FWF Project P 31762
During the last century, number theoretical problems arose in many applications, such as cryptography, communication systems or numerical methods. For example, number theory plays a central role for public key encryption as well as for their security analysis, for symmetric key encryption (for example design of stream ciphers or block ciphers), for wireless communications (for example code division multiple access) or for quasi Monte Carlo methods.
This project is devoted to the study of pseudorandom number generators, applications of elliptic curves, and highly nonlinear Boolean and vectorial Boolean functions.
We use a collection of different methods from number theory and their combinations including
- exponential and character sum techniques
- arithmetic over finite fields and residue rings
- elliptic curves over finite fields
- methods from algebraic geometry
The preprints of all publications are avaible via arXiv.org: https://arxiv.org/search/?searchtype=author&query=Mérai,+L.
- Dartyge, C.; Merai, L.; Winterhof, A. (2021) On the distribution of the Rudin-Shapiro function for finite fields.
- Anbar, N.; Kalaycı, T.; Meidl, W.; Mérai, L. (2020) On functions with the maximal number of bent components.
- Barroero, F.; Capuano, L.; Mérai, L.; Ostafe, A.; Sha, M. (2020) Multiplicative and linear dependence in finite fields and on elliptic curves modulo primesFabrizio Barroero, Laura Capuano, László Mérai, Alina Ostafe, Min Sha.
- B. Kerr, L. Mérai, I. E. Shparlinski (2020) On digits of Mersenne numbers.