FWF Project P 31762
Runtime: 01.01.2019-31.08.2022

Project Team

Project Abstract

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

Publications

The preprints of all publications are avaible via arXiv.org: https://arxiv.org/search/?searchtype=author&query=Mérai,+L.

Peer Reviewed Journal Publication

  • Mérai, L.; Ostafe, A.; Shparlinski, I.E. (2021) Dynamical irreducibility of polynomials in reduction modulo primes. Mathematische Zeitschrift, Bd. 298 (3-4), S. 1187--1199.
  • Barroero, F.; Capuano, L.; Mérai, L.; Ostafe, A.; Sha, M. (2021) Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes. International Mathematics Research Notices, Bd. to appear, S. 23.
  • Anupindi, V.; Merai, L. (2021) Linear complexity of some sequences derived from hyperelliptic curves of genus 2. Cryptography and Communications, Bd. to appear, S. 19.
  • Dartyge, C.; Merai, L.; Winterhof, A. (2021) On the distribution of the Rudin-Shapiro function for finite fields. Proceedings of the American Mathematical Society, Bd. 149 (12), S. 5013-5023.
  • Merai, L. (2020) Values of rational functions in small subgroups of finite fields and the identity testing problem from powers. Int. J. Number Theory, Bd. 16 (2), S. 219-–231.
  • Gómez-Pérez, D.; Mérai, L. (2020) Algebraic dependence in generating functions and expansion complexity. Adv. Math. Commun., Bd. 14 (2), S. 307-–318.
  • 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.
  • 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.

Workingpaper

  • 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.