Course title
6M0096001
Topics in applied algebra

 SHIMIZU Kenichi Click to show questionnaire result at 2019
Course content
The theory of finite fields and its applications to cryptography and coding theory.
Purpose of class
The theory of finite fields and its applications to cryptography and coding theory.
Goals and objectives
  1. Understand basics on finite fields
  2. Understand some applications of finite fields to coding theory
  3. Understand some applications of finite fields to cryptography
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Report Total.
1. 30% 30%
2. 30% 30%
3. 40% 40%
Total. 100% -
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1． Algebra and information science Survey some applications of algebra to information science 200minutes
2． Basics on the theory of ring and fields Review basics on the theory of rings and fields 200minutes
3． Construction of finite fields Review the last class 200minutes
4． Classification of finite fields Review the last class 200minutes
5． Pseudo-random numbers Review the last class 200minutes
6． Examples of pseudo-random numbers Review the last class 200minutes
7． Coding theory Review the last class 200minutes
8． Linear code Review the last class 200minutes
9． BCH code Review the last class 200minutes
10． Cryptography Review the last class 200minutes
11． RSA Review the last class 200minutes
12． Discrete logarithm Review the last class 200minutes
13． Elliptic-curve Cryptography (1) Review the last class 200minutes
14． Elliptic-curve Cryptography (2) Review the last class 200minutes
Total. - - 2800minutes
Evaluation method and criteria
Evaluated as indicated in "Course Outcomes" section. A score of 60 or more out of 100 points is required to pass this course. To pass this course, students should be able to understand and explain some applications of the theory of finite fields, including its algebraic background, which will be covered in the lecture.
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
Reference materials (in Japanese):
坂庭好一・渋谷智治「代数系と符号理論入門」（コロナ社）
結城浩「暗号技術入門―秘密の国のアリス―」（SBクリエイティブ）
Prerequisites
Algebra I, II and III are assumed.
Office hours and How to contact professors for questions
  • 12:30-13:10 of Monday, or anytime I'm in the lab.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Non-social and professional independence development course
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Tue Mar 12 04:09:25 JST 2024