SM486 Cryptology and Number Theory
Instructor: Professor William P. Wardlaw
Rough Course outline:
The course will begin with some very elementary
cryptology, using a text designed for talented highschool
students. Then there will be an introduction to
elementary number theory, concentrating on modular
arithmetic. A graduate level text will then be
used to look into several
new (about 1978) crypto systems, especially the
RSA public key cipher. Computer programs will be used
to make and break elementary ciphers,
and the RSA public key cipher will be implemented in Maple.
Detailed Outline:
The first third of the course introduces terminology and some
elementary cryptanalysis from the book
Elementary Cryptanalysis, by
Abraham Sinkov. We cover various monoalphabetic substitutions:
- Direct Standard,
- Decimation,
- Linear Transformation,
- Keyword Mixed,
- Keyword Transposed Mixed.
In the process, we learn something about arithmetic
modulo 26. We discuss polyalphabetic ciphers and polygraphic
ciphers, and
look especially at the Playfair Cipher and the
2 x 2 and 3 x 3 matrix
ciphers. We briefly look into the cryptanalysis of the
matrix ciphers.
We discuss the transposition ciphers, but do not attempt any
cryptanalysis.
The second third of the course treats elementary
number theory,
concentrating on divisibility and modular arithmetic. We cover the
Euclidean algorithm, modular arithmetic, the Euler totient
function,
Euler's Theorem, and the Chinese remainder Theorem.
This is done without a text.
The final third of the course is taken from our second text,
Neal Koblitz'
A Course in Number Theory and Cryptography. We touch upon
various topics, including time estimates for doing arithmetic,
factorization, the RSA Public Key Cipher,
and other such topics as time
and student ability allow.
Last updated 4-3-98.