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The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction Factors

Mårtensson, Erik LU (2019) 2019 IEEE International Symposium on Information Theory
Abstract
The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. In this paper, we improve that algorithm by using different reduction factors in different steps of the sieving part of the algorithm. In the Regev setting, where $q = n^2$ and $\sigma = n^{1.5}/(\sqrt{2\pi}\log_2^2 n)$, the asymptotic complexity is $2^{0.8917n}$, improving the previously best complexity of $2^{{0.8927n}}$. When a quantum computer is assumed or the number of samples is limited, we get a similar level of improvement.
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
host publication
IEEE International Symposium on Information Theory (ISIT)
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
2019 IEEE International Symposium on Information Theory
conference location
Paris, France
conference dates
2019-07-07 - 2019-07-12
language
English
LU publication?
yes
id
16992295-5f9a-4627-85bc-ee256fa7c415
date added to LUP
2019-08-13 11:10:56
date last changed
2019-08-20 16:02:41
@inproceedings{16992295-5f9a-4627-85bc-ee256fa7c415,
  abstract     = {The Learning with Errors problem (LWE) is one of the main candidates for post-quantum cryptography. At Asiacrypt 2017, coded-BKW with sieving, an algorithm combining the Blum-Kalai-Wasserman algorithm (BKW) with lattice sieving techniques, was proposed. In this paper, we improve that algorithm by using different reduction factors in different steps of the sieving part of the algorithm. In the Regev setting, where $q = n^2$ and $\sigma = n^{1.5}/(\sqrt{2\pi}\log_2^2 n)$, the asymptotic complexity is $2^{0.8917n}$, improving the previously best complexity of $2^{{0.8927n}}$. When a quantum computer is assumed or the number of samples is limited, we get a similar level of improvement.},
  author       = {Mårtensson, Erik},
  language     = {eng},
  location     = {Paris, France},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  title        = {The Asymptotic Complexity of Coded-BKW with Sieving Using Increasing Reduction Factors},
  year         = {2019},
}