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