A Note on Discrete Gaussian Combinations of Lattice Vectors

نویسندگان

Divesh Aggarwal

Oded Regev

چکیده

We analyze the distribution of ∑ m i=1 vixi where x1, . . . ,xm are fixed vectors from some lattice L ⊂ R (say Z) and v1, . . . , vm are chosen independently from a discrete Gaussian distribution over Z. We show that under a natural constraint on x1, . . . ,xm, if the vi are chosen from a wide enough Gaussian, the sum is statistically close to a discrete Gaussian over L. We also analyze the case of x1, . . . ,xm 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 [AGHS13]. Courant Institute of Mathematical Sciences, New York University. Email: [email protected]. Courant Institute of Mathematical Sciences, New York University. This material is based upon work supported by the National Science Foundation under Grant No. CCF-1320188. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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