• Journal of the Korea Institute of Information Security & Cryptology
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• v.33 no.2
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• pp.211-222
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• 2023

Multivariate quadratic equations (MQ)-based public-key cryptographic algorithms are one of promising post-quantumreplacements for currently used public-key cryptography. After selecting to NIST Post-Quantum Cryptography StandardizationRound 3 as one of digital signature finalists, Rainbow was cryptanalyzed by advanced algebraic attacks due to its multiple layered structure. The researches on MQ-based schemes are focusing on UOV with a single layer. In this paper, we propose a new MQ-signature scheme based on UOV using the combinations of the special structure of linear equations, spare polynomials and random polynomials to reduce the secret key size. Our scheme uses the block inversion method using half-sized blockmatrices to improve signing performance. We then provide security analysis, suggest secure parameters at three security levels and investigate their key sizes and signature sizes. Our scheme has the shortest signature length among post-quantumsignature schemes based on other hard problems and its secret key size is reduced by up to 97% compared to UOV.

• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.243-248
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• 2002

최근 다변량자료분석과 관련하여 이를 시스템으로 구현하려는 연구가 다양한 각도로 이루어지고 있다. 이러한 연구들의 공통적인 특징은 일반 사용자들에게 고급 통계분석기법을 편리하게 활용할 수 있도록 GUI(Graphical User Interface) 환경의 시스템을 제공해 준 것이다. 이런 연구의 연장선상에서 본 연구에서는 다변량자료분석 시스템을 구현하는데 있어 사회 각 분야에서 가장 널리 활용되고 있는 사무용 프로그램인 마이크로소프트(Microsoft) Excel을 활용하여 일반 사용자들도 다변량분석을 쉽게 활용할 수 있도록 대화식 시스템을 개발하였다.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.34 no.1
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• pp.1-9
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• 2024

Multivariate Quadratic (MQ)-based digital signature schemes have advantages such as ease of implementation and small signature sizes, making them promising candidates for post-quantum cryptography. To enhance the efficiency of such MQ-based digital signature schemes, utilizing sparse matrices have been proposed, including HiMQ, which has been standardized by Korean Telecommunications Technology Association standard. However, HiMQ shares a similar key structure with Rainbow, which is a representative MQ-based digital signature scheme and was broken by the MinRank attack proposed in 2022. While HiMQ was standardized by a TTA and recommended parameters were provided, these parameters were based on cryptanalysis as of 2020, without considering recent attacks. In this paper, we examine attacks applicable to MQ-based digital signatures, specifically targeting HiMQ, and perform a security analysis. The most effective attack against HiMQ is the combined attack, an improved version of the MinRank attack proposed in 2022, and none of the three recommended parameters satisfy the desired security strength. Furthermore, HiMQ-128 and HiMQ-160 do not meet the minimum security strength requirement of 128-bit security level.

• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.369-385
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• 2017

This study is to figure out the activity and disposition of gifted students with face plot in exploratory data analysis at middle school mathematics class. This study has begun on the basis of the doing mathematics at multivariate analysis beyond one variable and two variables. Gifted students were developed the good learning habits theirselves. According to this result, Many gifted students have an interesting experience at data analysis with Face Plot. And they felt the useful methods of creative thinking about graphics with doing mathematics at mathematical tasks. I think that teachers need to learn the visualization methods and to make and to develop the STEAM education tasks connected real life. It should be effective enough to change their attitudes toward teaching and learning at exploratory data analysis.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.81-90
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• 2008

It has been noticed the greater importance of mathematical education, particularly of multi-variable calculus in the undergraduate level with remarkable progress of all sorts of sciences requiring mathematical analysis. However, there was lack of variety of introducing the definition of differentiation of multi-variable functions - in fact, all of them basically rely on the chain rules. Here we will introduce a way of defining the geometrical differentiation of the multi-variable functions based upon our teaching experience. One of its merits is that it provides the geometric explanation of the differentiation of the multi-variable functions, so that it conveys the meaning of the differentiation better compared with the known methods.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1991.11a
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• pp.72-84
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• 1991

본 논문에서는 컴퓨터 통신에 적합한 공개 키 암호시스팀을 제안한다. 이 방식은 기존의 Knapsack 형래 암호시스템 보다 간단하면서 높은 안전성을 갖는다. 이 Knapsack 형태의 공개 키 암호시스팀은 다변수 다항식의 초증가한 근을 기초로 한 것으로 암호화와 복호화 앨고리듬의 타당성을 보였다. 또한 제안된 공개 키 암호시스팀의 안전성은 다변수 다항식 분해의 다양성, 각 다항식에서 초증가 특성을 만족하는 근을 얻기 위한 어려움, 그리고 평문과 암호문 관계의 모호성을 기반으로 하며 이를 기존의 Knapsack 암호시스팀과 비교분석 하였다.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.165-172
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• 2004

Recently, there have been several studies to develop the multivariate data analysis system which can be readily used. The common characteristic of these studies is to develop the GUI system to which advanced statistical methods can be conveniently applied. In an extension of these studies, this study aims to supply users in various fields an interactive system with the convenience of the environment of GUI, which is constructed with the Excel macro and VBA, to apply multivariate data analysis methods easily. This system provides a graphic-oriented and menu-centered user interface in the Microsoft Excel which is widely used spreadsheet and analysis program.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.385-388
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• 2006

비선형 주성분 분석은 기존에 널리 알려져 있는 주성분 분석기법과 유사한 다변수 데이터 분석을 위한 새로운 접근 방법이다. 비선형 주성분 분석은 AANN(Auto Associative Neural Network)으로 PCA와 마찬가지로 변수들 간에 존재하는 상관관계를 제거함으로써 고차의 다변수 데이터를 정보의 손실을 최소화하면서 최소 차원의 데이터로 변환하는 기법이다. AANN 기반 센서노드 고장검출 기법을 실제 센서 네트워크에 적용하여 봄으로써 센서 드리프트 등과 같은 센서 고장의 검출 및 유효한 센서 보정 성능을 확인하였다.

• Journal of Korea Game Society
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• v.11 no.2
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• pp.39-44
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• 2011

Computer games need game formulas which express game rules by mathematical functions because the game rules are automatically processed by computers. The game formulas are usually multi-variable functions. So the design of a game formula is a complex and difficult problem because it is the same problem of the design of a multi-variable function which should satisfy the related game rules. In this paper we propose a new method which can systematically design game formulas. The purposed method is the decomposing of tree structure for a game formula by analyzing the tree structure of the operands which have single-variable functions on the lowest levels. So the design method can change the complex and difficult problem of the design of a multi-variable function to the simple and easy problem of the design of the single-variable function which should satisfy the related game rules.

• Journal for History of Mathematics
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• v.10 no.2
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• pp.48-52
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• 1997

통계학이란 미래에 대한 예측을 하고 이에 대비하여 합리적인 의사결정을 내리는데 도움을 받을 수 있는 학문이다. 최근 다변량 통계분석은 관찰이나 실험의 대상이 되는 하나 이상의 변수들을 동시에 분석할 수 있는 매우 실제성이 높은 분석방법으로 통계학, 경영학, 사회학, 심리학, 생물학 등 여러 전공 분야에서 복잡하고 다양한 자료 분석에 폭넓게 활용되고 있다. 이 논문에서는 다변량 분석 방법 중 컴퓨터와 통계 분석 소프트웨어의 발전으로 인하여 최근에 활발히 연구되고 있는 군집방법의 역사와 여러 연구분야의 실제자료분석에 응용할 수 있도록 군집분석을 6가지로 나누어서 분류하였고 그 방법론을 제시하였다.