Hardness of approximating the shortest vector problem in high Lp norms

We show that for every ε > 0, there is a constant p(ε) such that for all integers p ≥ p(ε), it is NP-hard to approximate the shortest vector problem in L_p norm within factor p^{1 - ε} under randomized reductions. For large values of p, this improves the factor 2¹p/ - δ hardness shown by D. Micciancio (1998).