• Proceedings of the Korea Multimedia Society Conference
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• 2003.05b
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• pp.299-303
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• 2003

In this paper, We proposed a hash function based on the concept of 2-dimensional cellular automata which is a method of analyzing dynamical systems. The proposed hash function is designed for using and disusing key. And the key size is variable from 128 bits.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.571-579
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• 2016

Most of studies related to the distributions of quadratic forms are conducted under the assumption of multivariate normal distribution. In this paper, we suggested an approximation to the distribution of quadratic forms based on multivariate skew-normal distribution as alternatives for multivariate normal distribution. Saddlepoint approximations are considered and the accuracy of the approximations are verified through simulation studies.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2008.02a
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• pp.81-84
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• 2008

김재겸은 2005년 한국 멀티미디어 학회 논문지에 새로운 이차원 셀룰라 오토마타 설계 방법을 소개하고 이 설계 방법으로 구성된 이차원 셀룰라 오토마타를 이용한 해쉬함수를 제안하였다. 본 논문에서는 이 해쉬함수에 대한 첫 번째 분석 결과를 소개한다. 이 해쉬함수는 8 라운드로 구성되고 한 라운드는 두 개의 비선형 연산 부분을 포함하고 있으며, 메시지는 두 비선형 연산 부분에 모두 사용된다. 메시지 차분이 비선형 연산 부분을 거친 뒤 사라질 확률은 $2^{-14}$이다. 따라서 1 라운드 후 약 $2^{-28}$의 확률로 이 해쉬함수의 충돌쌍을 찾을 수 있다. 본 논문의 분석 결과를 통하여 이 해쉬함수는 매우 취약함을 알 수 있다.

• Journal of Korea Multimedia Society
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• v.8 no.5
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• pp.670-678
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• 2005

A Cellular Automaton(CA) is a dynamical system in which space and time are discrete, the state of each cell is unite and is updated by local interaction. Since the characteristics of CA is diffusion and local interaction, CA is used by crypto-systems and VLSI structure. In this study, we proposed a hash function based on the concept of 2-dimensional cellular automata and analyzed the proposed hash function.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.19 no.2
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• pp.23-30
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• 2009

Recently, rotation symmetric Boolean functions have attracted attention since they are suitable for fast evaluation and show good cryptographic properties. For example, important problems in coding theory were settled by searching the desired functions in the rotation symmetric function space. Moreover, they are applied to designing fast hashing algorithms. On the other hand, for some homogeneous rotation symmetric quadratic functions of simple structure, the exact formulas for their Hamming weights and nonlinearity were found[2,8]. Very recently, more formulations were carried out for much broader class of the functions[6]. In this paper, we make a further improvement by deriving the formula for the Hamming weight of quadratic rotation symmetric functions containing linear terms.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.149-156
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• 1991

The theory of the asymptotic behavior of Toeplitz forms is applicable to some problems concerning the local limit theorem.

• The Mathematical Education
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• v.54 no.4
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• pp.299-315
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• 2015

The aim of this qualitative case study is twofold: 1) to analyze how an eleventh-grader, Min-Seon, conceive and represent a pattern of change between two varying quantities in a quadratic functional situation, and 2) further to help her form a concept of 'derivative' as a tool to express the relationship with employing a concept of 'rate of change.' The result indicates that Min-Seon was able to construct graphs of piecewise functions that take average rates of change as range of the functions, and managed to conjecture the derivative of a quadratic function, $y=x^2$. In conclusion, we argue that covariational approach could not only facilitate students' construction of an initial function concept, but also support their understanding of the concept of 'derivative.'

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.525-547
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• 2015

This study analyzed the written texts of textbook and the teacher's discourse explaining 'the relationship between quadratic functions and quadratic equations' in the 9th grade high school mathematics class. Data consisted of the lecture recordings and the textbooks were analyzed based on the Halliday's systemic functional linguistics. According to the results, the written texts of the textbook used lexico-grammatical strategies such as generalization using hyponomy of meanings, mathematical objectification through nominalization and materialization of meaning through change in themes to compose mathematical concepts. The textbook generalized from an example in the description of formulating mathematical concepts, and in this process the organizational interactions of discourse-semantic level and lexico-grammartical level appeared. On the other hand, the teacher's doscourse appeared the change in transitivity and the addition of the reasons and the process. Also the teacher used explanation process of formulating the relationship between quadratic functions and quadratic equations. The linguistic characteristics of the teacher were linguistic implication and omission of lexemes due to contextual ommission. And there was no use of structural lexico-grammatical resources that influence the discourse-semantic level. This results provide a new framework for analyzing mathematical discourse, and suggest the lexico-grammatical strategies that can be used to explain mathematical concepts by teachers in math classrooms.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.883-898
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• 2013

The purpose of this study is to examine that high school students recognize mathematical situation when they are requested for changing identical mathematics situations into different situations. The results of the study are followings. First, percentage of correct answers to the questions of turning equal mathematical situation into function is higher than the one of turning equal mathematical situation into equation and inequality. As a result of individual interview for comprehensibility of the students on these relations, it is found that if degree goes up and there is different expressions of questionaries although mathematical situation is identical, it affects comprehensibility of the subjects. Second, we found that they cannot understand identical mathematics situations because they have trouble in drawing graph or applying to get the answer while many students understand a point of intersection on the graph as a correct answer. Third, As a result of individual interview for comprehensibility of the students on relation between equation, inequality and function, we found that students manage to get correct answer even without perfect comprehensibility on this relation.

• Journal of the Korean School Mathematics Society
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• v.15 no.2
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• pp.299-316
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• 2012

In this paper, we examine high school in order to know their ability for understanding about fundamental functions, such as polynomial, trigonometric, logarithm and exponential functions which have learned from high school. The result of this study shows as follows. More than half students are not able to draw shape of given functions, except polynomial. More students do not fully understand about function properties such as domain, codomain, range, maximum and minimum value.