• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.8 no.6
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• pp.15-20
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• 2008

Provable security has widely been used to prove a cryptosystem's security formally in crpytography. In this paper, we analyze the Cramer-Shoup public key cryptosystem that has been known to be provable secure against adaptive chosen ciphertext attack and argue that its security proof is not complete in the generic sense of adaptive chosen ciphertext attack. Future research should be directed toward two directions: one is to make the security proof complete even against generic sense of adaptive chosen ciphertext attack, and another is to try finding counterexamples of successful adaptive chosen ciphertext attack on the Cramer-Shoup cryptosystem.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2008.05a
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• pp.17-28
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• 2008

이 논문은 중학교 기하 영역의 수업에 대한 학생들의 성취도가 낮은 것을 관찰하고, 그에 대한 고민으로 교육과정을 분석하고, 수학교육의 질적 접근을 위한 교수 실험을 통해 실제 중학교 과정에서 운용되는 논증기하 교육의 문제점과 그 대안을 탐색하고자 하였다. 본 연구에서는 교사가 반드시 갖춰야 할 지식으로 Shulman(1986)이 제시한 교과 내용 지식과 교수학적 내용 지식, 그리고 교육과정 관련 지식을 받아들였으며, 중학교 기하 영역에서 이런 지식을 갖추기 위해 교사가 폭넓은 고민을 하여 수업의 개선점을 찾는 과정을 보여주고 있다. 연구를 통해서 학생들에게 명제를 지도할 때 주의할 점과 학습자에게 증명을 하도록 제시하는 방법상의 문제점, 그리고 이등변삼각형의 지도에서의 그 증명이 갖는 의미를 잘 이해하여 학생들에 증명 학습에 진정한 도움이 될 수 있는 방향을 탐색하였다. 그리고 절차만을 학습시키는 현행 작도 수업을 개선하기 위한 여러 시도와 등변사다리꼴의 학습에서와 같이 학생들이 수학 용어를 되돌아보는 수업이 필요성을 탐색하여, 많은 교수 실험을 통한 교육과정의 바람직한 개정을 제안하였다.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.245-263
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• 2002

인류 문명의 발달과 함께 폭넓게 활용된 수학적 내용 중의 하나가 피타고라스 정리이다. 특히, 이집트, 메소포타미아, 그리고 중국과 같은 고대 문명의 발생지에서 발굴되는 많은 역사적 기록 속에서 피타고라스 정리에 대한 내용을 찾아볼 수 있다. 피타고라스 정리는 중등학교 수학교육에서 매우 중요한 정리로써, 정리 내용 자체뿐만 아니라 다양한 증명 방법과 증명 과정에 내재된 수학적 아이디어는 수학교육적 측면에서 큰 의미를 가지고 있다. 본 연구에서는 중학교 수학 교과 내용과 관련된 피타고라스 정리의 증명 방법들을 소개하고, 각 증명에 내재된 수학적 아이디어를 기술할 것이다.

• The Transactions of the Korea Information Processing Society
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• v.4 no.6
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• pp.1557-1564
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• 1997

We propose an extension to Prolog called the count term for controlling Prolog execution. The purpose is to allow the programmers as well as the users to have greater flexibility in controlling the execution behavior of Prolog programs and for limiting the number of answers or proofs retrieved when Prolog is used as a database query language. Both syntax and operational semantics of the count term are defined. An implementation strategy based on WAM (Warren Abstract Machine) by modifying instructions related to backtracking behavior has been suggested.

• The Transactions of the Korea Information Processing Society
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• v.6 no.11
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• pp.2981-2988
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• 1999

A deductive database consists of facts being the extensional database and rules being the intensional database. Because of the difficulty of evaluating rules, many parallel evaluation algorithms for rules have been presented. But we have not gotten an acceptable result. This paper proposes a new methodology to evaluate proof-theoretic meaning of the linear recursion rule which contains transitive dependency by using a shared-nothing parallel architecture. As first, we prove that there exists the equivalent expression for a linear recursion rule, design the algorithm for evaluating the linear recursion rule based on the equivalent expression, and finally analyse performance of the proposed algorithm.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.20 no.3
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• pp.3-8
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• 2010

There are some efficient brute force algorithm for factorization. Fermat's factorization is one of the way of brute force attack. Fermat's method works best when there is factor near the square-root. This paper shows that why Fermat's method is effective and verify that there are only one answer. Because there are only one answer, we can start Fermat's factorization anywhere. Also, we convert from factorization to finding square number.

