A : Lattice Algorithms and Applications Spring 2007 Lecture 3 : Minimum distance

Computing the minimum distance of a lattice (and vectors achieving the minimum distance) is a fundamental problem in the algorithmic study of lattices, and the core of many applications in computer science and cryptography. Today, we will focus on mathematical properties of lattices, and answer questions like: is the quantity λ(Λ) always achieved by a pair of vectors? (I.e., can the inf in the definition be replaced by min?) Does the minimum distance of a lattice satisfy interesting upper or lower bounds? We will also see how simple bounds on the minimum distance of a lattice be used to prove seemingly unrelated mathematical facts like the following.