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

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 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 polynomial factorization, cryptography, number theory, and matrix canonical forms.