중등 수학교육과정에서 유도가능한 암호이론에 대한 연구

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.