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.
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Designs, Codes and Cryptography
Cryptanalysis of Lattice-based Cryptography

Ducas, L., & Pierrot, C. (2018). Polynomial time bounded distance decoding near Minkowski’s bound in discrete logarithm lattices. Designs, Codes and Cryptography, 87, 1737–1748. doi:10.1007/s10623-018-0573-3