# Research

At the Chair of Data Security and Cryptography we study diverse aspects of cryptography, in particular in the field of post-quantum cryptography (PQC). PQC is assumed to be resistant towards attacks with quantum computers. Our research mainly focuses on the four aspects Mathematical Foundations, Physical Security, Design and Application of PQC Schemes, and (Post-)Quantum Security, but is not limited to these.

## Mathematical Foundations

Since its beginnings, modern cryptography has been one of the main fields of applications of abstract mathematics and specifically number theory. At first, the mathematical problems underlying cryptographic protocols have been basic questions about congruences. Since the start of the post-quantum era, where many classical protocols cannot be considered secure in a long-term view, new foundational problems have arisen that build up the basics for constructions in cryptography. These new problems are again inherently mathematical, though, much more elaborate than the classical ones. In our research on mathematical foundations of cryptography we analyze the fundamental problems of modern cryptography in various aspects, such as the hardness of the computational problems. On the other hand, the construction of advanced primitives in cryptography requires new mathematical tools, which we develop as part of our research on mathematical foundations of cryptography.

## Physical Security

If the implementation of a cryptographic algorithm is not secured against physical attacks, information about the private key could be derived from this vulnerability. For this purpose, an adversary could use physical measurements (side-channel attack) or the targeted introduction of errors (fault attack) during the computation. In this research area, we investigate attacks on signature and encryption schemes that could be carried out by such a powerful attacker, and suggest countermeasures to make these schemes more resilient. We focus not only on the theoretical attacker model and error tracking, but also on the practical relevance of the respective scenario.

## Design and Application of PQC Schemes

This research topic aims at advances in the practical usability of post-quantum schemes. In particular, we design PQC schemes and build advanced protocols, such as threshold protocols or identity-based encryption, from PQC schemes. Furthermore, we work on mathematical optimizations of PQC schemes, which allow for more efficient implementations. This also includes considerations for real-world applications, such as constant-time implementations, or implementations for specific use cases.

## (Post-)Quantum Security

This research area deals with the security of cryptographic primitives against attackers with quantum computing power. On the one hand, we consider what is commonly referred to as post-quantum security: attackers have quantum computing power while end users of cryptographic primitives have classical computing power. This captures the scenario once the first large-scale quantum computers exist. On the other hand, we consider what is known as quantum security. In this scenario quantum computers are ubiquitously deployed. This scenario enables new attack vectors as an attacker can get quantum access to cryptographic devices.

## Contact

Prof. Dr. Juliane Krämer Data Security and Cryptography

Quantum and Physical Attack Resistant Cryptography

Bajuwarenstraße 4
93053 Regensburg