The Gaussian distribution is widely used in mechanism design for differential privacy (DP). Thanks to its sub-Gaussian tail, it significantly reduces the chance of outliers when responding to queries. However, it can only provide approximate $(\epsilon, \delta(\epsilon))$-DP. In practice, $\delta(\epsilon)$ must be much smaller than the size of the dataset, which may limit the use of the Gaussian mechanism for large datasets with strong privacy requirements. In this paper, we introduce and analyze a new distribution for use in DP that is based on the Gaussian distribution, but has improved privacy performance. The so-called offset-symmetric Gaussian tail (OSGT) distribution is obtained through using the normalized tails of two symmetric Gaussians around zero. Consequently, it can still have sub-Gaussian tail and lend itself to analytical derivations. We analytically derive the variance of the OSGT random variable and the $\delta(\epsilon)$ of the OSGT mechanism. We then numerically show that at the same variance, the OSGT mechanism can offer a lower $\delta(\epsilon)$ than the Gaussian mechanism. We extend the OSGT mechanism to $k$-dimensional queries and derive an easy-to-compute analytical upper bound for its zero-concentrated differential privacy (zCDP) performance. We analytically prove that at the same variance, the same global query sensitivity and for sufficiently large concentration orders $\alpha$, the OSGT mechanism performs better than the Gaussian mechanism in terms of zCDP.

翻译：Gausian 分布在不同的隐私(DP) 机制设计中被广泛使用。 由于它的 Gaussian 尾巴, 它大大降低了外部用户在回答询问时使用差异值的机会。 但是, 它只能提供大约$( epsilon,\ delta (\ epsilon) $- DP ) 。 实际上, $delta (\ epsilon) 的分布必须大大小于数据集的大小, 这可能会限制 Gausian 机制在具有强烈隐私要求的大数据集中使用。 在本文中, 我们引入并分析用于DP的新分配, 使用基于 Gaussian 分布的偏差值, 但却提高了隐私性能。 所谓的反正数高尾( OS Goss) 的分布, 通过使用两个对等值的平面的尾部, 它的尾部可能限制 Gausilantial 尾部, 并且能够进行分析。 我们分析得出OS GOGLO 高端(\ decle) rodual rodu droup 机制的数值, 然后我们可以显示GOs 的 GOGTal- dal- droup 。