### Abstract

Original language | Undefined |
---|---|

Article number | 1308.2405 |

Journal | arXiv |

State | Published - Aug 11 2013 |

### Keywords

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

### Cite this

*arXiv*, [1308.2405].

**A note on discrete gaussian combinations of lattice vectors.** / Aggarwal, Divesh; Regev, Oded.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - A note on discrete gaussian combinations of lattice vectors

AU - Aggarwal, Divesh

AU - Regev, Oded

PY - 2013/8/11

Y1 - 2013/8/11

N2 - 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}.

AB - 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}.

KW - cs.CR

KW - math.CO

KW - math.PR

M3 - Article

JO - arXiv

JF - arXiv

M1 - 1308.2405

ER -