#
An Introduction to Cryptography

# Math 395:01 - Spring 2002

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

##
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.
##
Prerequisites

The formal prerequisites are Math 250 and any Math course greater than
or equal to 300.

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

The enrollment is limited to 25 students and requires
consent of the instructor.

Prospective students should:
(1) fill out the special permission form
in the Undergraduate Math Office (Hill 303, Busch Campus) and

##
Textbook

Paul Garrett, *Making, Breaking Codes; an introduction to Cryptology,*
Prentice-Hall, 2001.
##
Description

As the title indicates, this is an introduction to modern cryptography.
Topics to be covered include:
**Symmetric Cryptography:** Simple Ciphers and Cryptograms.
Vigenère Cipher, Hill Cipher, 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. Finite fields,
primitive roots and discrete logarithms.
Finding large primes, pseudoprimes and primality testing.
Square root algorithms, factoring techniques.
Legendre and Jacobi symbols.

course syllabus and
homework assignments

Last updated: October 28, 2001