Murray R. Bremner 
Lattice Basis Reduction [PDF ebook] 
An Introduction to the LLL Algorithm and Its Applications

First developed in the early 1980s by Lenstra, Lenstra, and Lovasz, 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 i