On the complexity of lattice problems with polynomial approximation factors

Abstract

Lattice problems are known to be hard to approximate to withinsub-polynomial factors. For larger approximation factors, such as √n, lattice problems are known to be in complexity classes, such as NP ∩ coNP, and are hence unlikely to be NP-hard. Here, we survey known results in this area. We also discuss some related zero-knowledge protocols for lattice problems.