A Heuristic Method to Approximate the Closest Vector Problem

Abstract

The closest vector problem, or CVP for short, is a fundamental lattice problem. The purpose of this challenge is to identify a lattice point in its ambient space that is closest to a given point. This is a provably hard problem to solve, as it is an NP-hard problem. It is considered to be more difficult than the shortest vector problem (SVP), in which the shortest nonzero lattice point is required. There are three types of algorithms that can be used to solve CVP: Enumeration algorithms, Voronoi cell computation and seiving algorithms. Many algorithms for solving the relaxed variant, APPROX-CVP, have been proposed: The Babai nearest algorithm or the embedding technique. In this work we will give a heuristic method to approximate the closest vector problem to a given vector using the embeding technique and the reduced centered law.