담당교수:
담당조교: TBA
수업시간: 주당 1.5시간씩 2회 강의수업 = 총 3시간/주
대상:
과목소개:
교재: TBA
평가방법:
기타사항:
Weekly Plan: (updated after midterm exam)
Objective |
▶ Elementary Number Theory ▶ Important Concepts in Modern Algebra ▶ Finite Fields ▶ BCH and RS Codes, RSA/ElGamal Cryptography | ||
Week |
Summary |
Remark |
Homework |
1 |
Integers and Congruence |
|
HW#1 |
2 |
(응용) RSA/ElGamal Encryption Algorithms |
|
Project #1 |
3 |
Groups and Permutations |
|
HW#2 |
4 |
Theory of Counting - Burnside Lemma |
|
HW#3 |
5 |
Simultaneous Equations and Vector Spaces |
|
HW#4 |
6 |
Matrix/Determinants/Linear Transformations |
|
HW#5 |
7 |
Review of the first half semester |
|
|
8 |
Midterm Exam |
|
|
9 |
Some Concepts in Modern Algebra |
|
HW#6 |
10 |
Irreducible Polynomials over Fp |
|
HW#7 |
11 |
Multiplicative Structure of Finite Fields |
|
HW#8 |
12 |
Additive Structure of Finte Fields |
|
HW#9 |
13 |
(응용) Hamming/BCH Codes - Encoding/Decoding |
|
Project #2 |
14 |
(응용) Reed-Solomon Codes - Encoding/Decoding |
|
HW#10 |
15 |
Review of the second half semester |
|
|
16 |
Final Exam (12주-15주 수업내용) |
|
|
Weekly Plan:
Objective | ▶ Elementary Number Theory ▶ Important Concepts in Modern Algebra ▶ Finite Fields ▶ BCH and RS Codes, RSA/ElGamal Cryptography | ||
Week | Summary | Remark | Homework |
1 | Integers and Congruence |
| HW#1 |
2 | (응용) RSA/ElGamal Encryption Algorithms |
| Project #1 |
3 | Groups and Permutations |
| HW#2 |
4 | (응용) Burnside and Polya Theory of Counting |
| HW#3 |
5 | Simultaneous Equations and Vector Spaces |
| HW#4 |
6 | Matrix/Determinants/Linear Transformations |
| HW#5 |
7 | Some Concepts in Modern Algebra |
|
|
8 | Midterm Exam (5,6,7주 수업내용) |
|
|
9 | Irreducible Polynomials over Fp |
| HW#6 |
10 | Multiplicative Structure of Finite Fields |
| HW#7 |
11 | Additive Structure of Finte Fields |
| HW#8 |
12 | (응용) Linear Feedback Shift Register Sequences |
| HW#9 |
13 | (응용) Hamming/BCH Codes - Encoding/Decoding |
| Project #2 |
14 | (응용) Reed-Solomon Codes - Encoding/Decoding |
| HW#10 |
15 | (응용) Latin Squares and Finite Projective Planes |
|
|
16 | Final Exam (12주-15주 수업내용) |
|
|
Details
1주 Integers and Congruence
HW#1
2주 (응용) RSA/ElGamal Encryption Algorithms
Project #1: Implementation of ElGamal signature algorithm
3주 Groups and Permutations
HW#2
4주 (응용) Burnside and Polya Theory of Counting
HW#3
5주 Simultaneous Equations and Vector Spaces
HW#4
6주 Matrix/Determinants/Linear Transformations
HW#5
7주 Some Concepts in Modern Algebra
8주 Midterm Exam
9주 Irreducible Polynomials over GF(p)
HW#6
10주 Multiplicative Structure of Finte Fields
HW#7
11주 Additive Structure of Finite Fields
HW#8
12주 (응용) Linear Feedback Shift Register Sequences
HW#9
13주 (응용) Hamming/BCH Codes - Encoding/Decoding
Project #2: Implementation of BCH Encoder/Decoder
14주 (응용) Reed-Solomon Codes - Encoding/Decoding
HW#10
15주 (응용) Latin Squares and Finite Projective Planes
16주 Final Exam