M360 Mathematics of Information Security, Section 1, Fall 2005

Instructor:

Dr. A. Betten, room 207, Weber building

When and where:

M  W  F     9:00 - 9:50 ENGRG E205 or Weber 205 (the computer lab).

Texts:

W. Trappe, L. C. Washington: Introduction to Cryptography with Coding Theory, Prentice Hall, Second Edition

Prerequisites:

M229

Topics:

This course is about cryptography and coding theory, as well as the underlying algebra. The plan is to go right into applications, and present the underlying algebra in bits and pieces as we go along and as it is needed.

In detail, we cover to following subjects:

1 Overview Cryptography

2 Classical Cryptosystems: Shift, affine, Vigenére, substitution, 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.

4 DES

5 AES: Rijndael and finite fields

6 RSA

18 Error Correcting Codes (aka Coding Theory)

We will frequently use the computer lab, using both web forms and small Maple programs.

One word of caution: there is quite a bit of algebra involved in this course. We will get to a level of abstraction which some students may not have experienced before (unless you have taken abstract algebra, of course). I hope we can get through all of this with not too much friction. Be assured that we are going to see lots of examples and hopefully things become clear in the end.

Grading Rules:

homework / midterm 1 / midterm 2 / final as to 25 / 25 / 25 / 25.

The first midterm will take place September 21 (the 14th session). The second midterm is November 2nd (the 33rd session).

For further information:

Please contact A. Betten, Weber 207, office hours W 10am, F 1pm, or by appointment:
betten@math.colostate.edu betten@math.colostate.edu

or visit the course webpage at
http://www.math.colostate.edu/ betten/courses/M360/FA05/index.html. http://www.math.colostate.edu/~betten/courses/M360/FA05/index.html