• Title/Summary/Keyword: simple k-curve point

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Random Point Blinding Methods for Koblitz Curve Cryptosystem

  • Baek, Yoo-Jin
    • ETRI Journal
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    • v.32 no.3
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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.

Polar-Natural Distance and Curve Reconstruction

  • Kim, Hyoung-Seok;Kim, Ho-Sook
    • International Journal of Contents
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    • v.11 no.2
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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.

STRONG k-DEFORMATION RETRACT AND ITS APPLICATIONS

  • Han, Sang-Eon
    • Journal of the Korean Mathematical Society
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    • v.44 no.6
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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.

Simple Countermeasure to Cryptanalysis against Unified ECC Codes

  • Baek, Yoo-Jin
    • Journal of Communications and Networks
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    • v.12 no.1
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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.

A graph-based method for fitting planar B-spline curves with intersections

  • Bon, Pengbo;Luo, Gongning;Wang, Kuanquan
    • Journal of Computational Design and Engineering
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    • v.3 no.1
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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.

Prediction of Critical Reynolds Number in Stability Curve of Liquid Jet ( I )

  • No, S.Y.;Ryu, K.Y.;Rhim, J.H.;Lim, S.B.
    • Journal of ILASS-Korea
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    • v.4 no.1
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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.

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Prediction of Fracture Energy of Concrete

  • Oh, Byung-Hwan;Jang, Seung-Yup;Byun, Hyung-Kyun
    • KCI Concrete Journal
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    • v.11 no.3
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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.

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A Combined Random Scalar Multiplication Algorithm Resistant to Power Analysis on Elliptic Curves (전력분석 공격에 대응하는 타원곡선 상의 결합 난수 스칼라 곱셈 알고리즘)

  • Jung, Seok Won
    • Journal of Internet of Things and Convergence
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    • v.6 no.2
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    • pp.25-29
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    • 2020
  • The elliptic curve crypto-algorithm is widely used in authentication for IoT environment, since it has small key size and low communication overhead compare to the RSA public key algorithm. If the scalar multiplication, a core operation of the elliptic curve crypto-algorithm, is not implemented securely, attackers can find the secret key to use simple power analysis or differential power analysis. In this paper, an elliptic curve scalar multiplication algorithm using a randomized scalar and an elliptic curve point blinding is suggested. It is resistant to power analysis but does not significantly reduce efficiency. Given a random r and an elliptic curve random point R, the elliptic scalar multiplication kP = u(P+R)-vR is calculated by using the regular variant Shamir's double ladder algorithm, where l+20-bit u≡rn+k(modn) and v≡rn-k(modn) using 2lP=∓cP for the case of the order n=2l±c.

Stand Density Management Studies on Pine Stands in Korea (I) - The Simple Logistic Growth Curve and Its Application to Pine Stands - (소나무림(林)의 밀도관리(密度管理)에 관(關)한 연구(硏究)(I) - 단순(單純) logistic 곡선(曲線)과 소나무림(林)에 대한 그의 적용(適用) -)

  • Kwon, O Bok;Lee, Heung Kyun;Woo, Chong Chun
    • Journal of Korean Society of Forest Science
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    • v.57 no.1
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    • pp.1-7
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    • 1982
  • The simple logistic growth model on the logistic curve, being originally a kind of population growth curve has also been sometimes utilized to describe growth curves in herbaceous plants such as duckweed and sun-flowers. It has already been recognized that the agreement between the theoretical calculations and the empirical observations is quite satisfactory form a practical point of view. It remains, however, still doubtful whether the logistic curve could be applied to the growth or ordinary woody plants which is quite different in its character from that of herbaceous plants. In this study, the simple logistic model, being a basic tool of stand density management, is applied to yield data from pine stands in order to test the adequacy of the model An attempt of testing the significance of the fit is made by applying the Chi-square test.

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EDGE PROPERTIES OF THE 4-VALENT MULTI 3-GON GRAPHS

  • Jeong, Dal-Young
    • Communications of the Korean Mathematical Society
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    • v.19 no.3
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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.