## Research

### Post-Quantum Cryptography

Assuming a cyber attack initiated from a sufficiently powerful quantum computer, several classical public-key algorithms become insecure. These algorithms are based on factoring large integers and the discrete logarithm problem which are easy-to-solve in a post-quantum world. Thus, the National Institute of Standards and Technology (NIST) launched the Post-Quantum Cryptography Standardization. My research focuses on assessing the hardness of mathematical problems that can serve as the core to such cryptosystems, analysing the security of existing schemes and constructing new efficient public-key algorithms in the context of post-quantum cryptography.

### Fiber-Optic Communication

In today’s communication systems, virtually all IP-based traffic is transmitted over non-linear optical fiber channels. Scenarios of future demands indicate a requirement of higher and higher data-rates, making the improvement of optical communication systems especially important. A key technology for achieving a higher throughput is coherent fiber optic telecommunication. This development allows for the use of not only the power but also the phase of the signal to transmit information, i.e., higher order modulation techniques, like quadrature amplitude modulation, can be applied. However, uncompensated Kerr nonlinearity limits the effective signal-to-noise ratio and thus, the throughput cannot be increased by increasing the modulation alphabet size. Therefore, I'm interested in developing new methods that increase the spectral efficiency of nonlinear fiber systems.

### MIMO Communication

Modern wireless communication systems have to provide higher and higher data rates. Since conventional methods like using more bandwidth or higher order modulation types are limited, Multiple-Input Multiple-Output (MIMO) technology constitutes a breakthrough. The technology offers significant increases in data throughput without additional bandwidth or increased transmit power. This is possible by the fact, that the channel capacity of a MIMO channel is larger than the channel capacity of a Single-Input Single-Output channel. In order to have a rate close to channel capacity, the signals are encoded before the transmission and decoded at the receiver side. The used decoding algorithms require statements about the certainty of the received signals. Log-Likelihood-Ratios deliver such information, but since they have a continuous range, their standard representation as floating point numbers requires a disproportional large amount of bandwidth. Thus, I investigate new quantization strategies that improve the bandwidth efficiency but still allow a good decoding performance.