Paper 2020/1467
Making the BKW Algorithm Practical for LWE
Alessandro Budroni, Qian Guo, Thomas Johansson, Erik Mårtensson, and Paul Stankovski Wagner
Abstract
The Learning with Errors (LWE) problem is one of the main mathematical foundations of post-quantum cryptography. One of the main groups of algorithms for solving LWE is the Blum-Kalai-Wasserman (BKW) algorithm. This paper presents new improvements for BKW-style algorithms for solving LWE instances. We target minimum concrete complexity and we introduce a new reduction step where we partially reduce the last position in an iteration and finish the reduction in the next iteration, allowing non-integer step sizes. We also introduce a new procedure in the secret recovery by mapping the problem to binary problems and applying the Fast Walsh Hadamard Transform. The complexity of the resulting algorithm compares favourably to all other previous approaches, including lattice sieving. We additionally show the steps of implementing the approach for large LWE problem instances. The core idea here is to overcome RAM limitations by using large file-based memory.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- BKWLWELattice-Based CryptographyFWHTPost-Quantum Cryptography
- Contact author(s)
-
alessandro budroni @ uib no
budroni alessandro @ gmail com
erik martensson @ eit lth se - History
- 2020-11-24: received
- Short URL
- https://ia.cr/2020/1467
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/1467,
author = {Alessandro Budroni and Qian Guo and Thomas Johansson and Erik Mårtensson and Paul Stankovski Wagner},
title = {Making the {BKW} Algorithm Practical for {LWE}},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/1467},
year = {2020},
url = {https://eprint.iacr.org/2020/1467}
}
