• Proceedings of the Korea Information Processing Society Conference
• /
• 2010.11a
• /
• pp.1320-1323
• /
• 2010

2009년 Yang과 Chang은 Computers and Security에 "An ID-based-remote mutual authentication with key agreement scheme on elliptic curve cryptosystem"을 제안하였다. 하지만 제안된 방법에서 사용한 타원곡선 곱셈에서 수학적 오류를 범하였고, 수학적 오류를 수정한 방법을 제안하고자 한다.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.25 no.5
• /
• pp.979-984
• /
• 2015

In this paper, we proposed a Semi-Systolic multiplier of $GF(2^n)$ with Type II optimal Normal Basis. Comparing the complexity of the proposed multiplier with Chiou's multiplier proposed in 2012, it is saved $2n^2+44n+26$ in total transistor numbers and decrease 4 clocks in time delay. This means that, for $GF(2^{333})$ of the field recommended by NIST for ECDSA, the space complexity is 6.4% less and the time complexity of the 2% decrease. In addition, this structure has an advantage as applied to Chiou's method of concurrent error detection and correction in multiplication of $GF(2^n)$.

• Journal of The Korean Association of Information Education
• /
• v.26 no.4
• /
• pp.285-293
• /
• 2022

The COVID-19 outbreak, which took longer than expected, caused considerable damage to students' basic academic ability in mathematics. In this paper, a multiplication table practice application that can help students improve their basic multiplication arithmetic skills has been developed based on a cloud-service. The performance of the application was improved by integrating the Flutter framework, Google Cloud, and Google Sheets. As a result of applying this application to 72 6th graders in elementary schools located in K Metropolitan City, for one week. students' spending time required for solving multiplication table problems was reduced by more than 28% compared to the initial period, while students' learning data was able to be accurately collected without errors. It is hoped that the development case conducted through the Flutter framework in this study can lead to the development of other educational learning applications.

• School Mathematics
• /
• v.6 no.3
• /
• pp.235-249
• /
• 2004

The purpose of this study was to analyze the error patterns and sentence types in word problems with respect to 1$\frac{3}{4}$$\div$$\frac{1}{2}$ which were made by the pre-service elementary teachers, and to suggest the clues to the education in pre-service. Korean elementary teachers in pre-service misunderstood 'divide with $\frac{1}{2}$' to 'divide to 2' by the Korean linguistic structure. And they showed a new error type of 1$\frac{3}{4}$$\times$2 by the result of calculation. Although they are familiar to 'inclusive algorithm' they are not good at dealing with the fractional divisor. And they are very poor at the 'decision the unit proportion' and the 'inverse of multiplication'. So, it is necessary to teach the meaning of the fractional division as 'decision the unit proportion' and 'inverse of multiplication' and to give several examples with respect to the actual situation and context.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2004.05b
• /
• pp.247-250
• /
• 2004

Goldschmidt 알고리즘에 의한 부동소수점 1.f2의 역수는 q=NK1K2....Kn (Ki=1+Aj, j=2i)이다. 본 논문에서는 N과 A 값을 1.f2의 값에 따라서 선정하고 Aj의 값이 유효자리수의 반이하 값을 가지면 연산을 종료하는 개선된 Goldschmidt 부동소수점 역수 알고리즘을 제안한다. 1.f2가 1.01012보다 작으면 N=2-1.f2, A=1.f2-1로 하며, 1.01012보다 크거나 같으면 N=2-0.lf2, A=1-0.lf2로 한다. 한편 Goldschmidt 알고리즘은 곱셈을 반복해서 수행하므로 계산 오류가 누적이 된다. 이러한 누적 오류를 감안하면 배정도실수 역수에서는 2-57, 단정도실수 역수에서는 2-28의 유효자리수까지 연산해야 한다. 따라서 Aj가 배정도실수 역수에서는 2-29, 단정도실수 역수에서는 2-14 보다 작아지면 연산을 종료한다. 본 논문에서 제안한 개선한 Goldschmidt 역수 알고리즘은 N=2-0.1f2, A=1-0.lf2로 계산하는 종래 알고리즘과 비교하여 곱셈 연산 회수가 배정도실수 역수는 22%, 단정도실수 역수는 29% 감소하였다. 본 논문의 연구 결과는 테이블을 사용하는 Goldschmidt 역수 알고리즘에 적용해서 연산 시간을 줄일 수 있다.

