This book is based on a course in cryptography at the upper-level under- graduate and beginning graduate level that has been given at the University of Maryland since 1997, and a course that bos been taught at Rutgers Uni- versity since 2003. When designing the courses, we decided on the following requirements:

• The courses should be up-to-date and cover a broad selection of topics from a mathematical point of view.

• The material should be accessible to mathematically mature students huving little background in number theory and computer program- ming.

• There should be examples involving numbers large enough to demon- strate how the algorithms really work.

We wanted to avoid concentrating solely on RSA and discrete logarithms, which would have made the courses mostly about number theory. We also did not want to focus on protocols and how to hack into friends' computers. That would have made the courses less mathematical than desired.

There are numerous topics in cryptology that can be discussed in an introductory course. We have tried to include many of them. The chapters represent, for the most part, topics that were covered during the differ- ent semesters we taught the course. There is certainly more material here than could be treated in most one-semester courses. The first nine chapters represent the core of the material. The choice of which of the remaining chapters are used depends on the level of the students and the objectives of the lecturer.