• ETRI Journal
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• 제32권3호
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• pp.362-369
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• 2010

While the elliptic curve cryptosystem (ECC) is getting more popular in securing numerous systems, implementations without consideration for side-channel attacks are susceptible to critical information leakage. This paper proposes new power attack countermeasures for ECC over Koblitz curves. Based on some special properties of Koblitz curves, the proposed methods randomize the involved elliptic curve points in a highly regular manner so the resulting scalar multiplication algorithms can defeat the simple power analysis attack and the differential power analysis attack simultaneously. Compared with the previous countermeasures, the new methods are also noticeable in terms of computational cost.

• International Journal of Contents
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• 제11권2호
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• pp.9-14
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• 2015

We propose a new distance measure between 2-dimensional points to provide a total order for an entire point set and to reflect the correct geometric meaning of the naturalness of the point ordering. In general, there is no total order for 2-dimensional point sets, so curve reconstruction algorithms do not solve the self-intersection problem because the distance used in the previous methods is the Euclidean distance. A natural distance based on Brownian motion was previously proposed to solve the self-intersection problem. However, the distance reflects the wrong geometric meaning of the naturalness. In this paper, we correct the disadvantage of the natural distance by introducing a polar-natural distance, and we also propose a new curve reconstruction algorithm that is based on the polar-natural distance. Our experiments show that the new distance adequately reflects the correct geometric meaning, so non-simple curve reconstruction can be solved.

• 대한수학회지
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• 제44권6호
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.

• Journal of Communications and Networks
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• 제12권1호
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• pp.1-4
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• 2010

As a countermeasure to simple power attack, the unified point addition codes for the elliptic curve cryptosystem were introduced. However, some authors proposed a different kind of power attacks to the codes. This power attack uses the observation that some internal operations in the codes behave differently for addition and doubling. In this paper, we propose a new countermeasure against such an attack. The basic idea of the new countermeasure is that, if one of the input points of the codes is transformed to an equivalent point over the underlying finite field, then the code will behave in the same manner for addition and doubling. The new countermeasure is highly efficient in that it only requires 27(n-1)/3 extra ordinary integer subtractions (in average) for the whole n-bit scalar multiplication. The timing analysis of the proposed countermeasure is also presented to confirm its SPA resistance.

• Journal of Computational Design and Engineering
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• 제3권1호
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• pp.14-23
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• 2016

The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing outliers. A skeleton representation is utilized to represent the topological structure which is further used to create a weighted graph for deciding the merging of curve segments. Different to existing approaches which utilize local shape information near intersections, our method considers shape characteristics of curve segments in a larger scope and is thus capable of giving more satisfactory results. By fitting each group of data points with a B-spline curve, we solve the problems of curve structure reconstruction from point clouds, as well as the vectorization of simple line drawing images by drawing lines reconstruction.

• 한국분무공학회지
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• 제4권1호
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• pp.55-61
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• 1999

The first maximum point in the stability curve of liquid jet, i.e., the critical point is associated with the critical Reynolds number. This critical Reynolds number should be predicted by simple means. In this work, the critical Reynolds number in the stability curve of liquid jet are predicted using the empirical correlations and the experimental data reported in the literatures. The critical Reynolds number was found to be a function of the Ohnesorge number, nozzle lengh-to-diameter ratio, ambient Weber number and nozzle inlet type. An empirical correlation for the critical Reynolds number as a function of the Ohnesorge number and nozzle length-to-diameter ratio is newly proposed here. Although an empirical correlation proposed in this work may not be universal because of excluding the effects of ambient pressure and nozzle inlet type, it has reasonably agrees with the measured critical Reynolds number.

• KCI Concrete Journal
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• 제11권3호
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• pp.211-221
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• 1999

A method to determine the fracture energy of concrete is investigated. The fracture energy may be calculated from the area under the complete load-deflection curve which can be obtained from a stable three-point bend test. Several series of concrete beams have been tested. The Present experimental study indicates that the fracture energy decreases as the initial notch-to-beam depth ratio increases Some problems to be observed to employ the three-point bend method are discussed. The appropriate ratio of initial notch-to-beam depth to determine the fracture energy of concrete is found to be 0.5. It is also found that the influence of the self-weight of a beam to the fracture energy is very small A simple and accurate formula to predict the fracture energy of concrete is proposed.

• 사물인터넷융복합논문지
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• 제6권2호
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• pp.25-29
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• 2020

타원곡선 암호 알고리즘은 RSA 공개키 알고리즘에 비해 짧은 키의 길이와 적은 통신 부하 때문에 IoT 환경에서 인증용으로 많이 사용되고 있다. 타원곡선 암호 알고리즘의 핵심연산인 스칼라 곱셈이 안전하게 구현되지 않으면, 공격자가 단순 전력분석이나 차분 전력분석을 사용하여 비밀 키를 찾을 수 있다. 본 논문에서는 스칼라 난수화와 타원곡선점 가리기를 함께 적용하고, 연산의 효율성이 크게 떨어지지 않으며 전력분석 공격법에 대응하는 결합 난수 타원곡선 스칼라 알고리즘을 제안한다. 난수 r과 랜덤 타원곡선 점 R에 대해 변형된 Shamir의 두 배 사다리 알고리즘을 사용하여 타원곡선 스칼라 곱셈 kP = u(P+R)-vR을 계산한다. 여기에서 위수 n=2^l±c일 때, 2^lP=∓cP를 이용하여 l+20 비트 정도의 u≡rn+k(modn)과 ν≡rn-k(modn)를 구한다.

• 한국산림과학회지
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• 제57권1호
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• pp.1-7
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• 1982

원래 인구증가곡선(人口增加曲線)으로 알려진 단순(單純) logistic 곡선(曲線)은 초본식물(草本植物)의 성장표현(成長表現)에도 이용(利用)되어 왔다. 초본(草本)의 경우 이론치(理論値)와 실측치(實測値) 사이의 적합도(適合度)는 만족(滿足)스러운 것으로 알려져 있다. 그러나 초본(草本)과는 특성(特性)이 상이(相異)한 목본식물(木本植物)의 성장(成長)에 단순(單純) logistic 곡선(曲線)이 적용(適用)된 예는 극히 드물다. 따라서 그에 대한 적합성(適合性) 여부는 아직 의문시 되고 있다. 본연구(本硏究)에서는 임분밀도관리(林分密度管理)의 기초(基礎)가 되고 있는 단순(單純) logistic 곡선(曲線)의 적합성(適合性)을 조사하기 위하여 이것을 소나무임분(林分)에 적용(適用)시켜 보았다. 적합성검정(適合性檢定)을 위해서는 Chi-square test가 채용되었다.

• 대한수학회논문집
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• 제19권3호
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• pp.577-584
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• 2004

In a 4-valent multi 3-gon graph, every cut-through curve forms a simple closed circuit. Hence it is a weak arrangement of simple curves that is defined by Branko Grunbaum. In this paper, we study the edge properties of the 4-valent multi 3-gon graphs from the point of view of arrangement, and we show that they are 3 colorable.