Math 4450/6450
Cryptology and Computational Number Theory
Call #: 22-563/87-024
Time, location: MWF, 10:10-11:00, 222 Boyd
Instructor: Patrick Corn, 527A Boyd, corn (at) math (dot) uga (dot)
edu
Office hours: T Th 2-4, MWF 1-2:30 (on MWF I am usually
in my office at these times; the T Th office hours are ironclad). Extra
office hours will always be available upon request.
Course web page: You're looking at it.
Final exam: Friday, May 4, 8-11 am. I may instead give a take-home
final exam to be completed earlier; we will decide this sometime during
the semester.
Book: Introduction to Cryptography with Coding Theory, by
Trappe and Washington.
Course outline: The goal of this course is to introduce students to
various aspects of cryptology, highlighting especially the role of
abstract and interesting mathematics in the creation (and decryption) of
codes and security systems. Topics to be covered include: classical
cryptosystems, elementary number theory, DES, RSA, Diffie-Hellman and
discrete logarithms, hash functions. Optional topics: elliptic curve
cryptography, error-correcting codes, telephone games, quantum
cryptography, plus any others you might suggest.
There will be
computer projects using Maple as part of the homework. No previous
experience with Maple or any other computer package will be assumed. Math
6450 students will be asked to write a short paper and give a brief
presentation in class on their choice of topics related to the course (for
instance, the optional topics suggested above that we will not have time
to cover in class; here is a list of
suggestions). They will also be given extra homework problems; these will
often be more open-ended and theoretically inclined than the rest of the
homework.
Homework and tests: There will be weekly homework assignments,
posted on this webpage. There will be one midterm (tentatively scheduled
for the last week of February--probably take-home).
The grading will break down as follows:
Homework 50%
Midterm 25%
Final 25%
A note on collaboration: I would like you to work on the weekly
assignments in small groups of 2-4 people each. If you like, send me an
email with your contact information and any preferences you might have,
and I will help form study groups myself. I don't want you to work alone
unless you're having no trouble with the class at all--and even if that is
the case, you will still be strongly encouraged to collaborate with your
fellow students.
Of course, group work will help you solve problems that you might not have
solved on your own. Sometimes your study partners will solve a problem
that you cannot; I merely ask that you write homework solutions in your
own words, so that it is clear that you understand what you are writing. A
less obvious benefit of group study is that the best way to test your
reasoning is to explain it to your peers.
Homework 1, due 1/19.
Comments and solutions.
Homework 2, due 1/26.
Comments and solutions.
Homework 3, due 2/2.
Comments and solutions.
Homework 4, due 2/9.
Comments and solutions.
Homework 5, due 2/16.
Comments and solutions.
Homework 6, due 2/23.
Comments and solutions.
Take-home midterm, due 3/2. The ciphertext to be considered in problem 1
on the midterm.
Homework 7, due 3/23.
Comments and solutions.
Homework 8, due 4/2.
Comments and solutions.
Homework 9, due 4/13.
Comments and solutions.
Homework 10, due 4/20.
Comments and solutions
Final exam, due 5/4.