$$\delta $$-subgaussian Random Variables in Cryptography

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.