TY - GEN

T1 - Solving the Search-LWE Problem by Lattice Reduction over Projected Bases

AU - Nakamura, Satoshi

AU - Tateiwa, Nariaki

AU - Kinjo, Koha

AU - Ikematsu, Yasuhiko

AU - Yasuda, Masaya

AU - Fujisawa, Katsuki

N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Number 16H02830.
Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

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U2 - 10.1007/978-981-15-8061-1_3

DO - 10.1007/978-981-15-8061-1_3

M3 - Conference contribution

AN - SCOPUS:85098137953

SN - 9789811580604

T3 - Advances in Intelligent Systems and Computing

SP - 29

EP - 42

BT - Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020

A2 - Giri, Debasis

A2 - Buyya, Rajkumar

A2 - Ponnusamy, S.

A2 - De, Debashis

A2 - Adamatzky, Andrew

A2 - Abawajy, Jemal H.

PB - Springer Science and Business Media Deutschland GmbH

T2 - 6th International Conference on Mathematics and Computing, ICMC 2020

Y2 - 23 September 2020 through 25 September 2020

ER -