The LLL Algorithm Survey and Applications /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Nguyen, Phong Q. (Editor), Vallě, Brigitte. (Editor)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Series: Information Security and Cryptography,
• Subjects: Computer science.; Data structures (Computer science).; Computer software.; Computational complexity.; Algorithms.; Number theory.; Mathematical optimization.; Computer Science.; Data Structures, Cryptology and Information Theory.; Algorithm Analysis and Problem Complexity.; Discrete Mathematics in Computer Science.; Number Theory.; Optimization.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-02295-1

The LLL algorithm is a polynomial-time lattice reduction algorithm, named after its inventors, Arjen Lenstra, Hendrik Lenstra and Ls̀zl ̤Lovs̀z. The algorithm has revolutionized computational aspects of the geometry of numbers since its introduction in 1982, leading to breakthroughs in fields as div...

Table of Contents:

• A Tale of Two Papers
• Polynomial Factorization and Lattices in the Very Early 1980s
• Floating-Point LLL: Theoretical and Practical Aspects
• Progress on LLL and Lattice Reduction
• Probabilistic Analyses of Lattice Reduction Algorithms
• LLL: A Tool for Effective Diophantine Approximation
• Selected Applications of LLL in Number Theory
• The van Hoeij Algorithm to Factor Polynomials
• The LLL-Algorithm and Integer Programming
• The Geometry of Provable Security: Some Proofs of Security in Which Lattices Make a Surprise Appearance
• Practical Lattice-Based Cryptography: NTRUEncrypt and NTRUSign
• Using LLL-Reduction for Solving RSA and Factorization Problems: A Survey
• Lattice-Based Cryptanalysis
• Inapproximability Results for Computational Problems on Lattices
• On the Complexity of Lattice Problems with Polynomial Approximation Factors
• Cryptographic Functions from Worst-Case Complexity Assumptions.