# Cryptography:

An Introduction to Cryptology

# Math 348:01 - Spring 2006

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

### Professor S. Miller

##
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 edition and Errata
to 1st edition)
##
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: Data Encryption Standard (DES),
IDEA, 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 15, 2006