• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1467-1474
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• 2014

In this paper, we consider the two computer intensive methods for extended Euclidean algdrithm. Two methods we propose are C-programming based approach and Microsoft excel based method, respectively. Thses methods are applied to the derivation of greatest commnon devisor, multiplicative inverse for modular operation and the solution of diophantine equation. Concrete investigation for extended Euclidean algorithm with the computer intensive process is given. For the application of extended Euclidean algorithm, we consider the RSA encrytion method which is still popular recently.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.8
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• pp.867-873
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• 2014

Since the computation of a multiplicative inverse using MONB includes many squarings and thus calculating inverse is expensive, we, in this paper, propose a low cost inverse algorithm requiring $nb(2^nm-1)+w(2^nm-1)-2$ multiplications and $2^n-1$ squarings to compute an inverse in $GF(2^{2^nm})^*$ using special normal basis over $GF(2^{2^n})$, and give some implementation results using the algorithm and, show that the timing results of our implementation is faster than that of Itoh et al.'s method.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.995-1006
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• 2008

This article deals with the one-sided hypothesis testing problem in inverse Gaussian distribution. We propose Bayesian hypothesis testing procedures for the one-sided hypotheses of the shape parameter under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the objective Bayesian hypothesis testing procedures based on the fractional Bayes factor, the median intrinsic Bayes factor and the encompassing intrinsic Bayes factor under the reference prior. Simulation study and a real data example are provided.

• Journal of the Korean Data and Information Science Society
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• v.26 no.3
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• pp.739-748
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• 2015

This paper deals with the problem of testing about the equality of the scale parameters in several inverse Gaussian distributions. We propose default Bayesian testing procedures for the equality of the shape parameters under the reference priors. The reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. Therefore we propose the default Bayesian testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• Proceedings of the Korea Information Processing Society Conference
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• 2002.11b
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• pp.995-998
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• 2002

여러 내장형 시스템에 탑재되는 암호모듈의 구현에 있어, 공개키 알고리즘을 위한 ECC 연산의 지연시간을 단축시키기 위해 유한체 연산은 하드웨어로 구현되는 경우가 많다. 그 중에서도 역원 연산은 지연시간 및 전력 소모, 또한 회로 면적에 있어 가장 주요한 부분을 차지하기 때문에 보다 효율적으로 구현하는 것이 필요하다. 본 논문에서 우리는 효율적인 역원 연산, 즉 작은 회로의 역원기를 위한 하드웨어의 구조를 제안한다. 실험에서, 우리가 구현한 구조는 기존에 주로 쓰이는 Modified Inverse Algorithm의 구현에 비해 비슷한 지연시간을 가지면서 회로 면적에 있어 큰 감소를 보이며 이는 스마트 카드 뿐 아니라 여러 mobile 내장형 시스템에 광범위하게 쓰일 수 있다.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1569-1579
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• 2014

This article deals with the problem of testing for the equality of the shape parameters in two inverse Weibull distributions. We propose Bayesian hypothesis testing procedures for the equality of the shape parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Simulation study and an example are provided.

• The Mathematical Education
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• v.50 no.3
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• pp.337-354
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• 2011

The purpose of the study was to investigate how students understand multiplication and division of fractions and how their understanding influences the solutions of fractional word problems. Thirteen students from 5th to 6th grades were involved in the study. Students' understanding of operations with fractions was categorized into "a part of the parts", "multiplicative comparison", "equal groups", "area of a rectangular", and "computational procedures of fractional multiplication (e.g., multiply the numerators and denominators separately)" for multiplications, and "sharing", "measuring", "multiplicative inverse", and "computational procedures of fractional division (e.g., multiply by the reciprocal)" for divisions. Most students understood multiplications as a situation of multiplicative comparison, and divisions as a situation of measuring. In addition, some students understood operations of fractions as computational procedures without associating these operations with the particular situations (e.g., equal groups, sharing). Most students tended to solve the word problems based on their semantic structure of these operations. Students with the same understanding of multiplication and division of fractions showed some commonalities during solving word problems. Particularly, some students who understood operations on fractions as computational procedures without assigning meanings could not solve word problems with fractions successfully compared to other students.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.45-54
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• 2012

In this paper, we prove stabilities of multiplicative functional equations in three variables such as $r(\frac{x+y+z}{3})-r(x+y+z)$=$\frac{2r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$ and $r(\frac{x+y+z}{3})+r(x+y+z)$=$\frac{4r(\frac{x+y}{2})r(\frac{y+z}{2})r(\frac{z+x}{2})}{r(\frac{x+y}{2})r(\frac{y+z}{2})+r(\frac{y+z}{2})r(\frac{z+x}{2})+r(\frac{z+x}{2})r(\frac{x+y}{2})}$.

• East Asian mathematical journal
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• v.35 no.3
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• pp.285-288
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• 2019

Let $F_n$, $n{\in}{\mathbb{N}}$ be the n - th Fibonacci number, and let (p, q) be one of ordered pairs ($F_{n+2}$, $F_n$) or ($F_{n+1}$, $F_n$). Then we show that the multiplicative inverse of q mod p as well as that of p mod q are again Fibonacci numbers. For proof of our claim we make use of well-known Cassini, Catlan and dOcagne identities. As an application, we determine the number $N_{p,q}$ of nonzero term of a polynomial ${\Delta}_{p,q}(t)=\frac{(t^{pq}-1)(t-1)}{(t^p-1)(t^q-1)}$ through the Carlitz's formula.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.30 no.3
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• pp.337-347
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• 2020

In CRYPTO 2019, Gohr presents that Deep-learning can be used for cryptanalysis. In this paper, we verify whether Deep-learning can identify the structures of S-box. To this end, we conducted two experiments. First, we use DDT and LAT of S-boxes as the learning data, whose structure is one of mainly used S-box structures including Feistel, MISTY, SPN, and multiplicative inverse. Surprisingly, our Deep-learning algorithms can identify not only the structures but also the number of used rounds. The second application verifies the pseudo-randomness of and structures by increasing the nuber of rounds in each structure. Our Deep-learning algorithms outperform the theoretical distinguisher in terms of the number of rounds. In general, the design rationale of ciphers used for high level of confidentiality, such as for military purposes, tends to be concealed in order to interfere cryptanalysis. The methods presented in this paper show that Deep-learning can be utilized as a tool for analyzing such undisclosed design rationale.