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

Léo Ducas (1) , Cécile Pierrot (1, 2)

1 CWI - Centrum voor Wiskunde en Informatica
2 CARAMBA - Cryptology, arithmetic : algebraic methods for better algorithms

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 determin-istic 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 1 and 2 norms.

Domaines: Cryptographie et sécurité [cs.CR]

Léo Ducas, Cécile Pierrot. Polynomial Time Bounded Distance Decoding near Minkowski's Bound in Discrete Logarithm Lattices. Designs, Codes and Cryptography, 2018, ⟨10.1007/s10623-018-0573-3⟩. ⟨hal-01891713⟩