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Lattice Enumeration Using Extreme Pruning

Nicolas Gama 1 Phong Q. Nguyen 2 Oded Regev 3
1 Equipe AMACC - Laboratoire GREYC - UMR6072
GREYC - Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen
2 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : Lattice enumeration algorithms are the most basic algorithms for solving hard lattice problems such as the shortest vector problem and the closest vector problem, and are often used in public-key cryptanaly-sis either as standalone algorithms, or as subroutines in lattice reduction algorithms. Here we revisit these fundamental algorithms and show that surprising exponential speedups can be achieved both in theory and in practice by using a new technique, which we call extreme pruning. We also provide what is arguably the first sound analysis of pruning, which was introduced in the 1990s by Schnorr et al.
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Nicolas Gama, Phong Q. Nguyen, Oded Regev. Lattice Enumeration Using Extreme Pruning. Proceedings of the 29th International Conference on Cryptology - EUROCRYPT 2010, May 2010, Nice, France. pp.257 - 278, ⟨10.1007/978-3-642-13190-5_13⟩. ⟨hal-01083526⟩

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