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.
UR - http://www.scopus.com/inward/record.url?scp=85098137953&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85098137953&partnerID=8YFLogxK
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 -