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

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

doi:10.1007/978-981-15-8061-1_3

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 proceeding › Conference contribution

Abstract

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 language	English
Title of host publication	Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020
Editors	Debasis Giri, Rajkumar Buyya, S. Ponnusamy, Debashis De, Andrew Adamatzky, Jemal H. Abawajy
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	29-42
Number of pages	14
ISBN (Print)	9789811580604
DOIs	https://doi.org/10.1007/978-981-15-8061-1_3
Publication status	Published - 2021
Event	6th International Conference on Mathematics and Computing, ICMC 2020 - Sikkim, India Duration: Sep 23 2020 → Sep 25 2020

Publication series

Name	Advances in Intelligent Systems and Computing
Volume	1262
ISSN (Print)	2194-5357
ISSN (Electronic)	2194-5365

Conference

Conference	6th International Conference on Mathematics and Computing, ICMC 2020
Country	India
City	Sikkim
Period	9/23/20 → 9/25/20

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Computer Science(all)

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Nakamura, S., Tateiwa, N., Kinjo, K., Ikematsu, Y., Yasuda, M., & Fujisawa, K. (2021). Solving the Search-LWE Problem by Lattice Reduction over Projected Bases. In D. Giri, R. Buyya, S. Ponnusamy, D. De, A. Adamatzky, & J. H. Abawajy (Eds.), Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020 (pp. 29-42). (Advances in Intelligent Systems and Computing; Vol. 1262). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-981-15-8061-1_3

Solving the Search-LWE Problem by Lattice Reduction over Projected Bases. / Nakamura, Satoshi; Tateiwa, Nariaki; Kinjo, Koha; Ikematsu, Yasuhiko; Yasuda, Masaya; Fujisawa, Katsuki.

Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020. ed. / Debasis Giri; Rajkumar Buyya; S. Ponnusamy; Debashis De; Andrew Adamatzky; Jemal H. Abawajy. Springer Science and Business Media Deutschland GmbH, 2021. p. 29-42 (Advances in Intelligent Systems and Computing; Vol. 1262).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Nakamura, S, Tateiwa, N, Kinjo, K, Ikematsu, Y, Yasuda, M & Fujisawa, K 2021, Solving the Search-LWE Problem by Lattice Reduction over Projected Bases. in D Giri, R Buyya, S Ponnusamy, D De, A Adamatzky & JH Abawajy (eds), Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020. Advances in Intelligent Systems and Computing, vol. 1262, Springer Science and Business Media Deutschland GmbH, pp. 29-42, 6th International Conference on Mathematics and Computing, ICMC 2020, Sikkim, India, 9/23/20. https://doi.org/10.1007/978-981-15-8061-1_3

Nakamura S, Tateiwa N, Kinjo K, Ikematsu Y, Yasuda M, Fujisawa K. Solving the Search-LWE Problem by Lattice Reduction over Projected Bases. In Giri D, Buyya R, Ponnusamy S, De D, Adamatzky A, Abawajy JH, editors, Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020. Springer Science and Business Media Deutschland GmbH. 2021. p. 29-42. (Advances in Intelligent Systems and Computing). https://doi.org/10.1007/978-981-15-8061-1_3

Nakamura, Satoshi ; Tateiwa, Nariaki ; Kinjo, Koha ; Ikematsu, Yasuhiko ; Yasuda, Masaya ; Fujisawa, Katsuki. / Solving the Search-LWE Problem by Lattice Reduction over Projected Bases. Proceedings of the Sixth International Conference on Mathematics and Computing - ICMC 2020. editor / Debasis Giri ; Rajkumar Buyya ; S. Ponnusamy ; Debashis De ; Andrew Adamatzky ; Jemal H. Abawajy. Springer Science and Business Media Deutschland GmbH, 2021. pp. 29-42 (Advances in Intelligent Systems and Computing).

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