Arithmetic Primitives for Uniform Distribution Modulo 1

  • Hellekalek, Peter, (Projektleitung)

Projektdetails

Beschreibung

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
StatusAbgeschlossen
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