### Algebraic aspects of solving Ring-LWE, including ring-based improvements in the Blum-Kalai-Wasserman algorithm

Katherine E. Stange

##### Abstract

We provide a reduction of the Ring-LWE problem to Ring-LWE problems in subrings, in the presence of samples of a restricted form (i.e. (a,b) such that a is restricted to a multiplicative coset of the subring). To create and exploit such restricted samples, we propose Ring-BKW, a version of the Blum-Kalai-Wasserman algorithm which respects the ring structure. Off-the-shelf BKW dimension reduction (including coded-BKW and sieving) can be used for the reduction phase. Its primary advantage is that there is no need for back-substitution, and the solving/hypothesis-testing phase can be parallelized. We also present a method to exploit symmetry to reduce table sizes, samples needed, and runtime during the reduction phase. The results apply to two-power cyclotomic Ring-LWE with parameters proposed for practical use (including all splitting types).

Note: Minor revisions, plus section on advanced keying extended in this version.

Available format(s)
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
ring learning with errorslearning with errorsRing-LWEBKWBlum-Kalai-Wassermancyclotomic
Contact author(s)
History
2020-07-10: last of 2 revisions
See all versions
Short URL
https://ia.cr/2019/183

CC BY

BibTeX

@misc{cryptoeprint:2019/183,
author = {Katherine E.  Stange},
title = {Algebraic aspects of solving Ring-LWE, including ring-based improvements in the Blum-Kalai-Wasserman algorithm},
howpublished = {Cryptology ePrint Archive, Paper 2019/183},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/183}},
url = {https://eprint.iacr.org/2019/183}
}

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