SM468 Cryptography, codes, and information security
Syllabus
Course coordinator: Max Wakefield
Fall AY2014
Text: “Introduction to Cryptography with Coding Theory” by Trappe and Washington 2nd edition
Computing Platform: MATLAB. The website http://www2.math.umd.edu/ lcw/MatlabCode/ has relevant scripts that will be useful.
Here are some notes about the material to be covered and the problems required for homework:
1. We may have more problems given that are not in the book. I will provide those at the time we cover
the material.
2. Many of the sections that just say read will have problems or projects that I will give out after we
cover that section.
3. Some problems will not be required as we may choose to not cover an entire section. We may also
decide to cover some sections or material that are not on this list. This syllabus is just a wish list of
the core material that we should cover.
4. The problems listed below in the table with numbers only correspond to the numbered exercises at the
end of the respective chapter. The problems listed with the prefix “CP” correspond to the “Computer
Problems” listed at the end of the chapter.
5. The dates of which we cover this material is TBA. We may want to spend more time on some subjects
and less on others.
6. Sections which are bolded below are central to the course.
Section
1.1
1.2
2.1
3.1
3.2
3.3
2.2
2.3
2.4
2.7
2.8
2.9
2.10
2.12
4.1
4.2
4.4
Topic
Cryptography Overview
Cryptography Applications
Shift Ciphers
Elementary Number Theory
ax + by = gcd(a, b)
Modular arithmetic
Affine Ciphers
Vigenére Cipher
Substitution Ciphers
Block Ciphers
Binary Representation
One time pads
Pseudo-random Bit Generation
Enigma
DES Intro
Simplified DES algorithm
DES
Problems
read
read
1,CP1-2
4,5,6,CP1
1(a), CP2
2(a),3,7,8,CP4-5
2-7, CP3-5
10,12, CP7-9
read
13-17,CP10
23
read
19
read
read
1,2,CP1
4,5,11
4.5
4.6
4.8
5.1
5.2
3.4
3.5
3.6
6.1
3.7
3.9
6.2
6.3
6.4
6.7
7.1
7.2
7.4
7.5
8.1
8.3
8.4
18.1
18.2
18.3
18.5
18.7
18.9
18.10
Operation modes
Braking DES
Password Security
Intro to AES
AES
Chinese Remainder Theorem
Modular Exponentiation
Fermat’s little theorem and Euler’s theorem
RSA
Primitive Roots
Square roots mod n
Attacking RSA
Primality Testing
Factoring
Public Key Systems
Discrete Logs
Discrete log computations
Diffie-Hellman Key Exchange
ElGamal Cryptosystem
Hash functions
A simple Hash function
Birthday Attacks
Intro to Coding theory
Error correcting codes
Linear codes
Hamming codes
Cyclic codes
Reed-Solomon codes
The McElienceMcElice Cryptosystem
3
read
read
read
1,2
9,10
11,13,14
15,16,20,39
1-5,10,CP1-3
21
25,26
read
read
12-14,18, CP4-9
read
read
1-6
10
11
1-3
read
4,CP1-2
1,2
read
3,4,9,10
read
12-14
read
read