  We present the first explicit connection between quantum computation and
lattice problems. Namely, we show a solution to the Unique Shortest Vector
Problem (SVP) under the assumption that there exists an algorithm that solves
the hidden subgroup problem on the dihedral group by coset sampling. Moreover,
we solve the hidden subgroup problem on the dihedral group by using an average
case subset sum routine. By combining the two results, we get a quantum
reduction from $\Theta(n^{2.5})$-unique-SVP to the average case subset sum
problem.
