COOL CLASSES: “Introduction to Mathematical Cryptography”

Rooted in number theory, Visiting Assistant Professor Anthony Kling’s class examines how to protect critical information in our digital age.

Taught by: Visiting Assistant Professor of Mathematics and Statistics Anthony Kling

Says Kling about his class:
Cryptography is the practice and study of techniques used to secure communication and protect information from unauthorized access or malicious interception. In our modern digital age, it plays a vital role in ensuring the security of transactions and data transmission. For example, when you make an online purchase and send your credit card details to a retailer, that information is first scrambled before being sent off. Then the receiver unscrambles the transmitted message using some sort of key to get the original message. If an adversary gets a hold of the scrambled message, we want to make sure it’s nearly impossible for them to unscramble it without knowing the key. This process of scrambling and unscrambling relies on the difficulty of certain mathematical problems. This course studies the mathematics behind cryptography as well as its various implementations.

In this course, students also work in groups on problems as a way to reinforce and discover ideas, as well as enhance their mathematical communication skills. I also hope students realize there are still many questions in mathematics we don’t know the answer to. After all, this is partially what makes cryptography work.

Kling on why he wanted to teach this class:
Many of the mathematics that underlie cryptography are rooted in number theory, which is my research area. Number theory is a fascinating branch of mathematics that generally studies the integers and is home to many easy-to-state and understand yet difficult-to-solve problems. I thought it would be exciting to see some of the practical applications of number theory, especially since cryptography is such a widespread application.

Kling on what makes this class unique to his department:
This course is designed at the 200-level with only a prerequisite of multivariable calculus, although it doesn’t really build off any ideas in calculus. Rather, this class serves as a bridge to students in encountering new mathematical concepts for the first time, many of which stem from number theory. The students in my class all come from different points in mathematical studies, ranging from those who have just taken multivariable calculus to those who have completed upper-division math courses. As such, this class presents topics in an accessible, yet interesting way.

Learn more about other courses offered by the Department of Mathematics and Statistics