IPSJ Digital Courier
Online ISSN : 1349-7456
ISSN-L : 1349-7456
Dihedral Hidden Subgroup Problem: A Survey
Hirotada KobayashiFrançois Le Gall
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2005 Volume 1 Pages 470-477

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Abstract

After Shor's discovery of an efficient quantum algorithm for integer factoring, hidden subgroup problems play a central role in developing efficient quantum algorithms. In spite of many intensive studies, no efficient quantum algorithms are known for hidden subgroup problems for many non-Abelian groups. Of particular interest are the hidden subgroup problems for the symmetric group and for the dihedral group, because an efficient algorithm for the former implies an efficient solution to the graph isomorphism problem, and that for the latter essentially solves a certain lattice-related problem whose hardness is assumed in cryptography. This paper focuses on the latter case and gives a comprehensive survey of known facts related to the dihedral hidden subgroup problem.

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© 2005 by the Information Processing Society of Japan
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