文章基本信息

标题：Dihedral Hidden Subgroup Problem: A Survey
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作者：Hirotada Kobayashi ; François Le Gall
期刊名称：Information and Media Technologies
电子版ISSN：1881-0896
出版年度：2006
卷号：1
期号：1
页码：178-185
DOI：10.11185/imt.1.178
出版社：Information and Media Technologies Editorial Board
摘要：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.