Cryptography (암호론)

Class Info Class Number: MATH 406-001 Dates: Mar 02 2018 - Jun 22 2018 Room: NS 319 Meeting time: Tue 13:30 - 14:50 (5B) Thu 13:30 - 14:50 (5B) Prof: Mark Siggers Office Hours Text: Hoffstein Pipher and Silverman's "An Introduction to Mathematical Cryptography"

Links Class Infomation

Syllabus

We will cover substitution ciphers, discrete logarithms, Diffie-Hellman Key exchange, ElGamal and RSA and other public key cryptosystems, probabilistic encryption, the Vigenere cypher, elliptic curve cryptography, and digital signatures. To do this we will have to touch on the following background topics: computational complexity, modular arithmetic, finite fields, quadratic residues, probability, and elliptic curves.
Here is an approximate schedule.

Week	Sections	Topics
1	1.1, 1.6	Cryptography Basics
2	Various in Chapter 1	Complexity
3	1.3, 1.4	Basic Number Theory
4	1.5, 1.6	Finite fields
5	2.3, 2.4	Public Key Cryptosystems
6	2.7 - 2.9	Discrete Logarithms
7	-	Test 1
8	3.1 - 3.3	RSA
9	3.4	Primality Testing
10	3.5, 3.6, 3.9	Factorisation algorithms
11	3.10, 5.1	Probabilistic Encryption, Elliptic Curves
12	5.2 - 5.3	Groups over elliptic curves
13	5.4	Cryptography with elliptic curves
14	7.1 - 7.3	Digital Signatures
15	-	Test 2

Homework.

There will be suggested problems each class. There will be four homework assignments in which you have to write up some of these problems and hand them in. One should try to do all of the suggested problems as even if they are not on an assignment, they may show up on a test.

Attendence and participation

Your being there and presenting a problem when you are chosen will count for an attendence and participation grade.

Tests

There will be two tests. We will decide the date of the exams at least 2 weeks before the exam.

Evaluation

Attendence and participation: 10% Tests: 2 x 45%.