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I have found an ideal place at the intersection of basic and applied research: in cryptography

Vladimír Sedláček

Often, it does not take any deep mathematical theory for someone with a bit of sleight of hand to get at information that should be protected. Until we build a robust system of rules by which new technologies are created, and change the culture in this area, human error is likely to remain the biggest vulnerability.

Author: Marta Vrlová for

He chose the Centre for Research on Cryptography and Security (CRoCS) at Masaryk University's Faculty of Informatics (FI MU) for his PhD studies. He recently submitted his dissertation focusing on the security of cryptographic systems related to elliptic curves. In his spare time, he works on popularizing science and looking for ways to get people excited not only about interesting research, but especially about mathematical thinking. Vladimír Sedláček, this year's representative of FI MU at the Researcher’s Night 2021 and a participant of the Science Slam at MUNI, fought his way with a magic wand to the national final of the prestigious Fame Lab 2021 competition.

How would you explain what cryptography is?

Cryptography is a science, or even an art, of dealing with secure communication in situations where we assume presence of a hostile party. It is a relatively small part of security, but a very important one. If we consider that any security system is only as strong as its weakest link, then the system needs to be well set up as a whole. It is so because an attacker typically picks the weakest parts of a system. So cryptography will not save us from all threats, but it is a kind of last line of defence, and that is why we want it to be very strong. Practical applications today include data encryption in communications and the use of electronic signatures.

If we really are all magicians, as you noted in your candidate video for the Fame Lab, how come we do not have the power to control the leakage of our own "thoughts" or information? Where are we most vulnerable?

The trouble is that most of this magic was designed from the start with functionality in mind, not security. Often, it does not even take any deep mathematical theory for someone with a bit of sleight of hand to get at information that should be protected. Until we build a robust system of rules by which new technologies are created and change the culture in this area, the biggest vulnerability is likely to remain the human error factor.

So, as an average user of today's technology, can I completely prevent my own data from being leaked?

No absolute guarantees can be achieved; in practice, any attack is only a matter of cost. But we can raise the bar so that we are not a convenient target. It also depends on the model: who is the expected attacker, what are their capabilities and resources? The average user can typically be affected by mass, untargeted attacks on login credentials.

How should we protect ourselves?

A good starting point may be to set up a password manager that allows us to have a strong and unique password for each account that does not burden our memory. Uniqueness is important. If we share a password between multiple accounts, the password is potentially at risk if there is a problem with any one of them. Another defense is two- (or even multi-factor) authentication, which allows access only to whoever has control over all the factors instead of just one. A simple form of this represent, for example, mobile apps that periodically generate one-time codes. Just watch out for SMS. A clever attacker can theoretically catch them on the way from the operator.

These two steps will already dramatically improve our security against data leaks. And it also helps not to divulge sensitive data to random strangers, however innocently they may ask.

What brought you, as a theoretical mathematician, to computer science?

I have always enjoyed theory and abstraction, whereas I was hardly interested in practical applications. Over time, however, I began to look for a deeper meaning and found it important to work on something that has the potential to help people in my lifetime. Cryptography was a good compromise, because it uses beautiful algebra and number theory, while having a big impact on the real world. So, I found an ideal place at the intersection of basic and applied research.

I admit I still enjoy the relationship between mathematics and computer science. The two worlds have quite different cultures, language and approaches to problem solving. I find it very interesting to switch between them and always choose the optics that is useful in a given context.

Why FI MU? What do you like here and what was the most difficult for you?

What I have always appreciated about FI is how it encourages student involvement in teaching, research in labs and other activities. A good example is Spolek přátel severské zvěře, a student association, which organizes many events for high school students. It was thanks to this association that I started to engage with FI already during my studies of mathematics at the Faculty of Science at MU. I also value the cooperation with industrial partners and foreign institutions, which allows us to take the best from each area. My PhD in the CRoCS lab was an excellent, if often very challenging, experience. Finding the interfaces in interdisciplinary research and complementing each other's knowledge was a challenge, but in the end it was successful. In this respect, besides the local high research standards and the excellent organization of my supervisor Prof. Vasek Matyáš, I was greatly helped by sufficient personal freedom and strong social contact with colleagues, which I definitely do not take for granted.

What specifically were you involved in and with what result?

From many different angles, I have investigated the cryptography of elliptic curves. These are objects with a rich algebraic and geometric structure that are widely used today. For example, I have studied when a curve might be less secure than it first appears, and whether it is possible to deliberately hide such vulnerabilities in it. For example, my colleagues and I have created a free project called DiSSECT that allows anyone to easily explore curves standardized by different organizations.

I have also tried to challenge existing systems because elliptic curves are a very difficult area to program flawlessly. In order to build a solid defense, it is important to play the attacker role and alert the community to potential problems. Moreover, the destructive approach is quite fun because it requires a lot of curiosity and ingenuity. We just need to keep the ethical side in mind. My colleagues and I were able to find a few attacks; the one with probably the biggest practical impact we named Minerva.

Please tell us what the Minerva attack was?

In 2019, my colleague Ján Jančár, who works on side-channel attacks, explored various cryptographic libraries and smart cards that used elliptic curves. He noticed that in some implementations, the time of digital signature creation reveals the size of the auxiliary value (called a nonce) used by the signing algorithm. While this seems like relatively innocuous information, together we were able to exploit it through lattice techniques. With these, we put the pieces of information together and after observing several hundred to units of thousands of signatures, we were able to find the private key within minutes. This is every attacker's dream, because then they can forge the signature of any document.

What is the procedure following a detection of such a weakness?

We contacted the relevant companies and library developers to propose defense mechanisms. In many cases, this has fixed the vulnerability, but there is not much that can be done for previously sold smart cards. Our attack was not completely new, a few similar variants already existed. Therefore, we conducted extensive experiments to compare their effectiveness and added a few improved versions of our own. We won the Best Paper Award at the CHES 2020 conference for this systematic review.

You are involved in science not only professionally but also in your spare time. Why did you decide to focus on popularization of science and what are your future plans, after your success at Science Slam and Fame Lab?

I try to find ways to get people excited not only about interesting research, but especially about mathematical way of thinking. I have been organizing playful competitions and camps for high school students for a long time, and lately I have been trying to target the wider public as well. That is why I'm experimenting with new forms, such as Fame Lab or Science Slam. I'm discovering what is beneficial, what is fun, and what scales. It also inspired my friend and me to start a podcast Místo problémů, which is a project very close to my heart. I believe communicating science is a great way to sort out your thoughts, break down social barriers, and learn how to better communicate important ideas across disciplines, among other things.

You have recently submitted your dissertation at FI MU, where are you headed next?

I have just started a postdoc position in France, but I will be happy to continue my collaboration with FI if the opportunity arises. I want to continue to do research and use a mathematical perspective to solve difficult and important problems. Cryptography in academia fulfills me and for now I plan to continue in this direction, but I do not rule out other alternatives in the future. I also definitely want to continue to combine research with its dissemination into other circles, so that I do not remain locked in an isolated world.

Thanks for the interview.

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