Date Added: Sep 2012
This paper is a introduction to the present state-of-the-art in the field of security of lattice-based cryptosystems. After a short introduction to lattices, the authors describe the main hard problems in lattice theory that cryptosystems base their security on, and they present the main methods of attacking these hard problems, based on lattice basis reduction. They show how to find shortest vectors in lattices, which can be used to improve basis reduction algorithms. Finally they give a framework for assessing the security of cryptosystems based on these hard problems.