Introduction
The theory of numbers long enjoyed a reputation as gorgeously useless,
a creation of the mind unsullied by application. This reputation was
decisively shattered in the second half of the twentieth century by
the advent of modern cryptography. In this course you'll learn
the mathematics necessary to keep a secret, share one, break one, or
forge one. Broadly speaking, the topics are:
- Classical ciphers and basic number theory
- Public key cryptography and classical number theory
- Advanced public key techniques
- Hashing and randomness
- Information-theoretic methods
In addition to this material, you'll learn how to handle unfamiliar
problems with creativity, insight and rigor.
Prerequisites
Although the only formal prerequisite is M229, matrices and linear
algebra, there are certainly other prerequisites; you'll need a
flexible mind and a willingness to work hard.
Logistics
- Textbook: Wade Trappe and Lawrence Washington, Introduction to
Cryptography with Coding Theory, second edition, Prentice-Hall,
2006.
- MWF 2:10pm - 3:00pm, ENGRG E206.
- Computer labs On certain Fridays, we will
meet in Weber 205.
Requirements and other expectations
This may well be the first non-calculus class you take. You'll
find the rhythm and demands of this class significantly
different from those of the calculus sequence. Both in class
and outside it, you'll be expected to generate and explore
patterns. As a second step, you'll need to write down clear
statements (and proofs!) of your assertions.
If you miss an exam without a note from a doctor or dean you will receive
a zero for that exam. You must take the exam during the scheduled
time; no make-ups will be given. You must pass the final in
order to pass the course.
Help
This is challenging material; it's fully expected
that sometimes you'll need a little help. Unless specifically
noted, you're encouraged to work with other students in the class.
(Please observe that the work you actually turn in must be your own.)
Questions directed to j.achter@colostate.edu
will be answered swiftly.
However, some questions are best answered in person. You
can come by office hours or schedule an appointment.
This page is available at http://www.math.colostate.edu/~achter/360