Paper 2017/698

δ-subgaussian Random Variables in Cryptography

Sean Murphy and Rachel Player


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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Published elsewhere. ACISP 2019 : The 24th Australasian Conference on Information Security and Privacy
Ring Learning with ErrorsSubgaussian Random Variable.
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s murphy @ rhul ac uk
2019-04-04: last of 4 revisions
2017-07-21: received
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      author = {Sean Murphy and Rachel Player},
      title = {δ-subgaussian Random Variables in Cryptography},
      howpublished = {Cryptology ePrint Archive, Paper 2017/698},
      year = {2017},
      note = {\url{}},
      url = {}
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