On Some Computational Problems in Local Fields

doi:10.1007/s11424-021-0074-8

	On Some Computational Problems in Local Fields
	Deng, Yingpu 1,2; Luo, Lixia 1,2; Pan, Yanbin 1,2; Xiao, Guanju 1,2
刊名	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
	2021-06-28
页码	10
关键词	CVP lattice LVP local field SVP
ISSN号	1009-6124
DOI	10.1007/s11424-021-0074-8
英文摘要	Lattices in Euclidean spaces are important research objects in geometric number theory, and they have important applications in many areas, such as cryptology. The shortest vector problem (SVP) and the closest vector problem (CVP) are two famous computational problems about lattices. In this paper, we consider p-adic lattices in local fields, and define the p-adic analogues of SVP and CVP in local fields. The authors find that, in contrast with lattices in Euclidean spaces, the situation is different and interesting. The SVP in Euclidean spaces corresponds to the Longest Vector Problem (LVP) in local fields. The authors develop relevant algorithms, indicating that these problems are computable.
资助项目	National Key Research and Development Project[2018YFA0704705]
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000667621300012
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58869]
专题	中国科学院数学与系统科学研究院
通讯作者	Deng, Yingpu
作者单位	1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Deng, Yingpu,Luo, Lixia,Pan, Yanbin,et al. On Some Computational Problems in Local Fields[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2021:10.
APA	Deng, Yingpu,Luo, Lixia,Pan, Yanbin,&Xiao, Guanju.(2021).On Some Computational Problems in Local Fields.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,10.
MLA	Deng, Yingpu,et al."On Some Computational Problems in Local Fields".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2021):10.