Cryptology ePrint Archive: Report 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.

Category / Keywords: public-key cryptography / Lattice, Local field, SVP, CVP

Date: received 22 Dec 2018

Contact author: gjXiao at amss ac cn

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Version: 20181230:125742 (All versions of this report)

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