An Overview of Lattice Reduction Algorithms

The best generic tool currently known for attacking lattice-based cryptographic primitives is lattice reduction. Lattice reduction is a representation paradigm: it consists in finding a representation (a basis) of a given lattice that provides easier access to intrinsic properties of that lattice.

In this talk, I will give an overview of the state of the art in lattice reduction algorithms. I will also describe how lattice reduction may be used to solve standard problems from lattice-based cryptography, namely, the Learning With Errors (LWE) and Small Integer Solution (SIS) problems.