Lattice Basis Reduction: An Introduction to the LLL Algorithm and Its Applications by Murray R. Bremner [Repost]

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.