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Lattice Basis Reduction

An Introduction to the LLL Algorithm and Its Applications
 
Edition number: 1
Publisher: CRC Press
Date of Publication:
 
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Short description:

First realized in the 1980s by Lenstra, Lenstra, and Lovasz, the LLL algorithm was originally intended to factor polynomials with rational coefficients. It improved upon the existing lattice reduction algorithm in order to solve integer linear programming problems and was later adapted for use in crypanalysis. This book provides an introduction

Long description:

First developed in the early 1980s by Lenstra, Lenstra, and Lovász, the LLL algorithm was originally used to provide a polynomial-time algorithm for factoring polynomials with rational coefficients. It very quickly became an essential tool in integer linear programming problems and was later adapted for use in cryptanalysis. This book provides an introduction to the theory and applications of lattice basis reduction and the LLL algorithm. With numerous examples and suggested exercises, the text discusses various applications of lattice basis reduction to cryptography, number theory, polynomial factorization, and matrix canonical forms.



the book succeeds in making accessible to nonspecialists the area of lattice algorithms, which is remarkable because some of the most important results in the field are fairly recent.
?M. Zimand, Computing Reviews, March 2012

This text is meant as a survey of lattice basis reduction at a level suitable for students and interested researchers with a solid background in undergraduate linear algebra. ? The writing is clear and quite concise.
?Zentralblatt MATH 1237

Table of Contents:

Introduction to Lattices. Two-Dimensional Lattices. Gram-Schmidt Orthogonalization. The LLL Algorithm. Deep Insertions. Linearly Dependent Vectors. The Knapsack Problem. Coppersmith?s Algorithm. Diophantine Approximation. The Fincke-Pohst Algorithm. Kannan?s Algorithm. Schnorr?s Algorithm. NP-Completeness. The Hermite Normal Form. Polynomial Factorization.