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Author Bremner, Murray R.

Title Lattice basis reduction : an introduction to the LLL algorithm and its applications / Murray R. Bremner
Published Boca Raton, FL : CRC Press, ©2012


Description 1 online resource (xvii, 316 pages) : illustrations
Series Pure and applied mathematics
Monographs and textbooks in pure and applied mathematics
Monographs and textbooks in pure and applied mathematics.
Contents 1. Introduction to lattices -- 2. Two-dimensional lattices -- 3. Gram-Schmidt orthogonalization -- 4. The LLL algorithm -- 5. Deep insertions -- 6. Linearly dependent vectors -- 7. The knapsack problem -- 8. Coppersmith's algorithm -- 9. Diophantine approximation -- 10. The Fincke-Pohst algorithm -- 11. Kannan's algorithm -- 12. Schnorr's algorithm -- 13. NP-completeness -- 14. The hermite normal form -- 15. Polynomial factorization
Summary 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
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Lattice theory -- Textbooks
Data reduction -- Textbooks
MATHEMATICS -- Infinity.
Data reduction
Lattice theory
Genre/Form Electronic books
Form Electronic book
LC no. 2011032872
ISBN 9781439807040