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We present the first explicit connection between quantum computation and lattice problems. Namely, our main result is 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. Additionally, we present an approach to solving the hidden sub-group problem on the dihedral group by using an average case subset sum routine.
Oded Regev (Thu,) studied this question.
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