This CSUMS project prepares undergraduates in mathematics to pursue graduate work in cryptography, a field of mathematics where computation is of extreme importance. Indeed, cryptography is a multidisciplinary field. Designing secure communication protocols is a complex issue, requiring considerable training and research in a wide range of topics, including abstract number theory and computation. Consequently, major centers in cryptography worldwide feature strong links between mathematics and computer science. Research in this area requires skills from both fields, and this presents a major challenge for young researchers coming from either background alone. This program is designed to help students in mathematics gain the necessary skills so that they can succeed in their subsequent graduate and postgraduate career. Participating students are required to take a comprehensive program of study which (a) prepares them for graduate work in mathematics, (b) gives them the necessary foundation in number theory and cryptography, and (c) enables them to use computers in their research, including writing distributed programs that operate on large numbers -- a special requirement of the central research theme of this project. Second, participating students take part in a year-long research project, such as the following: implementation and analysis of new cryptosystems, distributed attacks on existing or developing cryptosystems, discovery through computation of numbers with special properties (e.g., large pseudosquares), or computational experiments to verify research conjectures in cryptography theory. All research projects revolve around computation. Moreover, the projects stem directly from the research efforts of the principal investigator and her colleague.
Each student participating in this project prepares for computationally-intensive mathematical research. As a group, the students also participate directly in such research, exploring basic questions about cryptography and related areas. After participating in the program, the students are well prepared to pursue graduate school in mathematics or cryptography. They also are able to perform research in others of the many branches of mathematics where computation plays a significant role. In short, the program helps strengthen the kind of education that prepares students for professional as well as academic careers in cryptography and the burgeoning field of information security and privacy. The project is supported by the MPS Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, the EHR Division of Undergraduate Education, and NSF's EPSCoR program.
