On Some Computational Problems in Local Fields

doi:10.1007/s11424-021-0074-8

CSpace

	On Some Computational Problems in Local Fields
	Deng, Yingpu 1,2; Luo, Lixia 1,2; Pan, Yanbin 1,2; Xiao, Guanju 1,2
	2021-06-28
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
页码	10
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.
关键词	CVP lattice LVP local field SVP
DOI	10.1007/s11424-021-0074-8
收录类别	SCI
语种	英语
资助项目	National Key Research and Development Project[2018YFA0704705]
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000667621300012
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58870
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.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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.