### Polar Sampler: A Novel Bernoulli Sampler Using Polar Codes with Application to Integer Gaussian Sampling

Jiabo Wang and Cong Ling

##### 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 R\'enyi 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.

Note: Constant-time analysis in Section 6.1 and Appendix B is improved.

Available format(s)
Category
Applications
Publication info
Preprint. MINOR revision.
Keywords
Bernoulli samplingDiscrete Gaussian samplingPolar codesInteger latticeKullback-Leibler divergenceConstant-time implementation
Contact author(s)
wangjiabo @ mail tsinghua edu cn
c ling @ imperial ac uk
History
2022-01-10: last of 3 revisions
See all versions
Short URL
https://ia.cr/2019/674

CC BY

BibTeX

@misc{cryptoeprint:2019/674,
author = {Jiabo Wang and Cong Ling},
title = {Polar Sampler: A Novel Bernoulli Sampler Using Polar Codes with Application to Integer Gaussian Sampling},
howpublished = {Cryptology ePrint Archive, Paper 2019/674},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/674}},
url = {https://eprint.iacr.org/2019/674}
}

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