Paper 2012/293
New Transference Theorems on Lattices Possessing n^\epsilon-unique Shortest Vectors
Wei Wei, Chengliang Tian, and Xiaoyun Wang
Abstract
We prove three optimal transference theorems on lattices possessing $n^{\epsilon}$-unique shortest vectors which relate to the successive minima, the covering radius and the minimal length of generating vectors respectively. The theorems result in reductions between GapSVP$_{\gamma'}$ and GapSIVP$_\gamma$ for this class of lattices. Furthermore, we prove a new transference theorem giving an optimal lower bound relating the successive minima of a lattice with its dual. As an application, we compare the respective advantages of current upper bounds on the smoothing parameter of discrete Gaussian measures over lattices and show a more appropriate bound for lattices whose duals possess $\sqrt{n}$-unique shortest vectors.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Published elsewhere. This paper hasn't been published anywhere.
- Keywords
- Transference theoremReductionGaussian measuresSmoothing parameter
- Contact author(s)
- wei-wei08 @ mails tsinghua edu cn
- History
- 2012-06-03: received
- Short URL
- https://ia.cr/2012/293
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2012/293,
author = {Wei Wei and Chengliang Tian and Xiaoyun Wang},
title = {New Transference Theorems on Lattices Possessing n^\epsilon-unique Shortest Vectors},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/293},
year = {2012},
url = {https://eprint.iacr.org/2012/293}
}
