M360 Mathematics of Information Security, Fall 2005, Section 2
- Lectures Monday, Wednesday and Friday 2:10-3:00 pm in ENGRG E203
Office hours: Monday 4-5pm, Wednesday 8-9am.
phone 491 1865, email betten at math dot colostate dot edu
W. Trappe, L. C. Washington: Introduction to Cryptography with Coding Theory, Prentice Hall, Second Edition
Homework and Quizzes
Homework will be assigned but not collected. Quizzes will be held
Friday every second week to review the material from the previous two weeks.
There will be three midterms and one final exam.
These will be held in the lecture room.
There will be no make-up exams. If you have a conflict, you need to
discuss the matter with the teacher well in advance.
- Midterm 1: September 25
Midterm 2: October 23
Midterm 3: November 15
Final: during final's week December 11-15, the exact
date can be found at the registrar's website.
It will not be published here.
Your final grade will be determined from a score of 600.
The quizzes and midterms count 100 points each,
the final counts 200 points.
This course is about cryptography and coding theory,
as well as the underlying algebra.
We will discuss various cryptosystems, presenting the
underlying algebra in bits and pieces as we go along
and as needed.
In detail, we will cover to following subjects:
We will frequently use the computer lab, using both web forms
and small Maple programs.
- 1 Overview Cryptography
2 Classical Cryptosystems:
- Shift cipher,
affine cipher, integers mod p, euclidean algorithm, inverse mod p
including probability analysis according to Friedman and Kasiski,
binary numbers and ascii,
3 Basic Number Theory:
Divisibility, primes, greatest common divisor,
extended Euclidean algorithm, congruences,
Chinese Remainder Theorem, modular exponentiation,
Fermat's little Theorem and Euler's Theorem,
primitive roots, finite fields.
6 public key cryptosystems, RSA
5 AES: Rijndael and finite fields
6.3 Primality testing, Fermat test, Miller Rabin, pseudoprimes,
6.4 Factoring: Fermat, p-1, Quadratic sieve
7 Discrete logarithm, Pohlig Hellman, El-Gamal, roots of unity modulo p
16 Elliptic curves and projective planes, large abelian groups
we are going to use the computer lab in Weber 205,
here are some general rules by the system administrator zube:
RSA encrypt / decrypt
compute x^a mod n (this one works for long integers!)
extended Euclidean algorithm for integers
multiply two polynomials over a finite field modulo a third one
extended Euclidean algorithm for polynomials over a finite field
MAPLE worksheet: intoduction to elliptic curves
File translated from
On 29 Nov 2006, 10:25.