Cryptographic constructions based on lattices have attracted considerable interest in recent years. The main reason is that, unlike many other cryptographic constructions, lattice based constructions can be based on the worst-case hardness of a problem. That is, breaking them would imply a solution to any instance of a certain lattice problem. In this paper we will be interested in the unique shortest vector problem (uSVP), a lattice problem that is believed to be hard.