TITLE:
Cyclic Lattices, Ideal Lattices and Bounds for the Smoothing Parameter
AUTHORS:
Zhiyong Zheng, Fengxia Liu, Yunfan Lu, Kun Tian
KEYWORDS:
Cyclic Lattice, Ideal Lattice, Finitely Generated R-Module, Smoothing Parameter
JOURNAL NAME:
Journal of Information Security,
Vol.13 No.4,
September
23,
2022
ABSTRACT: In this article, we introduce the discrete subgroup in ℝn as
preliminaries first. Then we provide some
theories of cyclic lattices and ideal lattices. By regarding the cyclic lattices and ideal lattices
as the correspondences of finitely generated R-modules, we prove our main theorem, i.e. the correspondence between cyclic
lattices in ℝn and finitely generated R-modules is one-to-one. Finally, we give an explicit and countable upper
bound for the smoothing parameter of cyclic lattices.