We propose 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. This construction is directly adapted from the Chor–Rivest cryptosystem (IEEE-TIT 1988). 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 large radius. Namely, we reach decoding radius within O(log n) Minkowski’s bound, for both ℓ1 and ℓ2 norms.
Bounded distance decoding (BDD), Dense lattices, Minkoswki’s bound
Designs, Codes and Cryptography

Ducas, L, & Pierrot, C.A. (2018). Polynomial time bounded distance decoding near Minkowski’s bound in discrete logarithm lattices. Designs, Codes and Cryptography. doi:10.1007/s10623-018-0573-3