# Cryptography:

An Introduction to Cryptology

# Math 348:01 - Spring 2012

### TF 2nd period in ARC 207 (Busch campus)

##
Announcements

REVIEW PROBLEMS for the Final exam
FINAL EXAM in ARC 207 May 09, 2012: 8:00 AM - 11:00 AM

OFFICE HOURS 4/30 - 5/4: M 4-5, T 10:30-11:30, W 4-5, Th 10:30-11:30 ,
F 3-4

Examples of Diffie-Helman key exchange, El Gamal
ciphers and RSA public key encryption

Extra credit related to the midterm exam.

The midterm exam is in class on Tuesday 3/20/2012. There is a brief description of the exam.

The Mathematics 348 project is due the
last day of class April 27, 2012.

OFFICE HOURS: M 4-5 PM, F 3-4 PM Hill 546

There will be a Mathematics 348 project due at the final day of class
(4/27/12).

A link to some cryptology applets has been added to the links at the
bottom of the syllabus.

Be sure to make note of the corrections below to the first and second
printings of the text.

Mathematical Careers and Ideas talk on Enigma. Wednesday 2/15/12
6:40 in Hill 703.

##
General Information

This is an upper level **MATH **course. It is directed at
students in mathematics, electrical engineering, or computer science
who have strong interest in mathematics and want to learn about the
exciting applications of algebra and number theory to cryptography
and cryptanalysis.
course syllabus and
homework assignments

**
Prerequisites: **
Linear Algebra (Math 250) and one of Math 300, 356, or 477, or
permission of department.

Part of the course will cover the needed background material on
number theory (see below).

## Textbook

Paul Garrett, *
Making, Breaking Codes; an Introduction to Cryptology, 2nd edition
*
Prentice-Hall, 2001.
(Errata
to 2nd printing and Errata
to 1st printing)
##
Description

As the title indicates, this is an introduction to modern cryptography.
Topics to be covered include:

**Symmetric Cryptography:
****
**- Classical Cryptography: Simple Ciphers and Cryptograms.
Vigenère Cipher, Hill Cipher;
- Modern Cryptography: Advanced Encryption Standard (AES).

**Public Key/Private Key Cryptography:**
- Ciphers: Rivest-Shamir-Adleman (RSA), El Gamal, Diffie-Hellman and trapdoors.
- Protocols: Kerberos, PGP, SSL, Digital Signatures.

**Number Theory:**
- Congruences and Finite fields,
- Primitive roots and discrete logarithms.
- Finding large primes, pseudoprimes and primality testing.
- Square root algorithms, factoring techniques.
- Legendre and Jacobi symbols.

Last updated: January 16, 2012