Modeling and simulating the sample complexity of solving LWE using BKW-style algorithms
(2023) In Cryptography and Communications 15(2). p.331-350- 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 hypotheses. We also... (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 via simulation that it performs much better than previous theory predicts and develop a sample complexity model that matches the simulations better. We also introduce an improved, pruned version of the 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/f3868cf4-18fd-4e60-96ad-bcf6eeaf2a73
- author
- Guo, Qian LU ; Mårtensson, Erik LU and Stankovski Wagner, Paul LU
- organization
- publishing date
- 2023
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Cryptography and Communications
- volume
- 15
- issue
- 2
- pages
- 20 pages
- publisher
- Springer
- external identifiers
-
- scopus:85135810051
- ISSN
- 1936-2455
- DOI
- 10.1007/s12095-022-00597-0
- project
- Lightweight Cryptography for Autonomous Vehicles
- language
- English
- LU publication?
- yes
- id
- f3868cf4-18fd-4e60-96ad-bcf6eeaf2a73
- date added to LUP
- 2022-08-30 12:00:01
- date last changed
- 2024-02-18 07:40:35
@article{f3868cf4-18fd-4e60-96ad-bcf6eeaf2a73, 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 hypotheses. We also show via simulation that it performs much better than previous theory predicts and develop a sample complexity model that matches the simulations better. We also introduce an improved, pruned version of the 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}}, issn = {{1936-2455}}, language = {{eng}}, number = {{2}}, pages = {{331--350}}, publisher = {{Springer}}, series = {{Cryptography and Communications}}, title = {{Modeling and simulating the sample complexity of solving LWE using BKW-style algorithms}}, url = {{http://dx.doi.org/10.1007/s12095-022-00597-0}}, doi = {{10.1007/s12095-022-00597-0}}, volume = {{15}}, year = {{2023}}, }