Cryptography 암호론

Class Info Class Number: Math 406-001 Dates: Mar 02 2016 - Jun 17 2016 Room: NS (자연대) 319 Meeting time: Tues 10:30 - 11:50 (2B - 3B) Thurs 9am - 10:20 (1A - 2B) Text: Hoffstein Pipher and Silverman's "An Introduction to Mathematical Cryptography" Prof: Mark Siggers Office Hours

Links Class Infomation Sage

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

For some homework you must use computers. We will use the online computer algebra system Sage for examples and worksheets, and if you use this for your homework I will be happy. You may use other languages for your homework, and I will only be marginally less happy. If you don't do homework, I will be angry.

Speaking of homework...

Homework.

There will be homework problems for each class. You don't have to do them, but the tests will be based on them. There will be one project, using a computer, that you will have to hand in.

Attendence and participation

Attendence will be monitored casually unless it becomes a problem.

Tests

There will be two tests. The first one will be on Apr 19 or 21, and the final will be on June 09 or 14 or 16. We will decide the date of the exams at least 2 weeks before the exam.

Evaluation

Attendence and participation: 5% Computer assignment: 5% Tests: 2 x 45%.