Cryptology ePrint Archive: Report 2017/698

δ-subgaussian Random Variables in Cryptography

Sean Murphy and Rachel Player

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.

Category / Keywords: Ring Learning with Errors, Subgaussian Random Variable.

Original Publication (in the same form): ACISP 2019 : The 24th Australasian Conference on Information Security and Privacy

Date: received 13 Jul 2017, last revised 4 Apr 2019

Contact author: s murphy at rhul ac uk

Available format(s): PDF | BibTeX Citation

Version: 20190404:110619 (All versions of this report)

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