My research involves applications of algebraic and combinatorial methods
in cryptography and in the theory of error-correcting codes.
My current research areas are:
- Non-linear functions. These functions are of essential importance in symmetric cryptography to prevent some fundamental attacks against ciphers such as linear cryptanalysis and differential cryptanalysis. In the algebraic approach I use finite fields, exponential sums and algebraic curves. In the combinatorial approach I use finite geometries to construct non-linear functions.
- Error-control codes. I work on algebraic and combinatorial error-correcting codes for the classical channel and for the quantum channel. The algebraic methods involve cyclic codes and their various generalizations, and the combinatorial methods involve finite geometries. Further I work on adapting construction methods for classical codes so they can be used to construct quantum codes.
- Steganography. This is the science of information hiding, concerned with developing communication channels that obscure the very existence of the message that they carry. I work on steganographic schemes that use linear codes.
- Computer algebra. I am interested in the algorithmic aspects of the above three topics in the context of computer algebra (symbolic computation).
For more information such as the list of my publications and conference organization please see my personal website.