International Conference on the Theory and Application of Cryptology and Information Security

ASIACRYPT 2008: Advances in Cryptology - ASIACRYPT 2008 pp 390-405

Rigorous and Efficient Short Lattice Vectors Enumeration

  • Xavier Pujol
  • Damien Stehlé
Conference paper

DOI: 10.1007/978-3-540-89255-7_24

Volume 5350 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Pujol X., Stehlé D. (2008) Rigorous and Efficient Short Lattice Vectors Enumeration. In: Pieprzyk J. (eds) Advances in Cryptology - ASIACRYPT 2008. ASIACRYPT 2008. Lecture Notes in Computer Science, vol 5350. Springer, Berlin, Heidelberg

Abstract

The Kannan-Fincke-Pohst enumeration algorithm for the shortest and closest lattice vector problems is the keystone of all strong lattice reduction algorithms and their implementations. In the context of the fast developing lattice-based cryptography, the practical security estimates derive from floating-point implementations of these algorithms. However, these implementations behave very unexpectedly and make these security estimates debatable. Among others, numerical stability issues seem to occur and raise doubts on what is actually computed. We give here the first results on the numerical behavior of the floating-point enumeration algorithm. They provide a theoretical and practical framework for the use of floating-point numbers within strong reduction algorithms, which could lead to more sensible hardness estimates.

Keywords

LatticesSVPlattice cryptanalysisnumerical stability
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xavier Pujol
    • 1
  • Damien Stehlé
    • 1
    • 2
  1. 1.LIP Arénaire, CNRS/INRIA/ENS Lyon/UCBL/Université de LyonFrance
  2. 2.University of Macquarie/University of SydneyAustralia