Research areas and topics


Two main directions in my current research

My research is in discrete mathematics applied to information theory and security: cryptography and coding theory. More specifically, my current work focuses on applications of algebraic and combinatorial methods in symmetric cryptography and coding theory. The two main topics of my current research are:
  • The non-linear functions: these functions are of a high importance in symmetric cryptography to avoid some fundamental attacks against ciphers (stream ciphers and bloc ciphers) such as linear and differential cryptanalysis. In the algebraic approach I use finite fields, exponential sums, algebraic curves and arithmetic tools. In the combinatorial approach, I use finite geometries to construct non-linear functions and provide answers to enumerative questions;
  • Error correcting codes: I work on algebraic and combinatorial aspects of error correcting codes in the classical channel. The algebraic methods give rise to constructions of good codes for various applications.

  • I am also interested in the algorithmic aspects in the above topics in the context of computer algebra.