A physical study of the LLL algorithm

DOI10.1016/j.jnt.2022.09.013OpenAlexW4307289112MaRDI QIDQ2112788

Seungki Kim, Bo-Yin Yang, Tsuyoshi Takagi, Jintai Ding, Yun-Tao Wang

Publication date: 12 January 2023

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.02158

zbMATH Keywords

LLL algorithmlattice reductionsandpile modelsfinite-size scaling theory

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics (82C20)

Uses Software

• BKZ

Cites Work

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• Basic properties of strong mixing conditions. A survey and some open questions
• The LLL algorithm. Survey and applications
• Factoring polynomials with rational coefficients
• Lattice reduction: a toolbox for the cryptoanalyst
• Lattice basis reduction: Improved practical algorithms and solving subset sum problems
• Measuring, simulating and exploiting the head concavity phenomenon in BKZ
• Second order statistical behavior of LLL and BKZ
• A stochastic variant of the abelian sandpile model
• BKZ 2.0: Better Lattice Security Estimates
• Modelling the LLL Algorithm by Sandpiles
• Self-organized critical state of sandpile automaton models
• The Behavior of Random Reduced Bases
• Analyzing Blockwise Lattice Algorithms Using Dynamical Systems
• Algorithmic Number Theory

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