Solving the Search-LWE Problem by Lattice Reduction over Projected Bases

Satoshi Nakamura, Nariaki Tateiwa, Koha Kinjo, Yasuhiko Ikematsu, Masaya Yasuda, Katsuki Fujisawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


The learning with errors (LWE) problem assures the security of modern lattice-based cryptosystems. It can be reduced to classical lattice problems such as the shortest vector problem (SVP) and the closest vector problem (CVP). In particular, the search-LWE problem is reduced to a particular case of SVP by Kannan’s embedding technique. Lattice basis reduction is a mandatory tool to solve lattice problems. In this paper, we give a new strategy to solve the search-LWE problem by lattice reduction over projected bases. Compared with a conventional method of reducing a whole lattice basis, our strategy reduces only a part of the basis and, hence, it gives a practical speed-up in solving the problem. We also develop a reduction algorithm for a projected basis, and apply it to solving several instances in the LWE challenge, which has been initiated since the middle of 2016 in order to assess the hardness of the LWE problem.

Original languageEnglish
Title of host publicationProceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020
EditorsDebasis Giri, Rajkumar Buyya, S. Ponnusamy, Debashis De, Andrew Adamatzky, Jemal H. Abawajy
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages14
ISBN (Print)9789811580604
Publication statusPublished - 2021
Event6th International Conference on Mathematics and Computing, ICMC 2020 - Sikkim, India
Duration: Sept 23 2020Sept 25 2020

Publication series

NameAdvances in Intelligent Systems and Computing
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365


Conference6th International Conference on Mathematics and Computing, ICMC 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • General Computer Science


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