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

  • Character sums over sparse elements of finite fields. / Merai, L; Shparlinski, I; Winterhof, A.
    in: Bulletin of the London Mathematical Society, Jahrgang 56, Nr. 4, 27.02.2024, S. 1488--1510.
    DOIRISENWBIB
  • On divisors of sums of polynomials. / Merai, L.
    in: Finite Fields and their Applications, Jahrgang 83, 01.10.2022, S. Paper No. 102090.
    DOIRISENWBIB
  • Multiplicative and linear dependence in finite fields and on elliptic curves modulo primes. / Barroero, F; Capuano, L; Mérai, L et al.
    in: International Mathematics Research Notices, Jahrgang 2022, Nr. 20, 01.10.2022, S. 16094--16137.
    DOIRISENWBIB
  • On a class of functions with the maximal number of bent components. / Anbar, N; Kalaycı, T; Meidl, W et al.
    in: IEEE Transactions on Information Theory, Jahrgang 68, Nr. 9, 01.09.2022, S. 6174--6186.
    DOIRISENWBIB
  • Pseudorandom sequences derived from automatic sequences. / Merai, L; Winterhof, A.
    in: Cryptography and Communications, Jahrgang 14, Nr. 4, 19.04.2022, S. 783--815.
    DOIRISENWBIB
  • On digits of Mersenne numbers. / Kerr, B; Mérai, L; Shparlinski, I E.
    in: Revista Matematica Iberoamericana, Jahrgang 38, Nr. 6, 19.04.2022, S. 1901--1925.
    DOIRISENWBIB
  • Linear complexity of sequences on Koblitz curves of genus 2. / Anupindi, V.
    in: Uniform Distribution Theory, Jahrgang 17, Nr. 2, 25.03.2022, S. 1-20.
    DOIRISENWBIB
  • Linear complexity of some sequences derived from hyperelliptic curves of genus 2. / Anupindi, V; Merai, L.
    in: Cryptography and Communications, Jahrgang 14, Nr. 1, 25.03.2022, S. 117--134.
    DOIRISENWBIB
  • Dynamical irreducibility of polynomials in reduction modulo primes. / Mérai, L; Ostafe, A; Shparlinski, I.
    in: Mathematische Zeitschrift, Jahrgang 298, Nr. 3-4, 14.09.2021, S. 1187--1199.
    DOIRISENWBIB
  • On the distribution of the Rudin-Shapiro function for finite fields. / Dartyge, C; Merai, L; Winterhof, A.
    in: Proceedings of the American Mathematical Society, Jahrgang 149, Nr. 12, 12.05.2021, S. 5013--5023.
    DOIRISENWBIB
  • On the dynamical system generated by the Möbius transformation at prime times. / Merai, Laszlo; Shparlinski, Igor E.
    in: Research in Mathematical Sciences, Jahrgang 8, Nr. 1, 01.02.2021, S. ARTN 10.
    DOIRISENWBIB
  • Algebraic dependence in generating functions and expansion complexity. / Gómez-Pérez, D; Mérai, L.
    in: Advances in Mathematics of Communications, Jahrgang 14, Nr. 2, 07.09.2020, S. 307-–318.
    RISENWBIB
  • Values of rational functions in small subgroups of finite fields and the identity testing problem from powers. / Merai, L.
    in: International Journal of Number Theory, Jahrgang 16, Nr. 2, 07.09.2020, S. 219-–231.
    RISENWBIB
  • Distribution of short subsequences of inversive congruential pseudorandom number generator. Math. Comp. / Mérai, L; Shparlinski, I E.
    in: Mathematics of Computation, Jahrgang 89, Nr. 322, 21.02.2020, S. 911--922.
    DOIRISENWBIB
  • Unlikely intersections over finite fields: polynomial orbits in small subgroups. / Merai, L; Shparlinski, I.E.
    in: Discrete and Continuous Dynamical Systems- Series A, Jahrgang 40, Nr. 2, 21.02.2020, S. 1065--1073.
    DOIRISENWBIB

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.