Paper 2007/105
Isodual Reduction of Lattices
Nicholas A. Howgrave-Graham
Abstract
We define a new notion of a reduced lattice, based on a quantity introduced in the LLL paper. We show that lattices reduced in this sense are simultaneously reduced in both their primal and dual. We show that the definition applies naturally to blocks, and therefore gives a new hierarchy of polynomial time algorithms for lattice reduction with fixed blocksize. We compare this hierarchy of algorithms to previous ones. We then explore algorithms to provably minimize the associated measure, and also some more efficient heuristics. Finally we comment on the initial investigations of applying our technique to the NTRU family of lattices.
Note: Revised to include an algorithmic description of a practical and useful isodual reduction technique.
Metadata
- Available format(s)
-
PDF
PS
- Category
- Foundations
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Lattice reduction
- Contact author(s)
- nhowgravegraham @ ntru com
- History
- 2007-08-27: last of 2 revisions
- 2007-03-23: received
- See all versions
- Short URL
- https://ia.cr/2007/105
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2007/105,
author = {Nicholas A. Howgrave-Graham},
title = {Isodual Reduction of Lattices},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/105},
year = {2007},
url = {https://eprint.iacr.org/2007/105}
}
