Sampling short lattice vectors and the closest lattice vector problem

We present a 2^O(n) time Turing reduction from the closest lattice vector problem to the shortest lattice vector problem. Our reduction assumes access to a subroutine that solves SVP exactly and a subroutine to sample short vectors from a lattice, and computes a (1+ε)-approximation to CVP As a consequence, using the SVP algorithm from (Ajtai et al., 2001), we obtain a randomized 2[O(1+ε ^-1)n] algorithm to obtain a (1+ε)-approximation for the closest lattice vector problem in n dimensions. This improves the existing time bound of O(n!) for CVP achieved by a deterministic algorithm in (Blomer, 2000)