Application of mixed integer quadratic program to shortest vector problems

Abstract

The security of lattice-based cryptography is mainly based on the fact that the shortest vector problem (SVP) is NP-hard. Our interest is to know how large-scale shortest vector problems can be solved by the state-of-the-art software for mixed-integer programs. For this, we provide a formulation for SVP via mixed integer quadratic program and show the numerical performance for TU Darmstadt's benchmark instances with the dimension up to 49.