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Polar sampler: a novel Bernoulli sampler using polar codes with application to integer Gaussian sampling

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Title: Polar sampler: a novel Bernoulli sampler using polar codes with application to integer Gaussian sampling
Authors: Wang, J
Ling, C
Item Type: Journal Article
Abstract: Cryptographic constructions based on hard lattice problems have emerged as a front runner for the standardization of post-quantum public-key cryptography. As the standardization process takes place, optimizing specific parts of proposed schemes, e.g., Bernoulli sampling and integer Gaussian sampling, becomes a worthwhile endeavor. In this work, we propose a novel Bernoulli sampler based on polar codes, dubbed “polar sampler”. The polar sampler is information theoretically optimum in the sense that the number of uniformly random bits it consumes approaches the entropy bound asymptotically. It also features quasi-linear complexity and constant-time implementation. An integer Gaussian sampler is developed using multilevel polar samplers. Our algorithm becomes effective when sufficiently many samples are required at each query to the sampler. Security analysis is given based on Kullback–Leibler divergence and Rényi divergence. Experimental and asymptotic comparisons between our integer Gaussian sampler and state-of-the-art samplers verify its efficiency in terms of entropy consumption, running time and memory cost. We envisage that the proposed Bernoulli sampler can find other applications in cryptography in addition to Gaussian sampling.
Issue Date: May-2023
Date of Acceptance: 6-Dec-2022
URI: http://hdl.handle.net/10044/1/103182
DOI: 10.1007/s10623-022-01164-7
ISSN: 0925-1022
Publisher: Springer
Start Page: 1779
End Page: 1811
Journal / Book Title: Designs, Codes and Cryptography
Volume: 91
Issue: 5
Copyright Statement: © The Author(s) 2023. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Publication Status: Published
Online Publication Date: 2023-01-13
Appears in Collections:Faculty of Engineering

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