Research

Network and information security is a central concern of all the working groups at the IEM. Problems in this area are tackled jointly, with each group making a contribution based on its particular expertise.

The Working Group on Digital Communications focuses on problems in the areas of information theory, communication theory and data security. Prof. Trung van Tran has been involved in the development of public key methods; he has developed public key algorithms and proposed and described new approaches to the realization of practical cryptographic algorithms. The group also concentrates its research on the area of digital communications.

The Alfried Krupp von Bohlen und Halbach Chair for Computer Networking Technology focuses on new network technologies, architectures and protocols. Besides carrying out projects on UMTS evolution and next-generation Internet architecture, the group is concerned with architectural issues of peer-to-peer and sensor network concepts. A long-term project deals with the definition, evaluation and further development of the new Internet transport protocol SCTP and the reliable server pooling framework based on it. In addition to research publications and doctoral dissertations, this project has resulted in official Internet standards. These activities contribute to the effort to make the Internet fit for telephony and multimedia applications. The second area of focus is network security. Here the group is developing new protocols to ensure secure and confidential communication via the Internet as well as innovative concepts to protect future Internet infrastructure. Prof. Rathgeb is the initiator and chairman of the ITG specialist group on network security. This working group has received substantial public funding (DFG, BMBF) and also cooperates intensively with partners in industry.
The research area of the Working Group on Theory of Numbers is arithmetic geometry. In addition to investigations in the realm of pure mathematics, the explicit aspects play a crucial role ranging from developing effective methods up to the implementation of fast algorithms. This research approach is closely linked to applications in the area of data security. The introduction of concepts from the area of arithmetic geometry has laid the foundation for major advances in public key cryptography. In numerous doctoral theses and publications, the members of this group have developed methods for the construction of appropriate curves and have discussed the possibility of attacks due to Weil descent and bilinear structures (Tate Pairing) essential for contemporary cryptography.

The main research interests of the Working Group on Finite Mathematics are in the areas of algebraic geometry and group and representation theory. In both areas research efforts not only concentrate on the theoretical underpinnings of the subject but also deal with the development and implementation of efficient algorithms to solve present-day problems. In this way, the group has made contributions in the form of programme systems (e. g. BRAID) for the computer algebra systems GAP and MAGMA.

Currently, work is in progress on a database for problems related to Riemann spheres and Riemann surfaces. Furthermore, the group is investigating problems lying in the area of intersection between finite mathematics, coding theory and cryptography in collaboration with other groups at the IEM.