FSEM 100E4 | Cryptology

cryptology

As early as the time of Julius Caesar, people have tried to communicate secretly with others. Today we use passwords and PINs to authenticate who we say we are and to link our actions to our identity. We purchase products online, never thinking twice about entering our credit card number – a direct link to our money – into a web browser. We do this comfortably because of high-powered mathematics. Cryptology is the area of mathematics that studies cryptography, the art of encrypting messages, and crypt-analysis, the science of breaking encrypted messages. This first-year seminar studies these ideas broadly through mathematical explorations accessible to the inquisitive student with only basic algebra skills. Modular arithmetic, greatest common divisors, and large prime numbers play a supporting role in our course, but learning to research, write, and speak effectively, both individually and in a team, are the featured acts. We look at how to encrypt text and images, and we exchange our encrypted messages, challenging our classmates to break our ciphers. Major advances in cryptology throughout history will also be explored, from the early times of Caesar and Vigenère to the more recent discoveries of public key ciphers used in modern electronic commerce. In the end, you will have gained insights into the deep mathematical and statistical ideas that drive the implementation and analysis of modern cryptological techniques, as well as the nuances and pitfalls of creating secure encryption systems.

Photo of Randall Helmstutler, Associate Professor of Mathmatics

Randall Helmstutler, Associate Professor of Mathmatics

I am in my 21st year as a faculty member here in the Department of Mathematics and I’ve been teaching FSEMs since 2007. I am a native Virginian, growing up in the south-central part of the state along the North Carolina border. I am also a first-generation college student. As a young student I always liked mathematics, but I didn’t really love it until I had a few life-changing mathematics courses as an undergraduate. Since then, this was all I wanted to do. What I love about mathematics is manifested in this FSEM on Cryptology: we can use ingenious mathematical structures to give creative—even elegant—solutions to very hard problems. One of my favorite parts of my job is guiding students in research in Cryptology and I’ve had numerous students go on to develop healthy careers in the field. Beyond mathematics, I have two incredibly energetic and funny kids that keep me more than busy when I’m away from work. My hobbies include sea kayaking (waves are fun), skateboarding (vert preferred to street), and reading (history, even though I got Ds in my history classes).