### Abstract

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 Θ̃ (n^{2.5})-unique-SVP to the average case subset sum problem. This is a better connection than the known classical results.

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundations of Computer Science - Proceedings |

Editors | D.C. Martin |

Pages | 520-529 |

Number of pages | 10 |

State | Published - 2002 |

Event | The 34rd Annual IEEE Symposium on Foundations of Computer Science - Vancouver, BC, Canada Duration: Nov 16 2002 → Nov 19 2002 |

### Other

Other | The 34rd Annual IEEE Symposium on Foundations of Computer Science |
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Country | Canada |

City | Vancouver, BC |

Period | 11/16/02 → 11/19/02 |

### ASJC Scopus subject areas

- Hardware and Architecture

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## Cite this

Regev, O. (2002). Quantum computation and lattice problems. In D. C. Martin (Ed.),

*Annual Symposium on Foundations of Computer Science - Proceedings*(pp. 520-529)