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 $n$, \[ \eta_{\varepsilon}({\cal L}) \le \sqrt{\frac{\ln \big(n1+\frac{2n}{\varepsilon}\big)}{\pi}}\tilde{bl}({\cal L}). \]
Metadata
 Available format(s)
 Publication info
 Preprint. MINOR revision.
 Keywords
 Latticesdiscrete Gaussian measuresmoothing parameter
 Contact author(s)
 gxu4uwm @ uwm edu
 History
 20180901: 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}, note = {\url{https://eprint.iacr.org/2018/786}}, url = {https://eprint.iacr.org/2018/786} }