Rigorous and Efficient Short Lattice Vectors Enumeration

Xavier Pujol and Damien Stehlé

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.

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The algorithms described in this article are implemented in fplll-3.0.