• Journal of the Korea Institute of Information Security & Cryptology
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• v.13 no.3
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• pp.57-64
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• 2003

Recently, it has been shown that cryptographic devices such as smart cards are vulnerable to power attacks. In this paper, by mixing the randomization concept and the folding in half for secret scalar integer on ECCs, we propose an efficient and fast scalar multiplication algorithm to resist against simple power analysis(SPA) and differential power analysis(DPA) attacks. Our proposed algorithm as a countermeasure against SPA and DPA is estimated as a 33% speedup compared to the binary scalar multiplication.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.333-336
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• 1999

In this paper, a new high speed parallel input and parallel output GF(2$^{m}$ ) multiplier based on standard basis is proposed. The concept of the multiplication in standard basis coordinates gives an easier VLSI implementation than that of the dual basis. This proposed algorithm and method of implementation of the GF(2$^{m}$ ) multiplication are represented by two kinds of basic cells (which are the generalized and fixed basic cell), and the minimum critical path with pipelined operation. In the case of the generalized basic cell, the proposed multiplier is composed of $m^2$ basic cells where each cell has 2 two input AND gates, 2 two input XOR gates, and 2 one bit latches Specifically, we show that the proposed multiplier has smaller complexity than those proposed in 〔5〕.

• Journal of Gifted/Talented Education
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• v.24 no.1
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• pp.17-43
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• 2014

On the subjects of elementary 3rd grade three child prodigies who had learned the four fundamental arithmetic operations and primary concepts of fraction, this study conducted a qualitative case research to examine how they composed schema of addition and multiplication of fractions and transformed schema through recognition of precise concepts and linking of concepts with addition and multiplication of fractions as the contents. That is to say, this study investigates what schema and transformed schema child prodigies form through composition of primary mathematic concepts to succeed in relational understanding of addition and multiplication of fractions, how they use their own formed schema and transformed schema for themselves to approach solutions to problems with addition and multiplication of fractions, and how the subjects' concept formation and schema in their problem solving competence proceed to carry out transformations. As a result, we can tell that precise recognition of primary concepts, schema, and transformed schema work as crucial factors when addition of fractions is associated with multiplication of fractions, and then that the schema and transformed schema that result from the connection among primary mathematic concepts and the precise recognition of the primary concepts play more important roles than any other factors in creative problem solving with respect to addition and multiplication of fractions.

• Journal of Educational Research in Mathematics
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• v.20 no.4
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• pp.445-458
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• 2010

This study intends to investigate the process of the development of quantity concept and how to deal with the quantity calculus in elementary school, and to find out the implication for improving the curriculum and mathematics textbooks of Korea. There had been the binary Greek categories of discrete number and continuous magnitude in quantity concept, but by the Stevin's introduction of decimal, the unification of these notions became complete. As a result of analyzing of the curriculum and mathematics textbooks of Korea, there is a tendency to disregard the teaching of quantity and its calculus compared to the other countries. Especially multiplication and division of quantity is seldom treated in elementary mathematics textbooks. So these should be reconsidered in order to seek the direction for improvement of mathematic teaching. And Korea's textbooks need the emphasis on the quantity calculus and on constructing quantity concept.

• Journal of the Korean School Mathematics Society
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• v.14 no.4
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• pp.477-490
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• 2011

The concept of pedagogical content knowledge (PCK) has been developed and expanded to identify essential components of mathematical knowledge for teaching (MKT) by Ball and her colleagues (2008). This study proposes an alternative perspective to view MKT focusing on key developmental understandings (KDUs) that carry through an instructional sequence, that are foundational for learning other ideas. In this study we provide constructive components of KDUs in fraction multiplication by focusing on the constructs of 'three-level-of-units structure' and 'recursive partitioning operation'. Expecially, our participating preservice elementary teacher, Jane, demonstrated that recursive partitioning operations with her length model played a significant role as a KDU in fraction multiplication.

• The Mathematical Education
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• v.4 no.1
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• pp.16-28
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• 1966

According to the modernization of mathematics education, new abstract concepts such as the concept of sets are introduced in many fields of it. The purpose of this thesis is to adopt the concept of sets to 'probability' which is included in the curriculum of high school matematics education. The considerations of the preceding chapter III, and their obvious generalizations to more complicated experiments, justify the conclusion that probability theory consists of the study of sets. An event is a set, its opposite event is the complementary set; mutually exclusive events are disjoint sets, and an event consisting of the simultaneous occurrence of two other events is a sets obtained by intersecting two other sets it is clear how this glossary, translating physical terminology into set theoretic terminology, may be continued. Furthermore, the important theorems of probability; Additional theorem, multiplication theorem, their applications and so on, are proved by the technical operations of sets. Thinking of the mathematics education introduced by the concept of sets is very important in future.

• East Asian mathematical journal
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• v.28 no.2
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• pp.135-158
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• 2012

The ideals of the rings of integers are used to induce rational number system as operators(=group homomorphisms). We modify this inducing method to be effective in teaching rational numbers in secondary school. Indeed, this modification provides a nice model for explaining the equality property to define addition and multiplication of rational numbers. Also this will give some explicit ideas for students to understand the concept of 'field' efficiently comparing with the integer number system.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.259-266
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• 2015

Let G be a group with identity e. Let R be a G-graded commutative ring and M a graded R-module. In this paper, we introduce the concept of graded quasi-prime submodules and give some basic results about graded quasi-prime submodules of graded modules. Special attention has been paid, when graded modules are graded multiplication, to find extra properties of these submodules. Furthermore, a topology related to graded quasi-prime submodules is introduced.

• The Mathematical Education
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• v.48 no.3
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• pp.353-358
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• 2009

The article discusses the independence concept occurring in the learning of probability. The author does not distinguishes the independence in the events from the independence in the trials. Instead, the author suggests the physico-empirical independence and the logico-mathematical independence to distinguish between the two concepts.

• Journal of Educational Research in Mathematics
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• v.19 no.2
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• pp.257-271
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• 2009

Stochastical independence is separated into two. One can be intuitively judged and the other is not. Independence is a concept based on assumption. However, It is defined as multiplication rule and it has produced extension of concept. Analysis on this issue is needed, assuming the cause is on the intersection sign which is used for both simultaneous events and compatible events. This study presented the extension process of independence concept in detail and constructed twofold interpretation of simultaneous events and compatible events which use the same sign $P(A\cap{B})$ with Pierce Semiotics.