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\(\delta \)-subgaussian Random Variables in Cryptography

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Information Security and Privacy (ACISP 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11547))

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Abstract

In the Ring-LWE literature, there are several works that use a statistical framework based on \(\delta \)-subgaussian random variables. These were introduced by Miccancio and Peikert (Eurocrypt 2012) as a relaxation of subgaussian random variables. In this paper, we completely characterise \(\delta \)-subgaussian random variables. In particular, we show that this relaxation from a subgaussian random variable corresponds only to the shifting of the mean. Next, we give an alternative noncentral formulation for a \(\delta \)-subgaussian random variable, which we argue is more statistically natural. This formulation enables us to extend prior results on sums of \(\delta \)-subgaussian random variables, and on their discretisation.

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Acknowledgements

We thank the anonymous referees for their comments on previous versions of this paper, and we thank Carlos Cid for his interesting discussions about this paper. Rachel Player was supported by an ACE-CSR Ph.D. grant, by the French Programme d’Investissement d’Avenir under national project RISQ P141580, and by the European Union PROMETHEUS project (Horizon 2020 Research and Innovation Program, grant 780701).

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Authors and Affiliations

  1. Royal Holloway, University of London, Egham, UK

    Sean Murphy & Rachel Player

Authors
  1. Sean Murphy
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  2. Rachel Player
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Correspondence to Rachel Player .

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Editors and Affiliations

  1. Massey University, Palmerston North, New Zealand

    Julian Jang-Jaccard

  2. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

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Murphy, S., Player, R. (2019). \(\delta \)-subgaussian Random Variables in Cryptography. In: Jang-Jaccard, J., Guo, F. (eds) Information Security and Privacy. ACISP 2019. Lecture Notes in Computer Science(), vol 11547. Springer, Cham. https://doi.org/10.1007/978-3-030-21548-4_14

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  • DOI: https://doi.org/10.1007/978-3-030-21548-4_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21547-7

  • Online ISBN: 978-3-030-21548-4

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