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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
Creative Commons Attribution
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}
}
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