CMSC 858K --- Advanced Topics in Cryptography

Spring 2004

Course Overview

This course is an advanced course in cryptography, intended primarily for those interested in research in this area. This course will not be an introductory survey of cryptography, as it was last year. Instead, I will focus on more advanced topics and on more recent results. The course will primarily be concerned with theoretical aspects of cryptography, and not with "algebraic" or "number-theoretic" techniques (although some basic group theory will be presented, as needed). The course will emphasize definitions, foundations, and formal proofs of security.

There will be no assigned textbook for this class (there are not really any suitable texts). However, the presentation will most closely match the "style" of the book Foundations of Cryptography, vol. 1, by O. Goldreich; we will also cover portions of Chapter 4 of that book. Most of the course will be based on articles from the literature, to which appropriate references will be given. Good background reading for this course includes the undergraduate lecture notes of Bellare and Rogaway, as well as my lecture notes from the undergraduate crypto course (CMSC 456). There is no specific material from these notes that is required per se. Rather, the important thing is to get a sense of what modern cryptography is about, as well as to gain some familiarity with the types of proofs common in cryptography. Unfortunately, this is not often taught in other cryptography courses.

It is my intention to make the course accessible to students who have not taken cryptography before. However, students who take no other cryptography course will miss out on some fundamental aspects of cryptography that are covered in the survey course, but not covered here. Also, students who have not had a prior course in cryptography may miss out on some of the context of what we discuss in this class (i.e., an understanding of why a particular problem is important, or how it relates to other results). Finally, students who have not previously taken a course in modern cryptography may have to work harder and do more outside reading in order to keep up.

There are no official prerequisites for the course, but mathematical maturity (especially comfortability with proofs and the ability to think abstractly) is assumed.

Course Requirements

It is expected that students taking this course are interested in cryptography and potential research in this area. As such, it is hoped that none of the course requirements will present a problem for anyone taking the class. The requirements are: Note that there will not be any homeworks; I think scribing lecture notes is a better way to learn this sort of material anyway.

For further information about the scribing, see here.

Lecture Notes

The course lecture notes will be updated throughout the semester.

General Information

Tentative Syllabus

To some extent, the topics covered will depend upon the interests of the students. A more detailed syllabus is also available. The current plan is tentatively to cover the following topics (topics marked "???" will be added as time permits):

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