Cryptology ePrint Archive: Report 2018/146

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

Léo Ducas and Cécile Pierrot

Abstract: 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 (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.

Category / Keywords: foundations / lattice techniques, Bounded Distance Decoding, Minkowski's bound

Date: received 7 Feb 2018

Contact author: cecile pierrot at inria fr

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Version: 20180208:163306 (All versions of this report)

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