On the Sample Complexity of solving LWE using BKW-Style Algorithms
(2021) 2021 IEEE International Symposium on Information Theory- Abstract
- The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for solving the Learning Parity with Noise (LPN) problem, performs well, especially for certain parameter settings with cryptographic importance. The BKW algorithm consists of two phases, the reduction phase and the solving phase.
In this work, we study the performance of distinguishers used in the solving phase. We show that the Fast Fourier Transform (FFT) distinguisher from Eurocrypt'15 has the same sample complexity as the optimal distinguisher, when making the same number of... (More) - The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for solving the Learning Parity with Noise (LPN) problem, performs well, especially for certain parameter settings with cryptographic importance. The BKW algorithm consists of two phases, the reduction phase and the solving phase.
In this work, we study the performance of distinguishers used in the solving phase. We show that the Fast Fourier Transform (FFT) distinguisher from Eurocrypt'15 has the same sample complexity as the optimal distinguisher, when making the same number of hypotheses. We also show that it performs much better than theory predicts and introduce an improvement of it called the pruned FFT distinguisher. Finally, we indicate, via extensive experiments, that the sample dependency due to both LF2 and sample amplification is limited. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/771b0359-d65b-40ca-a6de-3b26d96b6972
- author
- Guo, Qian LU ; Mårtensson, Erik LU and Stankovski Wagner, Paul LU
- organization
- publishing date
- 2021
- 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
- 2021 IEEE International Symposium on Information Theory
- conference location
- Melbourne, Australia
- conference dates
- 2021-07-12 - 2021-07-20
- external identifiers
-
- scopus:85115106421
- ISBN
- 978-1-5386-8210-4
- 978-1-5386-8209-8
- DOI
- 10.1109/ISIT45174.2021.9518190
- language
- English
- LU publication?
- yes
- id
- 771b0359-d65b-40ca-a6de-3b26d96b6972
- alternative location
- https://arxiv.org/abs/2102.02126
- date added to LUP
- 2021-06-01 10:28:26
- date last changed
- 2024-04-06 04:18:30
@inproceedings{771b0359-d65b-40ca-a6de-3b26d96b6972, abstract = {{The Learning with Errors (LWE) problem receives much attention in cryptography, mainly due to its fundamental significance in post-quantum cryptography. Among its solving algorithms, the Blum-Kalai-Wasserman (BKW) algorithm, originally proposed for solving the Learning Parity with Noise (LPN) problem, performs well, especially for certain parameter settings with cryptographic importance. The BKW algorithm consists of two phases, the reduction phase and the solving phase.<br/><br/>In this work, we study the performance of distinguishers used in the solving phase. We show that the Fast Fourier Transform (FFT) distinguisher from Eurocrypt'15 has the same sample complexity as the optimal distinguisher, when making the same number of hypotheses. We also show that it performs much better than theory predicts and introduce an improvement of it called the pruned FFT distinguisher. Finally, we indicate, via extensive experiments, that the sample dependency due to both LF2 and sample amplification is limited.}}, author = {{Guo, Qian and Mårtensson, Erik and Stankovski Wagner, Paul}}, booktitle = {{IEEE International Symposium on Information Theory (ISIT)}}, isbn = {{978-1-5386-8210-4}}, language = {{eng}}, publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}}, title = {{On the Sample Complexity of solving LWE using BKW-Style Algorithms}}, url = {{http://dx.doi.org/10.1109/ISIT45174.2021.9518190}}, doi = {{10.1109/ISIT45174.2021.9518190}}, year = {{2021}}, }