• Education of Primary School Mathematics
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• v.22 no.4
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• pp.281-294
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• 2019

The purpose of this study is to analyze errors and treatment behavior during the course of mathematics learning of academic achievement by applying reflective activities in the second semester of the third year of elementary school. The study participants are students from two classes, 21 from the third-grade S elementary school in Seoul and 20 from the comparative class. In the case of the experiment group, the multiplication unit was reconstructed into a mathematics class that applied reflective activities. They were pre-post-test to examine the changes in students' mathematics performance, and mathematical communication was recorded and analyzed for the focus group to analyze the patterns of learners' error handling in the reflective activities. In addition, they recorded and analyzed students' activities and conversations for error type and error handling. As a result of the study, the student's mathematics achievement was increased using reflective activities. When learning double digit multiplication, the error types varied. It was also confirmed that the reflective activities helped learners reflect on the multiplication algorithm and analyze the error-ridden calculations to reflect on and deal with their errors.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.457-477
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• 2016

The purpose of this study is to analyze and diagnose the type of errors indicated by the students in the process of calculation of the fractional multiplication and division, and to propose teaching methods, to effectively correct errors. The results obtained through this study are as follows. First, based on the results of the preliminary examination, 6 types of errors of the fractional multiplication and division has been organized. In particular, the most frequent types of errors are algorithm errors. Therefore, a teacher should explain the meaning and concept of fractional multiplication and division. Second, 4 prescription methods are proposed for understanding fractional multiplication and division. Third, according to the results of this study, it was effective to diagnose underachievers' error types and give corrective lesson according to the cause of the error types. Throughout the study, it's concluded that it is necessary to analyze and diagnose the error types of fractional multiplication and division, and then a teacher can correct error types by 4 proposed prescription methods. Also, 5 students showed interest while learning, and participated actively.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.24 no.1
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• pp.41-50
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• 2014

In this paper, we proposed an error detection in Gaussian normal basis multiplier over $GF(2^n)$. It is shown that by using parity prediction, error detection can be very simply constructed in hardware. The hardware overheads are only one AND gate, n+1 XOR gates, and one 1-bit register in serial multipliers, and so n AND gates, 2n-1 XOR gates in parallel multipliers. This method are detect in odd number of bit fault in C = AB.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.22 no.5
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• pp.1019-1025
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• 2012

Fault attacks manipulate the computation of an algorithm and get information about the private key from the erroneous result. It is the most powerful attack for the cryptographic device. Currently, the research on error detection methods and fault attacks have been studied actively. S. Pontarelli et al. introduced an error detection method in 2009. It can detect an error that occurs during Elliptic Curve Scalar Multiplication (ECSM). In this paper, we present a new fault attack. Our attack can avoid the error detection method introduced by S. Pontarelli et al. We inject a bit flip error in the Euclidean Addition Chain (EAC) on the private key in ECSM and retrieve the private key.

• The Journal of the Korea institute of electronic communication sciences
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• v.17 no.1
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• pp.173-180
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• 2022

Approximate Computing is a promising method for designing hardware-efficient computing systems. Approximate multiplication is one of key operations used in approximate computing methods for high performance and low power computing. An approximate 4-2 compressor can implement hardware-efficient circuits for approximate multiplication. In this paper, we propose an approximate multiplier with low area and low power characteristics. The proposed approximate multiplier architecture is segmented into three portions; an exact region, an approximate region, and a constant correction region. Partial product reduction in the approximation region are simplified using a new 4:2 approximate compressor, and the error due to approximation is compensated using a simple error correction scheme. Constant correction region uses a constant calculated with probabilistic analysis for reducing error. Experimental results of 8×8 multiplier show that the proposed design requires less area, and consumes less power than conventional 4-2 compressor-based approximate multiplier.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.1
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• pp.76-89
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• 2013

In this paper, we propose a novel optical fault detection scheme for RSA hardware based on Montgomery exponentiation, which can effectively detect optical fault injection during the exponent calculation. To protect the RSA hardware from the optical fault injection attack, we implemented integrity check logic for memory and optical fault detection logic for Montgomery-based multiplier. The proposed scheme is considered to be safe from various type of attack and it can be implemented with no additional operation time and small area overhead which is less than 3%.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.627-641
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• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.

• Journal of the Korean School Mathematics Society
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• v.17 no.3
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• pp.409-435
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• 2014

This study examines relations between the 5th graders' fraction operation skills and error types on constructed-response items. As results, first, the participants have lower fraction operation skills on 'multiplication of fraction' than 'addition and subtraction of fraction'. Second, the participants have different error types depend on their constructed-response items. Most of error types which group with high ability made was 'leap of solving process', both groups error type with medium ability as well as low ability is 'misunderstanding of questions'. Third, the operation skills on 'addition and subtraction of fraction' have an influence on their operation skills on 'multiplication of fraction', and error types of 'understanding of questions' and 'understanding of solving process' have the most effects on the influence.

• Proceedings of the Korea Information Processing Society Conference
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• 2004.05a
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• pp.1003-1006
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• 2004

본 논문에서는 몽고메리 모듈러 곱셈(Montgomery Modular Multiplication) 알고리즘을 이용하여 효율적인 모듈러 곱셈기를 제안한다. 본 논문에서 제안한 곱셈기는 프로그램 가능한 셀룰라 오토마타(Programmable Cellular Automata, PCA)를 기반의 구조로 설계되어 하드웨어 복잡도를 줄이고, 곱셈시 몽고메리 알고리즘을 이용하여 일반적인 나눗셈 없이 모듈러 연산을 수행하여 시간 복잡도를 최소화 한다. 제안된 곱셈기는 시간적, 공간적인 면에서 간단하고 효과적으로 구성되어 지수연산을 위한 하드웨어의 하부구조나 오류 수정 코드(Error Correcting Code)의 연산에서 효율적으로 이용될 수 있을 것이다.

• Proceedings of the Korean Information Science Society Conference
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• 2003.04a
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• pp.521-523
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• 2003

본 논문에서는 프로그램 가능한 셀룰라 오토마타(Programmable Cellular Automata, PCA)를 이용한 곱셈기를 제안한다. 본 논문에서 제안한 구조는 연산 후 늘어나는 원소의 수를 제한하기 위하여 이용되는 기약다항식(irreducible polynomial)으로서 All One Polynomial(AOP)을 사용하며, 주기적 경계 셀룰라 오토마타(Periodic Boundary Cellular Automata, PBCA)의 구조적인 특성을 사용함으로써 정규성을 높이고 하드웨어 복잡도와 시간 복잡도를 줄일 수 있는 장점을 가지고 있다. 제안된 곱셈기는 시간적. 공간적인 면에서 아주 간단히 구성되어 지수연산을 위한 하드웨어 설계나 오류 수정 코드(error correcting code)의 연산에 효율적으로 이용될 수 있을 것이다.