Arithmetic Primitives for Uniform Distribution Modulo 1

  • Hellekalek, Peter, (Projektleitung)



Project is part of FWF SFB F55N26.

Application of methods from metric number theory, algebra and combinatorics.

This project is about techniques relevant for the theory of uniform distribution modulo 1 (u.d.mod 1) of sequences and its applications in the field of random number generation and quasi-Monte Carlo methods. There is also a connection of this project to applied cryptography.
What do we want to achieve? We will contribute (i) to the question how well a given (finite) sequence is u.d.mod 1, by studying and developing appropriate figures of merit and investigating
their relation (keywords: discrepancy, diaphony, spectral test, inequality of Erd¨os-Tur´an-Koksma, inequality of Le Veque), (ii) to new construction methods for so-called low-discrepancy
sequences (keywords: b-adic arithmetics, lattice methods), and (iii) to applied cryptography (keywords: nonlinearity of Boolean functions, bit diffusion).
KurztitelArithmetic Primitives
Tatsächlicher Beginn/ -es Ende1/02/1431/01/18

Systematik der Wissenschaftszweige 2012

  • 101 Mathematik

Systematik der Wissenschaftszweige 2012 (6-Steller)

  • 101014 Numerische Mathematik
  • 101025 Zahlentheorie
  • 101001 Algebra

Systematik der Wissenschaftszweige 2002

  • 1119 Zahlentheorie
  • 1102 Algebra
  • 1114 Numerische Mathematik
  • 1104 Angewandte Mathematik