Section: New Results

Polynomial Time Bounded Distance Decoding near Minkowski's Bound in Discrete Logarithm Lattices

Participant : Cécile Pierrot [contact] .

In [6], together with Léo Ducas, we proposed a concrete family of dense lattices of arbitrary dimension $n$ in which the lattice Bounded Distance Decoding (BDD) problem can be solved in deterministic polynomial time. The lattice construction needs discrete logarithm computations that can be made in deterministic polynomial time for well-chosen parameters. Each lattice comes with a deterministic polynomial time decoding algorithm able to decode up to a large radius. Namely, we reached decoding radius within $O(logn)$ Minkowski's bound, for both ${\ell }_1$ and ${\ell }_2$-norms.