Paper 2018/146 Original: eprint.iacr.org/2018/146 ↗
Polynomial Time Bounded Distance Decoding near Minkowski’s Bound in Discrete Logarithm Lattices
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2018-02-08: last updated
- 2018-02-08: published
- Short URL
- https://ia.cr/2018/146
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2018/146,
author = {Léo Ducas and Cécile Pierrot},
title = {Polynomial Time Bounded Distance Decoding near Minkowski’s Bound in Discrete Logarithm Lattices},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/146},
year = {2018},
url = {https://eprint.iacr.org/2018/146}
}