• School Mathematics
• /
• v.11 no.4
• /
• pp.567-581
• /
• 2009

Many articles have reported that zero causes children's arithmetic errors. This article was designed to measure the effect of zero on children's arithmetic performances. For this, 222 of 3,4,5,6 graders in elementary school were tested with pencil and paper. The test were categorized into four parts: basic number fact, column subtraction, column multiplication, and column division. These data showed that the negative effect of zero on children's arithmetic was limited to several areas, concretely, multiplication facts with zero, column subtraction with numbers which have two successive zeros, column multiplication with numbers which have zero in a middle position, long division with zeros. But there was no evidence that students could self-control these negative effects of zero as grade went up. It implies that we should keep attention to children's arithmetic performance with zero in some special areas.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.24 no.8A
• /
• pp.1238-1244
• /
• 1999

In this paper, a new design of a triple-erroe-correcting (TEC) Reed-Solomon decoder is presented based on direct decoding method which is more efficient for the case of relatively small error correction capability. The proposed decoder requires only 9 GF(2m) multipliers in obtaining the error-locator polynomial and the error-evaluator polynomial, whereas other decoders needs 24 multipliers. Thus, the attractive feature of this decoder is its remarkable simplicity from the point of view of implementation. Futhermore, the proposed TEC Reed-Solomon decoder has very simple control circuit and short decoding delay. Therefore this decoder can be implemented by simple hardware and also save buffer memory which stores received sequence.

• Proceedings of the KIEE Conference
• /
• 2003.07d
• /
• pp.2702-2704
• /
• 2003

본 논문은 전력선통신시스템 (Power Line Communications)을 위한 초고속 오류정정 부호화기 회로에 관한 설계방법론과 회로의 동작속도, 회로복잡성과 레이턴시에 직접적으로 기여하는 핵심 GF (Galois Field) 연산기들의 역할 및 이들의 설계결과에 관해 설명한다. 특히, 이러한 설계방법에 충실한 오류정정 부호화기회로는 입출력 병렬구조의 세미-시스톨릭 (Semi-systolic) 아키텍처를 갖는 고속의 내부 핵심 GF 연산기회로들을 채택함으로써 고속 연산을 가능토록 한다. 최적화된 GF곱셈연산기를 기반으로 설계되어진 리드-솔로몬 (Reed-Solomon) 오류정정 부호화기는 전력선 채널상에서 데이터를 전송 시 발생되는 연집오류들을 효과적으로 복원하도록 하는 대표적인 부호화기로 이미 존재하는 다른 회로들에 비해 동작속도, 회로의 복잡성, 및 레이턴시 측면에서 그 성능이 월등히 뛰어나므로, 실제 초고속 전력선 통신시스템의 설계 및 구현 시 효과적으로 이용될 수 있다.

• Journal of IKEEE
• /
• v.26 no.4
• /
• pp.736-741
• /
• 2022

Lattice-based cryptography is the most practical post-quantum cryptography because it enjoys strong worst-case security, relatively efficient implementation, and simplicity. Ring learning with errors (R-LWE) is a public key encryption (PKE) method of lattice-based encryption (LBC), and the most important operation of R-LWE is the modular polynomial multiplication of rings. This paper proposes a method for optimizing modular multipliers based on approximate computing (AC) technology, targeting the medium-security parameter set of the R-LWE cryptosystem. First, as a simple way to implement complex logic, LUT is used to omit some of the approximate multiplication operations, and the 2's complement method is used to calculate the number of bits whose value is 1 when converting the value of the input data to binary. We propose a total of two methods to reduce the number of required adders by minimizing them. The proposed LUT-based modular multiplier reduced both speed and area by 9% compared to the existing R-LWE modular multiplier, and the modular multiplier using the 2's complement method reduced the area by 40% and improved the speed by 2%. appear. Finally, the area of the optimized modular multiplier with both of these methods applied was reduced by up to 43% compared to the previous one, and the speed was reduced by up to 10%.

• Journal of the Korean School Mathematics Society
• /
• v.13 no.3
• /
• pp.345-356
• /
• 2010

Variables and expressions are essential for doing mathematics. Especially abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ are current rules that we usually follow. In this paper, we devised a Card-Game for exercising abbreviations of the multiplication sign ${\times}$ and the division sign ${\div}$ in calculating expressions, designed a teaching unit for the calculation of expressions using the Card-Game in the variables and expressions strand, and discussed the implications of using the Card-Game for motivating students, cooperative learning, diagnosis and correction of errors, and so on.