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