Some recent progress on the complexity of lattice problems

Abstract

We survey some recent developments in the study of the complexity of lattice problems. After a discussion of some problems on lattices which can be algorithmically solved efficiently, our main focus is the recent progress on complexity results of intractability. We discuss Ajtai's worst-case/average-case connections, NP-hardness and non-NP-hardness, transference theorems between primal and dual lattices, and the Ajtai-Dwork cryptosystem.