Paper 2018/1229

On Some Computational Problems in Local Fields

Yingpu Deng, Lixia Luo, and Guanju Xiao

Abstract

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 define so-called p-adic lattices, and consider the p-adic analogues of SVP and CVP in local fields. We find that, in contrast with lattices in Euclidean spaces, the situation is completely different and interesting. We also develop relevant algorithms, indicating that these problems are computable.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MAJOR revision.
Keywords
LatticeLocal fieldSVPCVP
Contact author(s)
gjXiao @ amss ac cn
History
2018-12-30: received
Short URL
https://ia.cr/2018/1229
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2018/1229,
      author = {Yingpu Deng and Lixia Luo and Guanju Xiao},
      title = {On Some Computational Problems in Local Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2018/1229},
      year = {2018},
      url = {https://eprint.iacr.org/2018/1229}
}
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