Quantum Computation and Lattice Problems

Preprint

2 April 2003

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.cs/0304005

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 $\Theta(n^{2.5})$-unique-SVP to the average case subset sum problem.

Keywords

SHORTEST VECTOR PROBLEM
COMPUTATION AND LATTICE
AVERAGE CASE SUBSET
QUANTUM COMPUTATION
EXPLICIT CONNECTION
LATTICE PROBLEMS
CASE SUBSET SUM
ALGORITHM
SVP

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Version 1, 2003-04-02, ArXiv

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