Through engaging questions, we present selected research areas and contemporary mathematical concepts in an accessible way, while exploring the usefulness of mathematical research across various branches of science, the natural sciences, and the social sciences. This time, we spoke with Dr. Nastja Cepak, a young mathematician and cryptographer who is employed at the company CREA plus d.o.o., where she works on the practical aspects of encryption and computer security and delivers training on the use of cryptographic products abroad.

What is your favorite definition of the word mathematics?
For me, mathematics is the search for patterns. Rules. Ways of understanding, anticipating, and predicting the behavior of mathematical structures.

What or who was your main inspiration for deciding to study mathematics at UP FAMNIT?
When I was deciding to study at FAMNIT in high school, it was still a very young faculty. I became part of only the second generation of FAMNIT students. I did have some doubts, but I was strongly supported and encouraged by my advanced-level mathematics teacher at Gimnazija Koper. After the first few months at FAMNIT, all doubts quickly disappeared anyway.

How would you describe your colleagues at the university in three words?
International, humorous, innovative.

What are your favorite areas of mathematics and why?
Discrete mathematics, algebra, and more specifically, cryptography. It makes perfect sense that cryptography is my favorite field, as I also completed my PhD in this area. Interestingly, I was already very fond of cryptography in high school, even though at the time I couldn’t really imagine what it actually involved from a technical perspective. My early ideas were very romantic—word ciphers, shuffled numbers, nothing particularly related to 0s and 1s. In the end, however, the motivation for using both is the same—protecting information. This unchanged motivation in the search for better encryption has guided us for several millennia BCE. That consistency fascinates me.

As an author or co-author, you have published several articles in renowned mathematical journals. Could you briefly describe the main results of your research?
In my opinion, the best description stems from a good explanation of the motivation. For good ciphers, we need functions that map 0s and 1s to 0s and 1s in as unpredictable a way as possible. From what we learn in elementary and secondary school, we know that the most predictable functions are constant and linear ones. Therefore, it makes sense to try to find and understand functions that are as non-linear as possible. Most of my research focuses on understanding Boolean functions that are maximally distant from the set of linear functions.

Do you have a favorite place in Koper for finding answers to demanding mathematical questions?
Anywhere by the sea. (laughs) I now work and live in Ljubljana, and I miss the sea.

After completing your PhD, alongside your research and teaching work at the University of Primorska, you began collaborating with CREAPLUS, where you are currently employed. Did you acquire sufficient foundational knowledge during your studies for work in industry? How do you see your contribution to the company’s growth and development?
The initial technical knowledge was essential for being able to orient myself and continue learning independently everything my work required. Without that foundation, I wouldn’t have been able to understand what was relevant, what wasn’t, or even what questions to ask and which answers to seek. We essentially built the cryptography department from scratch, and for quite some time I was the only cryptographer in the company. When I received a question, I often didn’t know the answer—for example, questions related to code signing—but I understood the question and knew how to search for the right information online.

My role is to pursue professional excellence. I need to be familiar with advances in cryptography, which algorithms with which parameters are used in which cases, the cryptographic products we market, and similar matters. The technical information I provide must be reliable. If you don’t know something, you say you need to check. You must represent a trustworthy source of technically accurate information within your field of specialization.

In your work, you collaborate with people from various disciplines. How would you recognize a mathematician in a mixed team?
Our company has several departments, and in each one you can find at least one mathematician. Our tasks are very diverse—coding, preparing optimization models, testing, documentation, working with physical devices, managing and organizing meetings, to name just a few. If I look at what we have in common, we mostly stick to technical work. We are systematic and good at planning.

How do you explain complex mathematical concepts to non-mathematicians?
By always starting with concepts or ideas the person already knows. In fact, a large part of my job involves bringing specific areas of cryptography closer to both the general and professional public through lectures and webinars—explaining the current state of affairs, why something is not optimal, what challenges await us in the future, and what solution options we may have.

You are continuously involved in FAMNIT activities aimed at promoting mathematics among young people—for example, by organizing mathematics camps in Koper, popular science lectures called Trips into the Mathematical Universe, participating in the European Researchers’ Night, giving lectures for high school students, and organizing mathematics days at FAMNIT, and much more. What advice would you give to young people who are interested in this field and considering studying mathematics?
That they are thinking in an excellent direction. For most enthusiastic high school students I’ve met over the years, interest in mathematics was accompanied by interest in various other natural science fields. This is entirely expected—mathematics, as the discipline that defines some of the basic rules governing the natural world, is present in almost all other sciences. To see the beauty of mathematics is also to see the beauty of the many phenomena in which it is reflected. Returning to the original question, I believe that studying mathematics is an excellent choice, one that can also provide a better understanding of many other fields we enjoy.

What do you consider the most important thing mathematics has taught you?
The systematic definition of a problem—that is, the ability to approach a question, clearly define what the problem is, what is important, what is irrelevant, and then prepare a robust plan for solving it.