An Introduction to Cryptology
Math 348:01 - Spring 2005
TF 2nd period in ARC 207 (Busch campus)
The Mathematics 348 project is due at the final exam on May 5.
Office Hours before the final exam - Monday, Tuesday, Wednesday 2:30-3:30
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
course syllabus and
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).
Making, Breaking Codes; an Introduction to Cryptology, 2nd edition
to 2nd edition and Errata
to 1st edition)
As the title indicates, this is an introduction to modern cryptography.
Topics to be covered include:
Public Key/Private Key Cryptography:
- Symmetric Cryptography:
Classical Cryptography: Simple Ciphers and Cryptograms.
Vigenère Cipher, Hill Cipher;
- Modern Cryptography: Data Encryption Standard (DES),
IDEA, Advanced Encryption Standard (AES).
- Ciphers: Rivest-Shamir-Adleman (RSA), El Gamal, Diffie-Hellman and trapdoors.
- Protocols: Kerberos, PGP, SSL, Digital Signatures.
- 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: April 1, 2005