# CHOSUN

### 중등 수학교육과정에서 유도가능한 암호이론에 대한 연구

Author(s)
Issued Date
2011
Abstract
ABSTRACT

Research of cryptology derived by mathematical curriculum in secondary school

In Seong Oh
Advisor : Prof. Park, Soon Cheol
Major in Mathematics Education
Graduate School of Education, Chosun University

This research aims to understand the mathematical theory which is related to the cryptology and the cryptosystem which can be applied to the secondary school curriculum. Secondly, this research aims to figure out the development of learners' mathematical interest after learning the cryptology. Therefore, the following subjects for inquiry are selected for the purpose of this study.

1. What is the mathematical theory which is related to the cryptology and what is the cryptosystem which can be applied in the secondary school curriculum?
2. How is the development of learners' mathematical interest after learning the cryptology which is applied to the secondary school curriculum?

To solve the problems above, this study refers to the literature of mathematical theories which is related to the cryptology, and summarizes the cryptosystem which can be applied to the secondary school curriculum. Based on these research materials, this study investigates learners's mathematical interest after learning Ceasar cryptosystem in the optional course by conduction a survey.
The research has shown the results as follows.
First, Ceasar and Affine cryptosystem can be applied to the sections of numbers and operations, the character and expression, and the functions in middle school. Hill's cryptosystem can be applied to the matrix in "Math Ⅰ" and to the transformation of matrix in 'Geometry and Vectors'. ADFGVX cryptosystem encrypts plain texts through the several processes using concepts of functions in middle school and matrix in "Math Ⅰ". And for decoding process, students should be taught reverse thinking process because they can not use the inverse function in the middle school curriculum.
Second, students who didn't learn the cryptology tend to regard mathematics a theoretical subject. After the cryptology class, however, students understand that the cryptology is related to mathematics closely and mathematics is also available. Therefore, the cryptology classes is able to induce the interest of mathematics and can be a practical math education in the modern society.
Alternative Title
Research of cryptology derived by mathematical curriculum in secondary school
Alternative Author(s)
Affiliation
조선대학교 교육대학원 수학교육전공
Department
박순철
Awarded Date
2012. 2
목 차
Abstract
Ⅰ. 서 론 1
1. 연구의 필요성 및 목적 1
2. 연구 문제 2
3. 용어의 정의 2
4. 연구의 제한점 3

Ⅱ. 이론적 배경 4
1. 암호의 역사적 배경 4
2. 암호 체계의 소개 7
3. 암호이론의 요약 13

Ⅲ. 암호이론의 기초가 되는 수학이론 18
1. 정수의 기본 성질 18
2. 약수와 배수 19
3. 약수의 개수와 약수의 합 20
4. 최대공약수와 최소공배수 21
5. 소 수 24
6. 소인수분해 26
7. 특수한 유형의 소수 27
8. 소수 판정 27
9. 합 동 28
10. Fermat 정리와 Euler 정리 29
Ⅳ. 중 ㆍ고등학교에서 활용할 수 있는 암호체계 31
1. Ceasar 암호 32
2. Affine 암호 32
3. Vigenère 암호 33
4. Hill 암호 34

Ⅴ. 설문지 결과 비교분석 39
1. 암호학 수업 전 39
2. 암호학 수업 후 40
3. 설문지 결과 분석 41

Ⅵ. 결론 및 제언 44
참고문헌 45
부록1 교수-학습지도안 46
부록2. 설 문 지 50
Degree
Master
Publisher
조선대학교
Citation
오인성. (2011). 중등 수학교육과정에서 유도가능한 암호이론에 대한 연구
Type
Dissertation
URI
https://oak.chosun.ac.kr/handle/2020.oak/5394
http://chosun.dcollection.net/common/orgView/200000256919
Appears in Collections:
Education > Theses(Master)(교육대학원) 