4 no.2
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• pp.224-229
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• 1995

쌍곡선 모델을 사용하여 미시 통로죔을 통과하는 2차원 전자들의 양자 탄동적 수송현상을 연구하였다. 통로죔은 타원좌표계($\alpha$, $\beta$)에서 $\beta$=$\beta$o, $\pi$-$\beta$o로 주어지는 두 쌍곡선으로 기술하였다. 양자화된 88컨덕턴스 G는 타원좌표계에서 주어진 슈뢰딩거 방정식과 쌍곡선 경계조건을 만족하는 짝 매튜 함수를 이용하여 계산하였다. 그 결과는 채널수 Nc는 통로죔 폭 W뿐만 아니라 곡률 관련좌표 $\beta$o에 의존함을 나타내었다. 또한 곡률에 의존하는 터널링도 양자화된 G의 그래프의 모양을 나타내는 중요한 요소임을 나타내 주었다. 고정된 통로폭에서 Nc가 일정한 $\beta$o영역에서는 $\beta$o의 연속적 변화에 G는 연속적으로 변화하였지만 $\beta$o가 크게 변화할 때는 Nc가 변화하여 G는 불연속적으로 변화하였다. 만일 터널링이 거의 허용이 안되는 $\beta$o의 영역에서는 G는 계단식의 변화만 보여주었다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.49 no.4
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• pp.23-35
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• 2012

This paper presents a 3-D pose (position and orientation) estimation method for an elliptic object in 3-D space. It is difficult to resolve the problem of determining 3-D pose parameters with respect to an elliptic feature in 3-D space by interpretation of its projected feature onto an image plane. As an alternative, we propose a two points-based pose estimation algorithm to seek the 3-D information of an elliptic feature. The proposed algorithm determines a homogeneous transformation uniquely for a given correspondence set of an ellipse and two coplanar points that are defined on model and image plane, respectively. For each plane, two triangular features are extracted from an ellipse and two points based on the polarity in 2-D projection space. A planar homography is first estimated by the triangular feature correspondences, then decomposed into 3-D pose parameters. The proposed method is evaluated through a series of experiments for analyzing the errors of 3-D pose estimation and the sensitivity with respect to point locations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.10 no.1
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• pp.77-87
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• 2000

타원곡선 이산대수 문제에 기초한 공개키 암호시스템에서 타원곡선 멱승은 반드시 필요한 연산이며 연산들 중에서 가장 복잡도가 크다. 따라서 효율적인 암호시스템 구현을 위해서는 타원곡선 멱승연산을 효율적으로 구현하는 것이 중요하다. 본 논문에서는 복합 좌표계(mixed coordinate system)를 이용한 멱승 방법을 GF(pm)상에서 정의되는 타원 곡선을 적용하여 최적의 효율성을 갖는 타원곡선 멱승 구현법을 제안한다. 또한 ‘곱셈을 이용한 역원 연산 알고리즘(IM; Inversion with Multiplication)’을 이용하여 더욱 효율적인 구현이 가능함을 보인다.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.4
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• pp.548-555
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• 2022

This paper describes the hardware implementation of elliptic curve cryptography (ECC) used as a core operation in elliptic curve digital signature algorithm (ECDSA). The ECC processor supports eight operation modes (four point operations, four modular operations) on the NIST P-521 curve. In order to minimize computation complexity required for point scalar multiplication (PSM), the radix-4 Booth encoding scheme and modified Jacobian coordinate system were adopted, which was based on the complexity analysis for five PSM algorithms and four different coordinate systems. Modular multiplication was implemented using a modified 3-Way Toom-Cook multiplication and a modified fast reduction algorithm. The ECC processor was implemented on xczu7ev FPGA device to verify hardware operation. Hardware resources of 101,921 LUTs, 18,357 flip-flops and 101 DSP blocks were used, and it was evaluated that about 370 PSM operations per second were achieved at a maximum operation clock frequency of 45 MHz.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.19 no.2
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• pp.117-123
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• 2001

Requiring topographic information of map due to retaining russia map, which needed accuracy analysis of russia map and relation between its and south korea's map. In order to obtain exact location information from the map which has different reference datum. We have to operate coordinate transformation between maps applied different ellipsoid. In this paper, in order to evaluate accuracy between two maps applied different ellipsoid, it has studied theory of map projection and coordinate transformation. Then, select each point which can be recognized on the two maps for accuracy evaluation. After obtaining coordinate values for each point of same area, it is evaluated accuracy each geodetic coordinate and each TM coordinate. As a result of this study, the maps which have different reference datum could be used if the exact origin shift could be obtained and applied.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.42 no.1
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• pp.57-67
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• 2005

Fast scalar multiplication of points on elliptic curve is important for elliptic curve cryptography applications. In order to vary field sizes depending on security situations, the cryptography coprocessors should support variable length finite field arithmetic units. To determine the effective variable length finite field arithmetic architecture, two well-known curve scalar multiplication algorithms were implemented on FPGA. The affine coordinates algorithm must use a hardware division unit, but the projective coordinates algorithm only uses a fast multiplication unit. The former algorithm needs the division hardware. The latter only requires a multiplication hardware, but it need more space to store intermediate results. To make the division unit versatile, we need to add a feedback signal line at every bit position. We proposed a method to mitigate this problem. For multiplication in projective coordinates implementation, we use a widely used digit serial multiplication hardware, which is simpler to be made versatile. We experimented with our implemented ECC coprocessors using variable length finite field arithmetic unit which has the maximum field size 256. On the clock speed 40 MHz, the scalar multiplication time is 6.0 msec for affine implementation while it is 1.15 msec for projective implementation. As a result of the study, we found that the projective coordinates algorithm which does not use the division hardware was faster than the affine coordinate algorithm. In addition, the memory implementation effectiveness relative to logic implementation will have a large influence on the implementation space requirements of the two algorithms.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.5
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• pp.1209-1217
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• 1994

This paper proposed transformation coefficients suitable to South Korea for the establishment of coordinate transformation system between Bessel and WGS84 ellipsoids. For this, the coordinates transformation algorithms concerned with parameter methods was developed, and global test network which has 15 astronomical points in South Korea were designed. Based on signals received from GPS, computed the geoid undulation by GPS/Leveling, and derived parameters(3-, 4-, 6-, and 7-parameter) for transformation between each ellipsoid, applied global networks to study the characteristics of transformation according to parameters. Through the successful application of 7-parameters derived in this study and 7-parameters proposed by DMA for map projection, transformation coefficients suitable to South Korea was proposed.

• Geophysics and Geophysical Exploration
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• v.19 no.4
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• pp.236-248
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• 2016

In this review, the basic concepts of geodetic coordinate system and map projection are explained to practitioners in exploration geophysicists to enhance the understanding of geographic and projected coordinate system. The fundamental elements such as earth ellipsoid, geoid, geocentric and geodetic latitudes, rhumb line, and great circle are dealt with in detail. The geocentric and geodetic coordinate systems are also summarized neatly, together with coordinate conversion formulae. In addition, the concept and technique for datum transforms between local and world datum are presented, with special emphasis on Korean Geodetic System.