Primal-Dual Bases and Successive Minima

XIE Chao-hai; TAO Ran; WANG Yue; LI Ji-yong

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Primal-Dual Bases and Successive Minima

更新时间：2025-07-16

- Primal-Dual Bases and Successive Minima
- Acta Electronica Sinica Vol. 36, Issue 6, Pages: 1124-1129(2008)
- 作者机构：
  
  1. 北京理工大学信息科学技术学院,北京,100081
  2. 公安部信息安全等级保护评估中心,北京,100036
  3. 北京理工大学信息科学技术学院北京,100081
  4. 公安部信息安全等级保护评估中心北京,100036
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP393O15
- Published：2008
- 稿件说明：
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XIE Chao-hai, TAO Ran, WANG Yue, et al. Primal-Dual Bases and Successive Minima[J]. Acta Electronica Sinica, 2008, 36(6): 1124-1129.
DOI：

XIE Chao-hai, TAO Ran, WANG Yue, et al. Primal-Dual Bases and Successive Minima[J]. Acta Electronica Sinica, 2008, 36(6): 1124-1129. DOI：

摘要

最近Koy提出一种质量优于LLL规约基的原-对偶规约基

但没有给出该规约基与最小元比值因子的上界和下界.本文首先分析了原-对偶规约基的性质

然后给出并证明了原-对偶规约基与连续最小元比值因子的上界和下界

最后用原-对偶规约基改进Babai的近似CVP算法——舍入算法

提高了其近似因子.

Abstract

Recently Koy proposed primal-dual bases which have better quality than LLL-reduced bases in high-dimensional lattice

but his efforts did not take into account the low and upper bounds for the ratios of primal-dual bases to successive minima.In this paper some useful properties of Koy’s primal-dual bases are analyzed and then the low and upper bounds for the ratios of primal-dual bases to successive minima are introduced and proved.At the end

the Round-off algorithm for the approximate-CVP is improved using primal-dual bases and its result has a better approximation factor than L.Babai’s.

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