Second order statistical behavior of LLL and BKZ

DOI10.1007/978-3-319-72565-9_1zbMath1384.94111OpenAlexW2750592818MaRDI QIDQ1746949

Léo Ducas, Yang Yu

Publication date: 26 April 2018

Full work available at URL: https://ir.cwi.nl/pub/27302

zbMATH Keywords

cryptanalysisstatisticsBKZlattice reductionLLL

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Cryptography (94A60)

Related Items (12)

A trace map attack against special ring-LWE samples ⋮ Solving the search-LWE problem over projected lattices ⋮ An extension of Kannan's embedding for solving ring-based LWE problems ⋮ Shortest vector from lattice sieving: a few dimensions for free ⋮ NTRU Fatigue: How Stretched is Overstretched? ⋮ Self-dual DeepBKZ for finding short lattice vectors ⋮ On the measurement and simulation of the BKZ behavior for \(q\)-ary lattices ⋮ Development and analysis of massive parallelization of a lattice basis reduction algorithm ⋮ Dynamic self-dual DeepBKZ lattice reduction with free dimensions and its implementation ⋮ Learning strikes again: the case of the DRS signature scheme ⋮ Faster enumeration-based lattice reduction: root Hermite factor \(k^{1/(2k)}\) time \(k^{k/8+o(k)}\) ⋮ A physical study of the LLL algorithm

Cites Work

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• Practical, Predictable Lattice Basis Reduction
• Lattice Signatures and Bimodal Gaussians
• Lattice Point Enumeration on Block Reduced Bases
• BKZ 2.0: Better Lattice Security Estimates
• Modelling the LLL Algorithm by Sandpiles
• Lattice Enumeration Using Extreme Pruning
• Improved Analysis of Kannan’s Shortest Lattice Vector Algorithm
• On the equidistribution of Hecke points
• On the Tractability of Public Persuasion with No Externalities
• Analyzing Blockwise Lattice Algorithms Using Dynamical Systems
• Predicting Lattice Reduction
• Rankin’s Constant and Blockwise Lattice Reduction
• The Kolmogorov-Smirnov Test for Goodness of Fit
• Algorithmic Number Theory
• Algorithmic Number Theory

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