Paper 2018/786
Discrete Gaussian Measures and New Bounds of the Smoothing Parameter for Lattices
Zhongxiang Zheng, Guangwu Xu, and Chunhuan Zhao
Abstract
In this paper, we start with a discussion of discrete Gaussian measures on lattices. Several results of Banaszczyk are analyzed, different approaches are suggested. In the second part of the paper we prove two new bounds for the smoothing parameter of lattices. Under the natural assumption that $\varepsilon$ is suitably small, we obtain two estimations of the smoothing parameter: 1. \[ \eta_{\varepsilon}(\mathbb{Z}) \le \sqrt{\frac{\ln \big(\frac{\varepsilon}{44}+\frac{2}{\varepsilon}\big)}{\pi}}. \] 2. For a lattice ${\cal L}\subset \mathbb{R}^n$ of dimension $n$, \[ \eta_{\varepsilon}({\cal L}) \le \sqrt{\frac{\ln \big(n-1+\frac{2n}{\varepsilon}\big)}{\pi}}\tilde{bl}({\cal L}). \]
Metadata
- Available format(s)
-
PDF
- Publication info
- Preprint. MINOR revision.
- Keywords
- Latticesdiscrete Gaussian measuresmoothing parameter
- Contact author(s)
- gxu4uwm @ uwm edu
- History
- 2018-09-01: received
- Short URL
- https://ia.cr/2018/786
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2018/786,
author = {Zhongxiang Zheng and Guangwu Xu and Chunhuan Zhao},
title = {Discrete Gaussian Measures and New Bounds of the Smoothing Parameter for Lattices},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/786},
year = {2018},
url = {https://eprint.iacr.org/2018/786}
}