• 대한수학회논문집
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• 제12권3호
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• pp.539-541
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• 1997

Let X be a smooth projective threefold. Let C be a smooth projective curve and let $f : X \to C$ be a fiber space with connected fiber S. Assume that $q_1(S) = 0$. Then we have $-X(O_C)X(O_S) \leq -X(O_X)$.

• 대한전자공학회논문지SD
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• 제42권1호
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• pp.57-67
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• 2005

고속 스칼라곱 연산은 타원곡선 암호 응용을 위해서 매우 중요하다. 보안 상황에 따라 유한체의 크기를 변경하려면 타원곡선 암호 보조프로세서가 크기 가변 유한체 연산 장치를 제공하여야 한다. 크기 가변 유한체 연산기의 효율적인 연산 구조를 연구하기 위하여 전형적인 두 종류의 스칼라곱 연산 알고리즘을 FPGA로 구현하였다. Affine 좌표계 알고리즘은 나눗셈 연산기를 필요로 하며, projective 좌표계 알고리즘은 곱셈 연산기만 사용하나 중간 결과 저장을 위한 메모리가 더 많이 소요된다. 크기 가변 나눗셈 연산기는 각 비트마다 궤환 신호선을 추가하여야 하는 문제점이 있다. 본 논문에서는 이로 인한 클록 속도저하를 방지하는 간단한 방법을 제안하였다. Projective 좌표계 구현에서는 곱셈 연산으로 널리 사용되는 디지트 serial 곱셈구조를 사용하였다. 디지트 serial 곱셈기의 크기 가변 구현은 나눗셈의 경우보다 간단하다. 최대 256 비트 크기의 연산이 가능한 크기 가변 유한체 연산기를 이용한 암호 프로세서로 실험한 결과, affine 좌표계 알고리즘으로 스칼라곱 연산을 수행한 시간이 6.0 msec, projective 좌표계 알고리즘의 경우는 1.15 msec로 나타났다. 제안한 타원곡선 암호 프로세서를 구현함으로써, 하드웨어 구현의 경우에도 나눗셈 연산을 사용하지 않는 projective 좌표계 알고리즘이 속도 면에서 우수함을 보였다. 또한, 메모리의 논리회로에 대한 상대적인 면적 효율성이 두 알고리즘의 하드웨어 구현 면적 요구에 큰 영향을 미친다.

• ETRI Journal
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• 제30권3호
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• pp.365-376
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• 2008

This paper presents the design and implementation of a hyperelliptic curve cryptography (HECC) coprocessor over affine and projective coordinates, along with measurements of its performance, hardware complexity, and power consumption. We applied several design techniques, including parallelism, pipelining, and loop unrolling, in designing field arithmetic units, group operation units, and scalar multiplication units to improve the performance and power consumption. Our affine and projective coordinate-based HECC processors execute in 0.436 ms and 0.531 ms, respectively, based on the underlying field GF($2^{89}$). These results are about five times faster than those for previous hardware implementations and at least 13 times better in terms of area-time products. Further results suggest that neither case is superior to the other when considering the hardware complexity and performance. The characteristics of our proposed HECC coprocessor show that it is applicable to high-speed network applications as well as resource-constrained environments, such as PDAs, smart cards, and so on.

• 대한수학회지
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• 제53권2호
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• pp.461-473
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• 2016

Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$ and the equality holds if and only if C is a P loski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.

• 대한수학회지
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• 제37권3호
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• pp.359-369
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• 2000

Let X be an integral Gorenstein projective curve with g:=pa(X) $\geq$ 3. Call $G^r_d$ (X,**) the set of all pairs (L,V) with L$\epsilon$Pic(X), deg(L) = d, V $\subseteq$ H^0$(X,L), dim(V) =r+1 and V spanning L. Assume the existence of integers d, r with 1 $\leq$ r$\leq$ d $\leq$ g-1 such that there exists an irreducible component, , of $G^r_d$(X,**) with dim($\Gamma$) $\geq$ d - 2r and such that the general L$\geq$$\Gamma$ is spanned at every point of Sing(X). Here we prove that dim( ) = d-2r and X is hyperelliptic.

