Mathematics, computer science, and electrical and computer engineering majors can take a cryptography class to learn how modern communications and transactions are kept secure. 

UMD mathematics, computer science, and electrical and computer engineering majors can take a cryptography class to learn how modern communications and transactions are kept secure.

What keeps our emails and messages private? How do passwords protect our online accounts from hackers? Why is it safe to make purchases from retailers using our credit cards?

The answer to all those questions is cryptography—the process of hiding or coding information so that only the intended users can access it.

In 1997, just as the internet and digital communications like email became more commonplace, University of Maryland Mathematics Professor Larry Washington designed a new cryptography course. An expert in number theory and cryptography, Washington wanted to make sure students had some exposure to the rapidly advancing field and its potential applications before they graduated and encountered cryptography in real-life situations.

“There’s a lot of interest in cryptography here at UMD because the National Security Agency and other government agencies use cryptographic methods,” Washington said. “Cryptography is a subject that has developed very greatly in the past 50 years and a lot of that development happened in the past 20 years. As a result, we continually update the course to keep up.”

An evolving interdisciplinary approach

Nearly 30 years later, UMD’s cryptography course still lives on as MATH 456, CMSC 456 and ENEE 456. Due to its interdisciplinary nature, faculty members from the mathematics and computer science departments have taught the class and influenced the curriculum.

“It’s a blend of math and computer science ideas,” Washington explained. “The students see real-world applications of theoretical math ideas while students who are accustomed to only theoretical math have the chance to see the issues that arise in applied areas.”

Senior computer science major Harshit “Archie” Garg says the course was among the toughest classes he had ever taken at UMD but also one of the most eye-opening. He took the class in fall 2023, when it was taught by Computer Science Professor Daniel Gottesman, who also holds a Brin Family Endowed Professorship in Theoretical Computer Science. Initially unfamiliar with topics like encryption, Garg believes that the class gave him the tools he needed to understand cryptography’s place in everyday life and how it could be applied to seemingly unrelated fields.  

“The class showed that you could use these fundamental math concepts like logarithms and exponents to create these very robust encryption protocols. I learned how we could generate key hashes dynamically on the fly, where something can be understood in one context but be complete nonsense in another,” explained Garg, who plans to pursue a career in machine learning. “I ultimately feel confident that wherever life takes me after graduation, I can use the concepts I learned from this class.”

That sentiment was echoed by many other students, including computer engineering Ph.D. student Russell Chiu (B.S. ’23, computer engineering), who took the class as an undergraduate. The class made such an impression on Chiu that he decided to become a graduate teaching assistant for the course in spring 2024. He hopes to apply what he learned in the course to his graduate research and eventually pursue a career where he can put his knowledge of cryptography and algorithms to work.

“With the rise in new types of computing, there are many interesting questions within both academia and industry. In fact, there were several new topics introduced to the course curriculum within the two years since I took it,” he added. “I definitely recommend this class to undergrads interested in cybersecurity and beyond—it covers a wide scope of topics that quickly evolve over time.”

Cryptography today and tomorrow

Todd Rowland, who worked at computational technology company Wolfram Research before he joined UMD as a mathematics lecturer, is excited to teach the newest iteration of the class in fall 2024. He hopes his experience with more abstract forms of cryptography at Wolfram will add an extra dimension to the course and underscore the ever-changing impact of cryptography.

“It’s no longer just about secret messages and passwords,” Rowland said. “Cryptography has become increasingly relevant to us ever since the internet came into existence. There are obvious things that cryptography plays a role in, like keeping credit card information safe while making secure payments over the internet. But it’s also helping you make sure the webpage you’re on is the right one and that no one altered it—authentication of integrity is more important than ever.”

In Rowland’s class this fall, students will explore concepts from basic ciphers to secret sharing schemes (a technique where a “secret” is split into multiple shares to different parties and can’t be fully accessed unless all shares are recombined). The curriculum will also cover the Data Encryption Standard and the Advanced Encryption Standard, globally used ciphers established by the U.S. government to protect sensitive electronic data. Rowland hopes the class will help students become more aware of the technology around them and how newer trends in cryptography—like blockchains and quantum cryptography—can impact society.

“The class is a peek into how the world works today, from knowing how to manage passwords and authentications to dealing with things like cryptocurrencies,” Rowland said. “As technology advances, it’s better to be prepared as best we can to work with those advancements. If you want to understand all these processes, this would be the class to take.”

Chabria was recognized for her work in the Terrapin Teachers program and her commitment to mathematics education.

Zoe Chabria, a junior mathematics and secondary education double-degree student at the University of Maryland, was awarded the 2024 National Council of Teachers of Mathematics (NCTM) Prospective 7-12 Secondary Teacher Course Work Scholarship. Granted to only one recipient nationwide annually, this competitive scholarship recognizes outstanding university students preparing to become middle or high school mathematics educators. This year, Chabria was awarded the maximum amount of $10,000 to financially support her tuition and living expenses as she completes her studies at UMD.

