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Discrete Ziggurat: a time-memory trade-off for sampling from a Gaussian distribution over the integers. (English) Zbl 1362.94024

Lange, Tanja (ed.) et al., Selected areas in cryptography – SAC 2013. 20th international conference, Burnaby, BC, Canada, August 14–16, 2013. Revised selected papers. Berlin: Springer (ISBN 978-3-662-43413-0/pbk; 978-3-662-43414-7/ebook). Lecture Notes in Computer Science 8282, 402-417 (2014).
Summary: Several lattice-based cryptosystems require to sample from a discrete Gaussian distribution over the integers. Existing methods to sample from such a distribution either need large amounts of memory or they are very slow. In this paper, we explore a different method that allows for a flexible time-memory trade-off, offering developers freedom in choosing how much space they can spare to store precomputed values. We prove that the generated distribution is close enough to a discrete Gaussian to be used in lattice-based cryptography. Moreover, we report on an implementation of the method and compare its performance to existing methods from the literature. We show that for large standard deviations, the Ziggurat algorithm outperforms all existing methods.
For the entire collection see [Zbl 1321.94008].

MSC:

94A60 Cryptography
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