Faster exponential time algorithms for the shortest vector problem

We present new faster algorithms for the exact solution of the shortest; vector problem in arbitrary lattices Our main result shows that the shortest vector in any n-dimensional lattice can be found in time 2(3) (199n) (and space 2(1) (325n)), or in Space 2(1) (095n) (and still tune 2(O(n))). Tins improves the best previously known algorithm by Ajtai, Kumar and Sivakumar [Proceedings of STOC 2001] which was shown by Nguyen and Vidick [J Math Crypto. 2(2) 181-207] to inn in time 2(5) (9n) and space 2(2) (95n) We also present a practical variant of our algorithm which provably uses an amount of space proportional to tau(n), the "kissing" constant in dimension n. No upper bound on the running tune of our second algorithm is currently known, but experimentally the algorithm seems 1,0 perforin fairly well in practice with running Lime 2(0) (52n) and space complexity 2(0) (2n)