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Ajtai, M. (1996) Generating Hard Instances of the Short Basis Problem. Proceedings of 28th Symposium on the Theory of Computing, Philadephia, 22-24 May 1996, 99-108.

has been cited by the following article:

• 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.