Polynomial time bounded distance decoding near Minkowski’s bound in discrete logarithm lattices
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