• Journal of the Institute of Electronics Engineers of Korea CI
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• v.41 no.5
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• pp.17-23
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• 2004

In this paper, we proposed a mixed algerian to improve decimal division speed. In the binary number system, nonrestoring algorithm has a smaller number of operation than restoring algorithm. In decimal number system however, the number of operations differs with respect to quotient values. Since one digit ranges 0 to 9 in decimal, the proposed mixed algerian employs both nonrestoring and restoring algorithm considering current partial remainder values. The proposed algorithm chooses either restoring or nonrestoring algerian based on the remainder values. The proposed algorithm improves computation speed substantially over a single algorithm decreasing the number of operations.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.20 no.3
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• pp.135-140
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• 2010

The computation using Chinese Remainder Theorem in RSA cryptosystem is well suited in the digital signature or decryption processing due to its low computational load compared to the case of general RSA without CRT. Since the RSA-CRT algorithm is vulnerable to many fault insertion attacks, some countermeasures against them were proposed. Among several countermeasures, Yen et al. proposed two schemes based on fault propagation method. Unfortunately, a new vulnerability was founded in FDTC 2006 conference. To improve the original schemes, Kim et al. recently proposed a new countermeasure in which they adopt the AND operation for fault propagation. In this paper, we show that the proposed scheme using AND operation without checking procedure is also vulnerable to fault insertion attack with chosen messages.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.20 no.4
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• pp.155-160
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• 2010

Since the RSA cryptosystem based on Chinese Remainder Theorem is vulnerable to many fault insertion attacks, some countermeasures against them were proposed. Recently, Kim et al. or Ha et al. respectively proposed each countermeasure scheme based on fault propagation method. Unfortunately, Hur et al. insist that these countermeasures are vulnerable to their opcode modification fault attack. In this paper, we show that the proposed attack can not apply to almost CRT-RSA countermeasures which use multi-precision operations in long bit computation. Therefore, the countermeasure against fault attack proposed by Kim et al. or Ha et al. are still secure.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.4
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• pp.717-735
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• 2016

For teaching division-with-remainder(DWR) problems, it is necessary to know students' strategies and errors about DWR problems. The purpose of this study is to investigate and analyze students' strategies and errors of DWR problems and to make some meaningful suggestions for teaching various methods of solving DWR problems. We constructed a test which consists of fifteen DWR problems to investigate students' solving strategies and errors. These problems include mathematical as well as syntactic structures. To apply this test, we selected 177 students from eight elementary schools in various districts of Seoul. The results were analyzed both qualitatively and quantitatively. The sixth graders' strategies can be classified as follows : Single strategies, Multi strategies and Assistant strategies. They used Division(D) strategy, Multiplication(M) strategy, and Additive Approach(A) strategy as sub-strategies. We noticed that frequently used strategies do not coincide with strategies for their success. While students in middle group used Assistant strategies frequently, students in higher group used Single strategies frequently. The sixth graders' errors can be classified as follows : Formula error(F error), Calculation error(C error), Calculation Product error(P error) and Interpretation error(I error). In this study, there were 4 elements for syntaxes in problems : large number, location of divisor and dividend, divisor size, vocabularies. When students in lower group were solving the problems, F errors appeared most frequently. However, in case of higher group, I errors appeared most frequently. Based on these results, we made some didactical suggestions.

• Knowledge Management Research
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• v.10 no.3
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• pp.115-132
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• 2009

