On the Asymptotics of Solving the LWE Problem Using Coded-BKW with Sieving
(2019) In IEEE Transactions on Information Theory 65(8). p.5243-5259- Abstract
- The Learning with Errors problem (LWE) has become a central topic in recent cryptographic research. In this paper, we present a new solving algorithm combining important ideas from previous work on improving the Blum-Kalai-Wasserman (BKW) algorithm and ideas from sieving in lattices. The new algorithm is analyzed and demonstrates an improved asymptotic performance. For the Regev parameters $q=n^2$ and noise level $\sigma = n^{1.5}/(\sqrt{2\pi}\log_{2}^{2}n)$, the asymptotic complexity is $2^{0.893n}$ in the standard setting, improving on the previously best known complexity of roughly $2^{0.930n}$. The newly proposed algorithm also provides asymptotic improvements when a quantum computer is assumed or when the number of samples is limited.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/f96b3942-3d41-4ed8-bd8f-64f4b2e7747b
- author
- Guo, Qian LU ; Johansson, Thomas LU ; Mårtensson, Erik LU and Stankovski, Paul LU
- organization
- publishing date
- 2019-08
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- LWE, BKW, Coded-BKW, Lattice codes, Lattice sieving
- in
- IEEE Transactions on Information Theory
- volume
- 65
- issue
- 8
- pages
- 16 pages
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85069469947
- ISSN
- 0018-9448
- DOI
- 10.1109/TIT.2019.2906233
- language
- English
- LU publication?
- yes
- id
- f96b3942-3d41-4ed8-bd8f-64f4b2e7747b
- date added to LUP
- 2018-10-07 17:50:48
- date last changed
- 2024-02-14 04:03:34
@article{f96b3942-3d41-4ed8-bd8f-64f4b2e7747b, abstract = {{The Learning with Errors problem (LWE) has become a central topic in recent cryptographic research. In this paper, we present a new solving algorithm combining important ideas from previous work on improving the Blum-Kalai-Wasserman (BKW) algorithm and ideas from sieving in lattices. The new algorithm is analyzed and demonstrates an improved asymptotic performance. For the Regev parameters $q=n^2$ and noise level $\sigma = n^{1.5}/(\sqrt{2\pi}\log_{2}^{2}n)$, the asymptotic complexity is $2^{0.893n}$ in the standard setting, improving on the previously best known complexity of roughly $2^{0.930n}$. The newly proposed algorithm also provides asymptotic improvements when a quantum computer is assumed or when the number of samples is limited.}}, author = {{Guo, Qian and Johansson, Thomas and Mårtensson, Erik and Stankovski, Paul}}, issn = {{0018-9448}}, keywords = {{LWE; BKW; Coded-BKW; Lattice codes; Lattice sieving}}, language = {{eng}}, number = {{8}}, pages = {{5243--5259}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, series = {{IEEE Transactions on Information Theory}}, title = {{On the Asymptotics of Solving the LWE Problem Using Coded-BKW with Sieving}}, url = {{http://dx.doi.org/10.1109/TIT.2019.2906233}}, doi = {{10.1109/TIT.2019.2906233}}, volume = {{65}}, year = {{2019}}, }