Improved hardness results for unique shortest vector problem

• We give several incremental improvements on the known hardness of the unique shortest vector problem (uSVP) using standard techniques. One result that uses relatively new techniques is a deterministic reduction from the shortest vector problem to the uSVP.

The unique shortest vector problem on a rational lattice is the problem of finding the shortest non-zero vector under the promise that it is unique (up to multiplication by −1). We give several incremental improvements on the known hardness of the unique shortest vector problem (uSVP) using standard techniques. This includes a deterministic reduction from the shortest vector problem to the uSVP, the NP-hardness of uSVP on (1+1poly(n))-unique lattices, and a proof that the decision version of uSVP defined by Cai [4] is in co-NPco-NP for n1/4n1/4-unique lattices.