Certified lattice reduction (Q2008874)

A lattice is a free \(\mathbb{Z}\) module, equipped with a positive definite bilinear form on its ambient space. The authors give an adaptive-precision version of a generalized Lenstra-Lenstra-Lovász reduction algorithm for real lattices. Specifically, the floating-point arithmetic is replaced by interval arithmetic to certify the behavior of the algorithm. Additionally, they give an application of the result for the reduction of ideal lattices in number fields.