Lecture 6 Algorithms for Svp, Cvp

Above we have used the fact that dist(t,L) = minv∈L‖t − v‖ = minx∈t+L‖x‖, because L = −L. The two versions of CVP are equivalent by associating each v ∈ L with t − v ∈ t + L, and vice versa. Although the former version of the problem is the more “obvious” formulation, the latter version is often more convenient in algorithmic settings, so we will use it throughout these notes. We first show that SVPγ is no harder than CVPγ ; more specifically, given an oracle for CVPγ we can solve SVPγ efficiently.