Lattice algorithms for the closest vector problem with preprocessing - PowerPoint PPT Presentation

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Lattice algorithms for the closest vector problem with preprocessing Thijs Laarhoven mail@thijs.com http://www.thijs.com/ RISC seminar, Amsterdam, The Netherlands (May 3, 2019) Lattices Basics Lattices Basics O Lattices Basics b 2 b 1

Approximate Voronoi cells Estimating the volume [ Laa16, DLW19 ] Lemma (Good approximations, with heuristics) � Let L consist of the α n + o ( n ) shortest vectors of a lattice L , with α ≥ 2 + o ( 1 ) . Then: vol ( V L ) vol ( V ) = 1 + o ( 1 ) . (1) Lemma (Arbitrary approximations, with heuristics) � Let L consist of the α n + o ( n ) shortest vectors of a lattice L , with α ∈ ( 1.03396, 2 ) . Then: � n / 2 + o ( n ) α 2 − 1 � 16 α 4 � � vol ( V L ) vol ( V ) ≤ . (2) − 9 α 8 + 64 α 6 − 104 α 4 + 64 α 2 − 16
Approximate Voronoi cells Results for CVPP
Approximate Voronoi cells Results for BDDP

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Lattice algorithms for the closest vector problem with preprocessing - PowerPoint PPT Presentation

Lattice algorithms for the closest vector problem with preprocessing Thijs Laarhoven mail@thijs.com http://www.thijs.com/ RISC seminar, Amsterdam, The Netherlands (May 3, 2019) Lattices Basics Lattices Basics O Lattices Basics b 2 b 1

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