A Note on Sub-Gaussian Random Variables

Benjamin M.  Case; Colin Gallagher; Shuhong Gao

Paper 2019/520

A Note on Sub-Gaussian Random Variables

Benjamin M. Case, Colin Gallagher, and Shuhong Gao

Abstract

A sub-Gaussian distribution is any probability distribution that has tails bounded by a Gaussian and has a mean of zero. It is well known that the sum of independent sub-Gaussians is again sub-Gaussian. This note generalizes this result to sums of sub- Gaussians that may not be independent, under the assumption a certain conditional distribution is also sub-Gaussian. This general result is useful in the study of noise growth in (fully) homomorphic encryption schemes [CGHX19, CGGI17], and hopefully useful for other applications.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MINOR revision.
Keywords: sub-Gaussians fully homomorphic encryption FHE boostrapping error analysis lattices TFHE
Contact author(s): bmcase @ g clemson edu
bencase93 @ gmail com
History: 2019-05-20: received
Short URL: https://ia.cr/2019/520
License: CC BY

BibTeX

@misc{cryptoeprint:2019/520,
      author = {Benjamin M.  Case and Colin Gallagher and Shuhong Gao},
      title = {A Note on Sub-Gaussian Random Variables},
      howpublished = {Cryptology ePrint Archive, Paper 2019/520},
      year = {2019},
      note = {\url{https://eprint.iacr.org/2019/520}},
      url = {https://eprint.iacr.org/2019/520}
}