Unique Shortest Vector Problem for max norm is NP-hard
The unique Shortest vector problem (uSVP) in lattice theory plays a crucial role in many public-key cryptosystems. The security of those cryptosystems bases on the hardness of uSVP. However, so far there is no proof for the proper hardness of uSVP even in its exact version. In this paper, we show that the exact version of uSVP for `∞ norm is NP-hard. Furthermore, many other lattice problems including unique Subspace avoiding problem, unique Closest vector problem and unique Generalized closest vector problem, for any `p norm, are also shown to be NP-hard.