• International Journal of Advanced Culture Technology
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• 제6권4호
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• pp.323-330
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• 2018

The growth of the older population is expected to further increase social problems associated with population aging, such as isolation, poverty, and depression. The emerging issues associated with the older population are also expected to provide further momentum on studies about the dwelling environment as factors that ensure the health of older people as well as improve their quality of life. Therefore, approaches for explaining the issues of the older age group should be diversified using a variety of factors and appropriate analytic tools. Studies on measuring depression have principally focused on assessing an objective self-report questionnaire, usually in a highly structured, textual form which may not reflect the cognitive impairment of older adults. The aim of this study was to define and measure dwelling depression among older adults in Korea. There are two specific hypotheses in this study as follows: (a) there will be statistically significant relationships with dwelling dissatisfaction and depression, and (b) dwelling depression tools containing text and images will be, respectively, assessment tools that have a good construct with content validity and reliability. In the first experiment, to define and measure dwelling depression, 301 people over 65 years old living in single and two-person households were surveyed using a text-based dwelling depression questionnaires from September 1-30, 2017. In the second experiment, to examine whether the projective image questionnaire could serve as a suitable replacement for the text-based questionnaires, the same participants were surveyed from January 22 to February 2, 2018. The results show that depression has a close correlation with dwelling dissatisfaction. In addition, the geriatric dwelling depression index (GDDI) based on the projective image was refined. Additionally, the projective image questionnaire has a close correlation with the text-based questionnaire. Finally, through ROC curve analysis, it was found that the projective image questionnaire can accurately predict a depression group. To this end, this preliminary study examined the validity of the projective image questionnaire in older adults to make this instrument feasible for older populations and to contribute to a profound understanding of geriatric depression due to the living environment. We hope they will provide a basis for further research on psychological diagnoses using projective images.

• 대한수학회지
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• 제56권5호
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• 대한수학회논문집
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• 제10권1호
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• pp.1-10
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• 1995

In this paper we show that for each divisor class c of degree zero on a projective curve C (not necessarily smooth), there exists a unique function $\hat{h}_c$ on C up to bounded functions. Section 1 contain basic definitions and a brief summary of classical results on Jacobians and heights. In section 2, we prove the existence of "canonical height" on a singular curves and in section 3 we prove the analogouse results on N$\acute{e}$ron functions for singular curves. This is a part of the author's doctorial thesis at Ewha Womens University under the guidence of professor Sung Sik Woo.g Sik Woo.

• 대한수학회보
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• 제43권4호
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• pp.763-770
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• 2006

Let X be a four-dimensional projective variety defined over the field of complex numbers with only terminal singularities. We prove that if the intersection number of the canonical divisor K with every very general curve is positive (K is almost numerically positive) then every very general proper subvariety of X is of general type in ';he viewpoint of geometric Kodaira dimension. We note that the converse does not hold for simple abelian varieties.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2017년도 춘계학술대회
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• pp.188-190
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• 2017

투영(projective) 좌표계를 이용한 스칼라 곱셈(scalar multiplication) 연산을 지원하는 224-비트 타원곡선 암호(Elliptic Curve Cryptography; ECC) 프로세서의 설계에 대해 기술한다. 소수체 GF(p)상의 덧셈, 뺄셈, 곱셈 등의 유한체 연산을 지원하며, 연산량과 하드웨어 자원소모가 큰 나눗셈 연산을 제거함으로써 하드웨어 복잡도를 감소시켰다. 수정된 Montgomery ladder 알고리듬을 이용하여 스칼라 곱셈 연산을 제어하였으며, 단순 전력분석에 보다 안전하다. 스칼라 곱셈 연산은 최대 2,615,201 클록 사이클이 소요된다. 설계된 ECC-P224 프로세서는 Xilinx ISim을 이용한 기능검증을 하였다. Xilinx Virtex5 FPGA 디바이스 합성결과 7,078 슬라이스로 구현되었으며, 최대 79 MHz에서 동작하였다.