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:
Peer Reviewed Journal Publication
- L. Mérai, I. E. Shparlinski (2020) Distribution of short subsequences of inversive congruential pseudorandom number generator. Math. Comp. Math. Comp., Bd. 89 (322), S. 911--922.
- L. Merai, I.E. Shparlinski (2020) Unlikely intersections over finite fields: polynomial orbits in small subgroups. Discrete Contin. Dyn. Syst., Bd. 40 (2), S. 1065--1073.
- Merai, L. (2019) Values of rational functions in small subgroups of finite fields and the identity testing problem from powers. Int. J. Number Theory, Bd. to appear, S. 1-10.
- D. Gómez-Pérez, L. Mérai (2019) Algebraic dependence in generating functions and expansion complexity. Adv. Math. Commun., Bd. to appear, S. 1-10.
- B. Kerr, L. Mérai, I. E. Shparlinski (2020) On digits of Mersenne numbers.
- L. Mérai, A. Ostafe, I. E. Shparlinski Dynamical irreducibility of polynomials in reduction modulo primes.