The Mathematics of Coding Theory and Cryptography
Math 395:01 - Spring 2001

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 coding theory and cryptography.


The formal prerequisites are calc 1 and 2, Math 250, and either Math 477 or CS 206. The enrollment is limited to 25 students and requires consent of the instructor. Prospective students should send e-mail to the instructor Professor Shirlie Serconek describing their background and interest.


At least three textbooks in this highly active area have been published in the last 4 months. The current intention is to base this course on Lund University lecture notes written by J. L. Massey, although this may change.


Topics to be covered in the course will be selected from the following:

Cryptography: The goals of cryptography. Shannon's theory of perfect secrecy. Kerkhoff's hypothesis. Unconditional security and computational security. Public-key cryptography. One-way functions. Discrete exponentiation. The Diffie-Hellman public-key distribution system. The Rivest-Shamir-Adleman (RSA) (conjectured) trapdoor one-way function. Finding large primes and primality testing. Elliptic curves.

The elements of algebraic coding theory: Block codes. Linear codes. Reed Solomon codes. The discrete Fourier transform (DFT). Linear complexity and the DFT. Blahut's theorem.

The necessary foundational material on groups, rings, fields, and elementary number theory will also be covered.

Last updated: November 07, 2000