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History:  How this course came about

Below is a lightly edited version of a memo which I wrote in March 2000 to Fred Roberts (the Director of DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science) about the course.

The NSF-financed DREI summer program on Cryptography ("crypto") and Network Security which was held several years ago had some educational developments worth mentioning. Here is what has happened.

I was lucky enough to participate in that program. My participation was further enriched by my attendance at virtually every presentation made to the group of high school teachers by various experts in crypto. Thus the possibility of teaching a course covering topics in crypto without substantial mathematical prerequisites and with undeniable social and political policy impact was clear.

During the next year I was the Department of Mathematics representative on an interdisciplinary committee (with individuals from Biology, Chemistry, and Physics) preparing a proposal for the NSF's program, "Institution-wide Reform of Undergraduate Education in Science, Mathematics, Engineering and Technology." The committee constructed proposals for courses in four areas of science and mathematics. Our proposal was awarded support by the NSF (grant number DUE-9850071). The mathematics course described in the proposal was offered in both the fall and spring semesters of this academic year (1999-2000). Although we're about two-thirds of the way through the second rendition of the course, I think it is fair to say that the course has been successful. It is addressed to an audience of "liberal arts" students. In this context, such students have little college mathematics background. A "prospectus" for the course is available at the web page and specific information about the fall 1999 version of the course can be seen at the page while the spring version of the course (still under construction!) can be seen at and further, complete notes and other course material will be posted after the end of the academic year.

The course is notable not only for its non-traditional mathematics (e.g., consideration of such modern crypto protocols as RSA and Diffie-Hellman) but also for the pedagogy: almost everything that's considered is approached in a hands-on fashion, so students get actively involved with examples. The computer program Maple is introduced early in the course in a routine fashion, so that students can do arithmetic involving many digits "without tears". Maple is also used to solve modular equations, and to introduce students to simple asymptotic analysis of algorithms.

Additionally, students have been asked to write several papers (individually, papers on medical record privacy and the history of the DES algorithm, and in groups on government crypto policy). Groups of students presented papers on crypto policy and discussion is encouraged (e.g., a group presenting the FBI's position, a group presenting the situation in Russia, etc.). Crypto techniques relevant to e-business are studied. The role of copyright and patent in the era of digital intellectual property is also discussed. We try to make clear what is possible using techniques from mathematics and theoretical computer science, and what has been and can be done as a result of policy decisions.

For the instructor, the course has meant learning (sometimes not without pain or error!) some new teaching techniques. For example, how does one read and grade essays so that the process is useful to students and assesses the work fairly? How does one manage discussions in class: how to balance the tendency of certain students to dominate the interchange and how to move the class to cover the topics desired?

Further synergism has taken place. The instructor gave a lecture at a local high school to about 45 students on secret sharing, a topic in the course. A mathematics graduate student supported by NSF funds through the VIGRE program, having experience in crypto in the commercial world, has participated in the course, and another graduate student from Switzerland whose senior thesis was about secret sharing has also participated. An invited outside speaker to the course was Jim Reeds, a member of DIMACS from AT&T, who gave students some further idea of crypto techniques applied to the real world and to a medieval historic study.

The DUE grant also allowed speakers to be brought to campus to engage with a wider audience as Presidential Lecturers. Probably the most popular lecturer was Matt Blaze (also from AT&T and a member of DIMACS), whose presentation on aspects of crypto policy was followed by a considerable amount of discussion among undergraduates, graduate students, faculty, and staff members.

It seems likely that the course will continue, although the demands on the instructor for broad pedagogical skills and for keeping up with a rapidly moving subject (e.g., changes in import-export regulations, developments such as the DVD cracking case) make teaching the course rather non-routine. The course has also shown that undergraduate students may indeed appreciate a more technical approach: i.e., a crypto course at the junior/senior level with substantial math and computer science prerequisites offered by the Math or CS Departments (or both!). Interest in such a course has been expressed, but it is still hypothetical.

We certainly can conclude that the DREI topic was rather fruitful.

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