On Some Computational Problems in Local Fields
| Autor: | Yanbin Pan, Yingpu Deng, Guanju Xiao, Lixia Luo |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
0209 industrial biotechnology Computer science business.industry Lattice problem Complex system Contrast (statistics) Cryptography 02 engineering and technology 020901 industrial engineering & automation Number theory Vector problem Euclidean geometry 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) 020201 artificial intelligence & image processing Computational problem business Information Systems |
| Zdroj: | Journal of Systems Science and Complexity. 35:1191-1200 |
| ISSN: | 1559-7067 1009-6124 |
| DOI: | 10.1007/s11424-021-0074-8 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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