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How Hard Is Deciding Trivial Versus Nontrivial in the Dihedral Coset Problem?

unpublished

We study the hardness of the dihedral hidden subgroup problem. It is known that lattice problems reduce to it, and that it reduces to random subset sum with density > 1 and also to quantum sampling subset sum solutions. We examine a decision version of the problem where the question asks whether the hidden subgroup is trivial or order two. The decision problem essentially asks if a given vector is in the span of all coset states. We approach this by first computing an explicit basis for the

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