--- _id: '6726' abstract: - lang: eng text: Randomness is an essential part of any secure cryptosystem, but many constructions rely on distributions that are not uniform. This is particularly true for lattice based cryptosystems, which more often than not make use of discrete Gaussian distributions over the integers. For practical purposes it is crucial to evaluate the impact that approximation errors have on the security of a scheme to provide the best possible trade-off between security and performance. Recent years have seen surprising results allowing to use relatively low precision while maintaining high levels of security. A key insight in these results is that sampling a distribution with low relative error can provide very strong security guarantees. Since floating point numbers provide guarantees on the relative approximation error, they seem a suitable tool in this setting, but it is not obvious which sampling algorithms can actually profit from them. While previous works have shown that inversion sampling can be adapted to provide a low relative error (Pöppelmann et al., CHES 2014; Prest, ASIACRYPT 2017), other works have called into question if this is possible for other sampling techniques (Zheng et al., Eprint report 2018/309). In this work, we consider all sampling algorithms that are popular in the cryptographic setting and analyze the relationship of floating point precision and the resulting relative error. We show that all of the algorithms either natively achieve a low relative error or can be adapted to do so. article_processing_charge: No author: - first_name: Michael full_name: Walter, Michael id: 488F98B0-F248-11E8-B48F-1D18A9856A87 last_name: Walter orcid: 0000-0003-3186-2482 citation: ama: 'Walter M. Sampling the integers with low relative error. In: Buchmann J, Nitaj A, Rachidi T, eds. Progress in Cryptology – AFRICACRYPT 2019. Vol 11627. LNCS. Cham: Springer Nature; 2019:157-180. doi:10.1007/978-3-030-23696-0_9' apa: 'Walter, M. (2019). Sampling the integers with low relative error. In J. Buchmann, A. Nitaj, & T. Rachidi (Eds.), Progress in Cryptology – AFRICACRYPT 2019 (Vol. 11627, pp. 157–180). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-23696-0_9' chicago: 'Walter, Michael. “Sampling the Integers with Low Relative Error.” In Progress in Cryptology – AFRICACRYPT 2019, edited by J Buchmann, A Nitaj, and T Rachidi, 11627:157–80. LNCS. Cham: Springer Nature, 2019. https://doi.org/10.1007/978-3-030-23696-0_9.' ieee: 'M. Walter, “Sampling the integers with low relative error,” in Progress in Cryptology – AFRICACRYPT 2019, vol. 11627, J. Buchmann, A. Nitaj, and T. Rachidi, Eds. Cham: Springer Nature, 2019, pp. 157–180.' ista: 'Walter M. 2019.Sampling the integers with low relative error. In: Progress in Cryptology – AFRICACRYPT 2019. vol. 11627, 157–180.' mla: Walter, Michael. “Sampling the Integers with Low Relative Error.” Progress in Cryptology – AFRICACRYPT 2019, edited by J Buchmann et al., vol. 11627, Springer Nature, 2019, pp. 157–80, doi:10.1007/978-3-030-23696-0_9. short: M. Walter, in:, J. Buchmann, A. Nitaj, T. Rachidi (Eds.), Progress in Cryptology – AFRICACRYPT 2019, Springer Nature, Cham, 2019, pp. 157–180. conference: end_date: 2019-07-11 location: Rabat, Morocco name: 'AFRICACRYPT: International Conference on Cryptology in Africa' start_date: 2019-07-09 date_created: 2019-07-29T12:25:31Z date_published: 2019-06-29T00:00:00Z date_updated: 2023-02-23T12:50:15Z day: '29' department: - _id: KrPi doi: 10.1007/978-3-030-23696-0_9 ec_funded: 1 editor: - first_name: J full_name: Buchmann, J last_name: Buchmann - first_name: A full_name: Nitaj, A last_name: Nitaj - first_name: T full_name: Rachidi, T last_name: Rachidi intvolume: ' 11627' language: - iso: eng main_file_link: - open_access: '1' url: https://eprint.iacr.org/2019/068 month: '06' oa: 1 oa_version: Preprint page: 157-180 place: Cham project: - _id: 258AA5B2-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '682815' name: Teaching Old Crypto New Tricks publication: Progress in Cryptology – AFRICACRYPT 2019 publication_identifier: eisbn: - 978-3-0302-3696-0 isbn: - 978-3-0302-3695-3 issn: - 0302-9743 - 1611-3349 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' series_title: LNCS status: public title: Sampling the integers with low relative error type: book_chapter user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 11627 year: '2019' ...