Before revision: We show how to efficiently provide differentially private answers to counting queries (or integer-valued low-sensitivity queries) by adding discrete Gaussian noise , with essentially the same privacy and accuracy as the continuous Gaussian. The use of a discrete distribution is necessary in practice, as finite computers cannot  represent samples from continuous distributions and numerical errors may destroy the privacy guarantee .
After revision: A key tool for building differentially private systems is adding Gaussian noise to the output of a function evaluated on a sensitive dataset. Unfortunately, using a continuous distribution presents several practical challenges. First and foremost, finite computers cannot represent samples from continuous distributions and numerical errors may destroy the privacy guarantee .