This paper makes an analysis of economic spillover effects of credit guarantee by linking the remainder of guarantee according to industries from 2003 to 2006 in this study. Specifically, total remainder of guarantee in 2006 is approximately 3922 billion and 600 million won on the basis of unchangeable price in 2003, and each funds becomes the input of the last demand in 27 industries over the cow1try and, thereby, induces production, added value, and the effect of employment. The last demand according to industries shows that a lot of funds have been supported to the manufacturing industry for about 1200 billion won, the wholesale and retail for about 1299 billion and 500 million won, food and lodging industry for about 144 billion and 100 million won, education and health care industry for about 132 billion and 600 million won, and social and other service industry for about 339 billion and 300 million won. The spillover effect about the remainder of guarantee in 2006 classified by industries over the country on the basis of production shows the high effects on the manufacturing industry for 37.8%, 2625 billion and 90 million won, the wholesale and retail for 20.7%, 1439 billion and 290 million won, food and lodging industry for 9.4%, 654 billion and 570 million won, real estate and business service industry for 9.2%, 637 billion and 310 million won, social and other service industry for 5.3%, 369 billion and 90 million won, and education and health care industry for 2.9%, 199 billion and 300 million won of the effect causing production over the country, 6945 billion won in order. The effect causing added value shows high spillover effect on the wholesale and retail for 36.7%, 1186 billion and 830 million won, the manufacturing industry for 25.8%, 831 billion and 500 million won, food and lodging industry for 14.9%, 480 billion and 980 million won, social and other service industry for 9.3%. 300 billion and 160 million won, and real estate and business service industry for 4.2%, 135 billion and 36 million won of the effect causing added value over the country in order. Finally, the effect causing employment shows a lot of employment have occurred in the wholesale and retail for 37.4%, 23,060 people, the manufacturing industry for 18.9%, 11,637 people, food and lodging industry for 13.7%, 8,429 people, social and other service industry for 7.9%, 4,866 people, and real estate and business service industry for 5.6%, 3,429 people of 61,617 people in order.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.2
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• pp.21-34
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• 2002

In this paper we propos a new hardware architecture of modular exponentiation using a division chain method which has been proposed in (2). Modular exponentiation using the division chain is performed by receding an exponent E as a mixed form of multiplication and addition with divisors d=2 or $d=2^I +1$ and respective remainders r. This calculates the modular exponentiation in about $1.4log_2$E multiplications on average which is much less iterations than $2log_2$E of conventional Binary Method. We designed a linear systolic array multiplier with pipelining and used a horizontal projection on its data dependence graph. So, for k-bit key, two k-bit data frames can be inputted simultaneously and two modular multipliers, each consisting of k/2+3 PE(Processing Element)s, can operate in parallel to accomplish 100% throughput. We propose a new encoding scheme to represent divisors and remainders of the division chain to keep regularity of the data path. When it is synthesized to ASIC using Samsung 0.5 um CMOS standard cell library, the critical path delay is 4.24ns, and resulting performance is estimated to be abort 140 Kbps for a 1024-bit data frame at 200Mhz clock In decryption process, the speed can be enhanced to 560kbps by using CRT(Chinese Remainder Theorem). Futhermore, to satisfy real time requirements we can choose small public exponent E, such as 3,17 or $2^{16} +1$, in encryption and verification process. in which case the performance can reach 7.3Mbps.

• Proceedings of the KIPE Conference
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• 2003.07a
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• pp.182-185
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• 2003

Proposed Hybrid System is composed of phase leading capacitor banks, LC passive filters and active power filter. The passive power filter in parallel connection eliminate the 5th and 7th harmonics. The Variable capacitor banks correct the most of power factor, and the active power filter takes charge of remainder,

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.797-812
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• 1997

For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss-Radau and the Gauss-Lobatto rules with end points of multiplicity r and prove the convergence of the kernel we obtained. The error bound are obtained for the type $$\mid$R_n(f)$\mid$ \leq \frac{1}{\pi}l(\Gamma) max_{z \in \Gamma} $\mid$K_n(z)$\mid$ max_{z \in \Gamma} $\mid$f(z)$\mid$$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.627-634
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• 2001

Under contamination, Bahadur representations with a strong remainder term are derived for random central order statistics with a prescribed limiting rank, and asymptotic normalities for these statistics of truncated and contaminated data are proved, with a suitable limiting rank. From these results, an application to the fixed-width confidence interval problem is available.

• The Korean Journal of Pain
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• v.3 no.1
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• pp.11-14
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• 1990

Thirty-two cancer patients were treated with various pain control methods. In those who had localized pain or more than 1 year life expectancy. The author preferred neurolytic blockade for whom had localized pain or had more than 1 year life-expectancy to epidural or intrathecal narcotics. The latter methods were saved as a last resort. Effective pain relief was achieved in over 80% of those treated. There were no serious complications. Of the 12 epidural or intrathecally implanted catheter with subcutaneous tunneling cases, successful pain management was possible throughout the remainder of life which was from 1 week to 6 months.