### Abstract

We analyze the distribution of $\sum_{i=1}^m v_i \bx_i$ where $\bx_1,...,\bx_m$ are fixed vectors from some lattice $\cL \subset \R^n$ (say $\Z^n$) and $v_1,...,v_m$ are chosen independently from a discrete Gaussian distribution over $\Z$. We show that under a natural constraint on $\bx_1,...,\bx_m$, if the $v_i$ are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over $\cL$. We also analyze the case of $\bx_1,...,\bx_m$ that are themselves chosen from a discrete Gaussian distribution (and fixed). Our results simplify and qualitatively improve upon a recent result by Agrawal, Gentry, Halevi, and Sahai \cite{AGHS13}.

Original language | Undefined |
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Article number | 1308.2405 |

Journal | arXiv |

State | Published - Aug 11 2013 |

### Keywords

- cs.CR
- math.CO
- math.PR

## Cite this

Aggarwal, D., & Regev, O. (2013). A note on discrete gaussian combinations of lattice vectors.

*arXiv*, [1308.2405].