M360 Mathematics of Information Security, Fall 2005, Section 2
General Information
 Lectures Monday, Wednesday and Friday 2:103:00 pm in ENGRG E203

Instructor:
Anton Betten
Weber 207

Office hours: Monday 45pm, Wednesday 89am.

Contact details:
phone 491 1865, email betten at math dot colostate dot edu

Credits: 3
Prerequisites
M229
Textbook
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.
Exams
There will be three midterms and one final exam.
These will be held in the lecture room.
 Midterm 1: September 25

Midterm 2: October 23

Midterm 3: November 15

Final: during final's week December 1115, the exact
date can be found at the registrar's website.
It will not be published here.
diagram
There will be no makeup exams. If you have a conflict, you need to
discuss the matter with the teacher well in advance.
Grading Scheme
Your final grade will be determined from a score of 600.
The quizzes and midterms count 100 points each,
the final counts 200 points.
Course Syllabus
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:
 1 Overview Cryptography

2 Classical Cryptosystems:
 Shift cipher,

affine cipher, integers mod p, euclidean algorithm, inverse mod p

Vigenére cipher,
including probability analysis according to Friedman and Kasiski,

substitution cipher,

block ciphers,

binary numbers and ascii,

the Enigma.

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

4 DES

5 AES: Rijndael and finite fields

6.3 Primality testing, Fermat test, Miller Rabin, pseudoprimes,

6.4 Factoring: Fermat, p1, Quadratic sieve

7 Discrete logarithm, Pohlig Hellman, ElGamal, roots of unity modulo p

16 Elliptic curves and projective planes, large abelian groups
We will frequently use the computer lab, using both web forms
and small Maple programs.
Lab
we are going to use the computer lab in Weber 205,
here are some general rules by the system administrator zube:
rules
Homework
Cryptanalysis
shift cipher
substitution cipher
affine cipher
vigenere cipher
vigenere table
RSA Cryptosystem
RSA setup
RSA encrypt / decrypt
compute x^a mod n (this one works for long integers!)
extended Euclidean algorithm for integers
Finite Fields
multiply two polynomials over a finite field modulo a third one
extended Euclidean algorithm for polynomials over a finite field
Elliptic Curves
MAPLE worksheet: intoduction to elliptic curves
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On 29 Nov 2006, 10:25.