Chabria’s achievement also marks the second consecutive year that a UMD student enrolled in Terrapin Teachers won this national scholarship. Terrapin Teachers—a joint initiative between UMD’s College of Computer, Mathematical, and Natural Sciences and College of Education—aims to increase the number of high-quality science and mathematics teachers in middle and high schools. Based on the nationally recognized UTeach program, Terrapin Teachers enables undergraduate students in science, technology, engineering and mathematics (STEM) fields to receive a subject-matter degree and a teaching certification simultaneously.

“I’m thankful to not only the donors who funded the award but my professors, my advisor, my family and friends who supported me throughout the process,” Chabria said. “I’m also very proud to represent Terrapin Teachers and UMD with this achievement. It’s truly an honor.”

Dana Grosser-Clarkson, a senior lecturer at the UMD Department of Mathematics and Chabria’s Terrapin Teachers advisor, praised her work and her passion for mathematics education.

“Zoe is an outstanding student, which is why I encouraged her to apply for the scholarship. I am always impressed by her work ethic in the classroom and her ability to communicate her thinking with her peers,” Grosser-Clarkson said. “The Terrapin Teachers community is more than happy to celebrate Zoe’s achievement.”

From Chicago to College Park

Originally from Chicago, Chabria grew up with a natural affinity for math. She participated in and led math teams from fourth grade through high school, developing a passion for numerical puzzles and problem-solving. She developed an interest in teaching when she began tutoring her peers in math and chemistry after a classmate asked her for help.

“The first time I got to help someone else do math, I was just telling them what I knew and how I would personally solve a problem,” she recalled. “But then, I really started thinking. What are the different ways they can go about learning and thinking about the problem? How can I make it easier for them to understand? I tried out different teaching methods to better help them once I understood what they needed.”

Just like a puzzle piece sliding into place, Chabria realized that she had a knack for teaching, a skill that she wanted to develop further. She paid closer attention to her favorite teachers and as she noticed their different approaches to instructing students, she was inspired to incorporate some of their teaching styles in her own tutoring work.

“My teachers were inspirational because of how they empowered students every day,” Chabria said. “Watching them at work solidified my desire to teach and my plans to pursue a career in education. I got very interested in what it takes to be an effective math teacher, so I asked my own teachers and kept looking for colleges that could help prepare me to become one.”

Chabria was instantly drawn to UMD after learning about the Terrapin Teachers program, which offered a unique learning model and teaching certification process.  After speaking to the director and a student participating in the program, Chabria joined Terrapin Teachers and never looked back.

“You could say I specifically came to UMD to be part of Terrapin Teachers,” Chabria said. “It was really cool that I found a school that catered to exactly what I wanted to do and had high-quality math and education programs that I could be a part of. I felt like the people I spoke with were passionate about teaching and that they genuinely wanted to support both me and my goals.”

Once she got to UMD, Chabria worked to improve her teaching skills at every level, both in and out of the classroom—from tutoring peers in the Department of Mathematics to speaking at the Early Career Teaching Conference held at Towson University, where she presented on the topic of magic squares to local educators. Chabria is president of the Future Mathematics Teachers Council, a student organization dedicated to supporting future math teachers by providing a space to share ideas about teaching and learning math on UMD’s campus.

Being part of Terrapin Teachers also helped Chabria gain field experience as a teacher. She worked as a teaching assistant for introductory courses in the program, learning how to prepare for lessons and work with students from local schools.

“I’d recommend any undergrad take TLPL 101 and TLPL 102 if they’re interested in making use of their technical knowledge to help younger STEM students. The classes aren’t locked to education majors or Terrapin Teachers students,” she said. “We’re a small but tightly knit community, so we’ve always supported each other by sharing our problems and working together to solve them.”

Looking ahead, Chabria hopes to continue developing innovative teaching methods for middle and high school students. She plans to stay in Maryland to teach after she graduates in 2026.

“Even though Chicago will always be my hometown, I really love it here in Maryland—you guys don’t get much snow, which is nice,” she joked. “I’d like to stay here, continue my growth as an educator and build on the community connections I made through Terrapin Teachers. Growing up, I had inspirational teachers who made positive impacts on my life and I want to do the same for new generations of students.”

Donors Carol Fullerton and James A. Yorke met this year’s fellows at a luncheon in October.

Twenty-five graduate students in the Department of Mathematics at the University of Maryland received 2024-25 Herbert A. Hauptman Endowed Graduate Fellowships.

The fellowship program was created with an estate gift from Carol Fullerton that honors the memory of her late father, Nobel laureate Herbert A. Hauptman (Ph.D. ’55, mathematics), and launched in 2020 thanks to a gift from Distinguished University Professor Emeritus of Mathematics James A. Yorke (Ph.D. ’66, mathematics). 

The 2024-25 Hauptman Fellows are:

• Muhammad Aftab
• Marco  Bornstein
• Amandeep Chanda
• Philip Charles
• Spencer Durham
• Charles Dziedzic
• Shitao  Fan
• Wen-Tai Hsu
• Chenzi Jin
• Brandon Kolstoe
• Sze Kwong
• Qihang Li
• Zhirui Li
• Shenghao Li
• Nicholas McConnell
• Soyoung Park
• Vasanth Pidaparthy
• Shin Song
• Zezheng Song
• Ian Teixeira
• Maeve Wildes
• Valerie Wray
• Zhangchi Xu
• Yilin Zhang
• Shaoyang Zhou