Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications

Murray R. Bremner

August 12, 2011 by CRC Press
Reference - 332 Pages - 54 B/W Illustrations
ISBN 9781439807026 - CAT# K10358
Series: Chapman & Hall Pure and Applied Mathematics

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    • Includes numerous algorithms in structured form (without goto statements) in both pseudocode and Maple
    • Presents the essential concepts that should be familiar to all users of lattice algorithms
    • Based on fundamental research papers on lattice basis reduction and its applications
    • Designed as a complete introduction for non-specialists: the only prerequisites are basic linear algebra and elementary number theory
    • Includes two applications to cryptography: knapsack cryptosystems, and Coppersmith’s algorithm
    • Includes two applications to computer algebra: polynomial factorization, and the Hermite normal form of an integer matrix


    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.