Slide reduction, successive minima and several applications

Authors

  • J. Li Tsinghua University, Beijing, China
  • W. Wei Tsinghua University, Beijing, China

Keywords:

slide reduction, successive minima, SIVP, SMP, CVP

Abstract

Gama and Nguyen (2008) presented slide reduction which is currently the best SVP approximation algorithm in theory. In this paper, we prove the upper and lower bounds for the ratios ||b_{i}^{\ast}||/\lambda_{i}(L) and ||b_{i}||/\lambda_{i}(L)where b_1, ... , b_n is a slide reduced basis and \lambda_{1}(L), ..., \lambda_{n}(L) denote the successive minima of lattice L. We define generalized slide reduction and use slide reduction to approximate i-SIVP, SMP and CVP. Besides, we present a critical slide reduced basis for blocksize 2. 10.1017/S0004972713000257

Author Biographies

J. Li, Tsinghua University, Beijing, China

Institute for Advanced Study

W. Wei, Tsinghua University, Beijing, China

Institute for Advanced,

Published

2013-09-27

Issue

Vol. 88 No. 3 (2013)

Section

Articles
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