Discrete Gaussian measures and new bounds of the smoothing parameter for lattices

被引:1
|
作者
Zheng, Zhongxiang [1 ]
Zhao, Chunhuan [1 ]
Xu, Guangwu [2 ,3 ,4 ]
机构
[1] Tsinghua Univ, Inst Adv Study, Beijing, Peoples R China
[2] Minist Educ, Key Lab Cryptol Technol & Informat Secur, Qingdao 266237, Shandong, Peoples R China
[3] Shandong Univ, Sch Cyber Sci & Technol, Qingdao 266237, Shandong, Peoples R China
[4] Univ Wisconsin, Dept EE & CS, Milwaukee, WI 53211 USA
关键词
Lattices; Discrete Gaussian measure; Lattice based cryptography; Smoothing parameter; POLAR RECIPROCAL LATTICES; TRANSFERENCE THEOREM; CONVEX-BODIES; INEQUALITIES; GEOMETRY;
D O I
10.1007/s00200-020-00417-z
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
In this paper, we start with a discussion of discrete Gaussian measures on lattices. Several results of Banaszczyk are analyzed, a simple form of uncertainty principle for discrete Gaussian measure is formulated. In the second part of the paper we prove two new bounds for the smoothing parameter of lattices. Under the natural assumption that epsilon is suitably small, we obtain two estimations of the smoothing parameter: 1. eta(epsilon)(Z) <= root 1n(epsilon/44 + 2/epsilon)/pi. This is a practically useful case. For this case, our upper bound is very close to the exact value of eta(epsilon)(Z) in that root 1n(epsilon/44 + 2/epsilon)/pi - eta(epsilon)(Z) <= epsilon(2)/552. 2. For a lattice L subset of R-n of dimension n, eta(epsilon)(L) <= root 1n(n - 1 + 2n/epsilon)/pi (b) over tildel(L).
引用
收藏
页码:637 / 650
页数:14
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