• Journal of the Korea Society of Computer and Information
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• v.27 no.7
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• pp.35-48
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• 2022

In this study, it propose a proof theory method for expressing and reasoning knowledge in a multiagent environment. Since this method determines logical results in a mechanical way, it has developed as a core field from early AI research. However, since the proposition cannot always be proved in any set of closed sentences, in order for the logical result to be determinable, the range of expression is limited to the sentence in the form of a clause. In addition, the resolution principle, a simple and strong reasoning rule applicable only to clause-type sentences, is applied. Also, since the proof theory can be expressed as a meta predicate, it can be extended to the metalogic of the proof theory. Metalogic can be superior in terms of practicality and efficiency based on improved expressive power over epistemic logic of model theory. To prove this, the semantic method of epistemic logic and the metalogic method of proof theory are applied to the Muddy Children problem, respectively. As a result, it prove that the method of expressing and reasoning knowledge and common knowledge using metalogic in a cooperative multiagent environment is more efficient.

• Journal of Educational Research in Mathematics
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• v.18 no.4
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• pp.455-467
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• 2008

We need to reflect the establishment of meaning and level of 'proof and argumentation in middle school mathematics'. It should be considered as human activity through communication in community. Thus, we should design instruction from this standpoint. From this point of view, we had been operated 'Geometry Inquiry Class' aimed at middle school students in eighth grade for two years to improve current geometry class in middle school. In this study, we will observe how individual students' original proof schemes are developed and accepted to the class through the process of mutual negotiation between the teacher and students. The episode with four phases begins with the initial proof schemes students have offered. Through the negotiation of class participants, it gives birth to the proof scheme unique to the current geometry classroom. Why do we pay attention to the process? It is because we think that the value of this type of instruction lies in the process of communication and mutual understanding and mutual reference, not in the completeness of the final product. This is the very appropriate proof in the middle school mathematics classroom.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.887-921
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• 2009

Pythagorean theorem is one of mathematical contents which is widely used during human culture have developed. There are many historial records related to Pythagorean theorem made by Babylonian, Egyptian, and Mesopotamian. The theorem has the important meaning for mathematics education in secondary school education. Along with the importance of the proof itself, diverse proof methods and ideas included in their methods are also important since the methods improve students' ability to think mathematics. Hence, in this paper, we classify and analyze 390 proof methods published in the book "All that Pythagorean theorem" and other materials. Based on the results we derive educational meaning in mathematics with respect to main idea of the proof, the preliminaries of the study, and study skills used for proof.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.606-608
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• 1999

본 논문에서는 이동 로봇의 유연하고 짧은 경로 계획을 위하여 기존의 그리드 셀(grid cell)로 구성되는 지도 대신에 삼각형을 이용하여 지도를 구성하는 새로운 방법을 제안한다. 기존의 그리드 셀로 구성되는 지도의 경우 이동 로봇가 현재 셀에서 다음 셀로 진행시 진행 방향이 8 방향이나, 본 논문에서 제안한 방법에 의해 구성된 새로운 지도는 셀을 삼각형으로 표현함으로써, 이동 로봇의 진행 방향이 12 방향이 된다. 이와 같이 이동 로봇의 진행 방향이 증가한다는 것은 이동 로봇이 더욱 유연하게 장애물을 회피하며 더욱 짧은 경로로 주행할 수 있는 가능성을 의미한다. 한편, 본 논문에서 제안한 삼각형 지도 작성 방법의 효율성을 기존의 그리드 셀을 이용한 경로 계획 알고리즘인 거리 변환(path transform) 경로 계획을 통하여 증명한다. 또한 새로운 삼각형 지도 구성이 메모리의 효율성 위해 이동 로봇의 주행 환경을 장애물이 비어있는 공간을 가능한 하나의 셀로 병합하는 4진트리 방법(quadtree method)에도 적용 가능함을 보인다.