Theses topics, open

The following list describes possible theses or internships. The following descriptions are of course just a rough sketch and not binding in any way. The actual compilation may differ considerably. However, you should get an impression of which kind of theses you can do with us. If you are interested in writing a thesis with us, contact us.

About some counting and density problems in the ring of univariate integer polynomials: By applying sieve methods, modular techniques and Galois theory we want to analyse some counting and density problems in the ring of polynomials over the integers. Among other things, we want to estimate the order of some classes of irreducible polynomials over Z. This estimations are useful for constructing and analysing randomized factorization and irreducibility testing algorithms for univariate integer polynomials.
Secure mobile phone calls: Modern mobile phones allow for a lot of additional software. The aim of this thesis is to demonstrate by an actual implementation that secure mobile calls are possible (and transparent).
Simulators Bombe, Enigma: Various designs have been proposed for remote electronic voting. The purpose of this thesis is to analyse one. Security definitions, security reductions and social implications shall be considered.
Counting coarse-grained integers: A coarse-grained integer is an integer whose few prime factors stem from a given interval. The issue of this thesis is to learn more about the number of such integers below a given bound x. Develop and prove a formula for the number of coarse-grained integers in the spirit of Riemann. Transfer theory and algorithms for prime counting to counting coarse-grained integers.
Quantum cryptanalysis and cryptography: In recent years, quantum computers and quantum channels were often discussed. It is not clear whether we will ever have scalable quantum computers. But if so most of the known public key cryptography breaks down. This is so since a quantum computer can solve discrete log and factorization problems in polynomial time. Cryptographers are challenged to find new schemes on the one hand potentially unbreakable even if quantum computers were available, to break more nowadays schemes using quantum computers, to use quantum mechanisms to design new schemes. Several open.
Remote electronic elections: Various designs have been proposed for remote electronic voting. The purpose of this thesis is to analyse one. Security definitions, security reductions and social implications shall be considered.
Advancing CrypTool: The aim of the CrypTool software is to present cryptographical primitives and notions. This should be done in a easy to use way for learning and teaching. To a large extent software engineering is necessary to achieve that. However, also a substantial theoretical background is important to make it a really helpful tool. Several open.