MA 479 / CSSE 479: Cryptography

Rose-Hulman Institute of Technology
A joint effort of the
Department of Mathematics
and the Department of Computer Science & Software Engineering
Spring term, 2007-2008

Catalog Course Description

Introduction to basic ideas of modern cryptography with emphasis on mathematical background and practical implementation. Topics include:

• the history of cryptography and cryptanalysis,
• public and private key cryptography,
• digital signatures, and
• limitations of modern cryptography.

Touches upon some of the societal issues of cryptography. Crosslisted as MA 479 and CSSE 479.

Alice and Bob are connected by a public communication channel. Any message transmitted over this channel might be altered arbitrarily (by some attacker). One central question of this course is: How can Alice send a message M to Bob in such a way that:

1. No one except Bob can see M, and
2. In the end, Bob knows that what he received is what Alice intended to send.

This seminar investigates both methods for addressing the above question and attacks on such methods. The methods to be discussed include classical approaches (like Caesar's cipher), block-cipher systems (like DES and AES) and public-key cryptosystems (like RSA).

In addition, this seminar will:

• Touch upon some of the societal issues of cryptography.
• Provide an opportunity for you to:
• Investigate and present a research topic in cryptography.
• Hear many such presentations from your fellow students.

Prerequisites

• Mathematical maturity and familiarity with discrete mathematics, as evidenced by (for example) successful completion of MA 275 (Discrete and Combinatorial Algebra I).
• The ability to design and implement software solutions to small problems, in the language of your choice, as evidenced by (for example) successful completion of CSSE 220 (Fundamentals of Software Development II).

Instructor

Assignments (Provisional)

• Regular readings from the textbooks.
• Paper-and-pencil problems, perhaps solved with the assistance of Maple.
• Small programming projects, in the language(s) of your choice.
• An oral report on a research article that you will choose (from a list I provide).
• A research proposal.
• Discussions of the readings, often accompanied by a "2-minute essay" to help you summarize some of your thoughts from the reading.

• Problems inspired by mathematics.
• Problems inspired by computer science.

Each problem has a stated number of "points". For example, problem 1 of the Inspired by Computer Science Homework set 1 is 4 points. You should do problems as follows:

• To pass the course, on each homework set you must (correctly) do at least 4 points from the Inspired by Mathematics problems and at least 4 points from the Inspired by Computer Science problems.
• To get an A in the homework portion of this course, you must do considerably more points -- averaging perhaps a total of 16 points per homework set. (But don't hold me to that number.)
• If you don't make the 4+4 minimal mark on any given homework set, please talk to me right away.
• If you feel that a problem deserves more points than it was listed for, tell me (and explain why). (You should have some idea of how much time you spent on the problem.)
• Choose problems that you find enlightening and exciting. By working hard on problems that you find interesting, you'll succeed in this seminar.

Grading (Provisional)

There are no exams.

Paper-and-pencil exercises	60%
Small programming projects
Oral report on a research article	20%
Research proposal	10%
Discussions of the readings	10%