A Parallel Evolutionary Search for Shortest Vector Problem

Abstract

The hardness assumption of approximate shortest vector problem (SVP) within the polynomial factor in polynomial time reduced to the security of many lattice-based cryptographic primitives, so solving this problem, breaks these primitives. In this paper, we investigate the suitability of combining the best techniques in general search/optimization, lattice theory and parallelization technologies for solving the SVP into a single algorithm. Our proposed algorithm repeats three steps in a loop: an evolutionary search (a parallelized Genetic Algorithm), brute-force of tiny full enumeration (in role of too much local searches with random start points over the lattice vectors) and a single main enumeration. The test results showed that our proposed algorithm is better than LLL reduction and may be worse than the BKZ variants (except some so small block sizes). The main drawback for these test results is the notsufficient tuning of various parameters for showing the potential strength of our contribution. Therefore, we count the entire main problems and weaknesses in our work for clearer and better results in further studies. Also it is proposed a pure model of Genetic Algorithm with more solid/stable design for SVP problem which can be inspired by future works.