Lattices; Basis vectors; Dirichlet's theorem on arithmetic progressions
[en] Integer lattices enjoy increasing interest among mathematicians and cryptographers. However, there are still many elementary open questions, like finding specific vectors or particular bases of a given lattice. Our study consists in exhibiting which integer vectors may be chosen as basis vectors of a chosen lattice. The compelling part of our development is that this condition is obtained through an unusual application of Dirichlet's Theorem on primes in arithmetic progressions and that it has a surprising consequence for vectors achieving the successive minima.
Author, co-author :
Barthel, Jim Jean-Pierre ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Müller, Volker ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)